[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"term-poker-variance-en":3,"related-variance-en":37,"mdc--d2bgxn-key":38},{"id":4,"slug":5,"status":6,"section":7,"category":8,"difficulty":9,"aliases":10,"related_terms":14,"related_calculators":19,"term":25,"definition":26,"content":27,"example":28,"faq":29,"availableLocales":30},"82cc2d5d-d84e-4698-8117-64fc7552bcd8","variance","published","betting","metrics","intermediate",[11,12,13],"Statistical Variance","Standard Deviation","Result Variance",[15,16,17,18,12],"Expected Value","ROI","Bankroll Management","Kelly Criterion",[20,21,22,23,24],"\u002Fbetting\u002Fvariance-analyzer","\u002Fbetting\u002Frisk-of-ruin","\u002Fbetting\u002Fbankroll-growth-calculator","\u002Fbetting\u002Fkelly-calculator","\u002Fbetting\u002Fstaking-plan-calculator","Variance","The statistical measure of how spread out betting results are from the expected value, representing the natural randomness in short-term outcomes.","## What is Variance?\n\nPicture this: You've made 100 bets with a 55% win rate at -110 odds (genuinely profitable long-term), but you're down $500. Meanwhile, your friend made 100 bets with a 48% win rate (unprofitable long-term), but he's up $300. Your bankroll graph looks like a rollercoaster, his looks like steady growth.\n\nWhat's happening? **Variance.**\n\n> **In simple terms:** Variance is the mathematical way of saying \"results bounce around\" in the short run. Even perfect betting doesn't guarantee immediate profits - variance ensures that luck plays a role in short-term outcomes.\n\n## TL;DR - Quick Reference\n\n| Concept | Explanation |\n|---------|-------------|\n| **What it is** | Natural randomness causing results to deviate from expected value |\n| **Why it matters** | Your actual profit ≠ expected profit (short-term) |\n| **Key metric** | [Standard deviation](\u002Fen\u002Fglossary\u002Fbetting\u002Fstandard-deviation) (σ) measures swing size |\n| **Sample size needed** | 500+ bets to see true win rate with confidence |\n| **Mental game** | Understanding variance prevents tilt and strategy changes |\n| **Bankroll impact** | High variance requires larger bankroll (100+ units) |\n\n**The bottom line:** Variance doesn't change your long-term edge, but it dramatically affects your short-term experience and [bankroll management](\u002Fen\u002Fglossary\u002Fbetting\u002Fbankroll-management) requirements.\n\n---\n\n## Understanding Variance for Beginners\n\nVariance is why short-term results are unreliable. It's the reason:\n- Profitable bettors experience losing streaks\n- Poor bettors sometimes win big\n- 10 bets tell you almost nothing about skill\n- Emotions and tilt destroy even [value betting](\u002Fen\u002Fglossary\u002Fbetting\u002Fvalue-betting) strategies\n\n### The Coin Flip Analogy\n\nImagine flipping a fair coin:\n- **10 flips:** You might get 7 heads (70%) - huge variance\n- **100 flips:** You'll probably get 45-55 heads (reasonable variance)\n- **10,000 flips:** You'll almost certainly get 49%-51% heads (variance minimized)\n\n**Betting works the same way.** Your true win rate emerges only after hundreds of bets. Before that? Variance dominates.\n\n---\n\n## The Mathematics of Variance\n\n::chart-variance-distribution\n::\n\n**Standard deviation formula:**\n\n$$\\sigma = \\sqrt{\\frac{\\sum(x_i - \\mu)^2}{n}}$$\n\nWhere:\n- **σ** = Standard deviation (measure of variance)\n- **x_i** = Individual result (win\u002Floss for each bet)\n- **μ** = Expected value (mean result)\n- **n** = Number of bets\n\n**What this means practically:**\n\nIf your expected ROI is **+5%** with **20% standard deviation** over 100 bets at $100 each:\n\n- **Expected profit:** $500\n- **68% of the time (±1σ):** Between $300-$700 profit\n- **95% of the time (±2σ):** Between $100-$900 profit\n- **99.7% of the time (±3σ):** Between -$100 to $1,100 profit\n\n**Yes, you read that right** - even with a +5% edge, there's a ~2.5% chance you'll be losing money after 100 bets. That's variance.\n\n---\n\n## Why Variance Matters for Bettors\n\n### 1. Bankroll Requirements\n\nHigher variance = need bigger bankroll to survive swings.\n\n| Bet Type | Typical Variance | Recommended Bankroll |\n|----------|------------------|---------------------|\n| Favorites (-200+) | Low | 50-75 units |\n| Standard bets (-110) | Medium | 75-100 units |\n| Underdogs (+150+) | High | 100-150 units |\n| Parlays\u002FAccumulators | Very High | 150-200 units |\n\n**Example:** If you bet $100 per game on favorites (low variance), $5,000 bankroll is sufficient. But if you bet $100 on parlays (high variance), you need $15,000-$20,000 to have the same risk of ruin.\n\n### 2. Mental Game Protection\n\n**The Variance Trap:** After 20 losing bets, your brain screams \"the strategy doesn't work!\" But statistically, a 55% bettor will experience 20-bet losing streaks regularly.\n\n::chart-variance-losing-streaks\n::\n\n**Reality check:**\n- 50% win rate: Expect 8-bet losing streak every 256 bets\n- 55% win rate: Expect 6-bet losing streak every 128 bets\n- 60% win rate: Expect 5-bet losing streak every 64 bets\n\nUnderstanding this **prevents emotional betting decisions** during downswings.\n\n### 3. True ROI Assessment\n\nYou need **minimum 500 bets** to assess your true [ROI](\u002Fen\u002Fglossary\u002Fbetting\u002Froi) with statistical confidence.\n\n**Why 500?**\n- With 55% win rate, after 50 bets: 95% confidence interval = 40%-70% (useless!)\n- After 500 bets: 95% confidence interval = 51%-59% (meaningful)\n\n**Never evaluate a betting strategy on less than 500 bets.** You're just measuring variance, not skill.\n\n---\n\n## Common Variance Mistakes\n\n### Mistake #1: Changing Strategy Mid-Variance\n\n**❌ Wrong:** \"I'm down $1,000 after 30 bets. This system doesn't work. Switching to a different model.\"\n\n**✅ Right:** \"I'm down $1,000 after 30 bets. Expected variance for my bet size. Continuing with the plan until I have 500+ bet sample.\"\n\n**Why it's wrong:** You might be abandoning a winning strategy during normal variance. Most bettors quit right before variance swings positive.\n\n### Mistake #2: Overconfidence During Upswings\n\n**❌ Wrong:** \"I'm up $5,000 in 2 weeks! I'm a genius. Doubling my bet size!\"\n\n**✅ Right:** \"I'm up $5,000 in 2 weeks. Might be skill, might be variance. Maintaining bet size until I have larger sample.\"\n\n**Why it's wrong:** Increasing stakes during a hot streak (possibly just positive variance) leads to catastrophic losses when variance normalizes.\n\n### Mistake #3: Ignoring Variance in Bankroll Management\n\n**❌ Wrong:** \"I have $1,000 bankroll and 5% edge. I can bet $50 per game (5% of bankroll).\"\n\n**✅ Right:** \"I have $1,000 bankroll. With my variance, [Kelly Calculator](\u002Fbetting\u002Fkelly-calculator) suggests $12-15 per bet to survive swings.\"\n\n**Why it's wrong:** Ignoring variance causes bankroll ruin even with positive expectation.\n\n---\n\n## Reducing Variance Impact\n\nWhile you **can't eliminate variance**, you can reduce its impact on your bankroll and psychology:\n\n### 1. Use Kelly Criterion for Bet Sizing\n\nThe [Kelly Criterion](\u002Fen\u002Fglossary\u002Fbetting\u002Fkelly-criterion) automatically accounts for variance. It recommends smaller bets for high-variance situations and larger bets for low-variance edges.\n\n**Formula:**\n$$Kelly\\% = \\frac{(odds \\times probability) - 1}{odds - 1}$$\n\nThen apply **fractional Kelly** (25%-50% of full Kelly) to further reduce variance.\n\n### 2. Bet Lower Odds (Higher Probability)\n\n**Lower odds = lower variance:**\n- Betting -200 favorites: Win 66.7% of the time (predictable)\n- Betting +200 underdogs: Win 33.3% of the time (high swings)\n\nIf you have the same edge on both, favorites give smoother bankroll growth.\n\n### 3. Maintain Adequate Bankroll\n\n**Rule of thumb:**\n- **Minimum:** 50 units for low variance\n- **Recommended:** 100 units for medium variance\n- **Conservative:** 150 units for high variance\n\nUse the [Risk of Ruin Calculator](\u002Fbetting\u002Frisk-of-ruin) to determine your specific [risk of ruin](\u002Fen\u002Fglossary\u002Fbetting\u002Frisk-of-ruin) probability.\n\n### 4. Track Minimum 500 Bets\n\nDon't assess performance until you have meaningful sample size. Use [Variance Analyzer](\u002Fbetting\u002Fvariance-analyzer) to understand if you're winning due to skill or just experiencing positive variance.\n\n---\n\n## Variance vs Volatility vs Standard Deviation\n\nThese terms are often confused:\n\n| Term | Definition | Usage |\n|------|------------|-------|\n| **Variance** | Statistical measure (σ²) | Formal mathematical term |\n| **Standard Deviation (σ)** | Square root of variance | More intuitive measure |\n| **Volatility** | General term for \"swinginess\" | Casual usage |\n\n**They all measure the same concept:** How much results bounce around the expected value.\n\n---\n\n## Related Concepts\n\nUnderstanding variance connects to several critical betting concepts:\n\n- **[Expected Value (EV)](\u002Fbetting\u002Fexpected-value):** Variance doesn't change your EV, but it determines how reliably you reach it. High variance = long wait to realize EV.\n\n- **[ROI (Return on Investment)](\u002Fbetting\u002Froi):** Your measured ROI includes both edge and variance. True ROI only emerges after hundreds of bets.\n\n- **[Bankroll Management](\u002Fen\u002Fglossary\u002Fbetting\u002Fbankroll-management):** Proper bankroll sizing accounts for variance. The [Kelly Criterion](\u002Fen\u002Fglossary\u002Fbetting\u002Fkelly-criterion) explicitly balances edge vs. variance.\n\n- **[Risk of Ruin](\u002Fen\u002Fglossary\u002Fbetting\u002Frisk-of-ruin):** Variance is the primary driver of ruin risk. Higher variance = higher probability of going broke even with positive EV.\n\n---\n\n## Practical Tools\n\n### Calculators for Variance Management\n\nUse these tools to manage variance effectively:\n\n1. **[Variance Analyzer](\u002Fbetting\u002Fvariance-analyzer)** - Analyze your betting history to separate skill from luck\n2. **[Kelly Calculator](\u002Fbetting\u002Fkelly-calculator)** - Optimal bet sizing accounting for variance\n3. **[Risk of Ruin Calculator](\u002Fbetting\u002Frisk-of-ruin)** - Calculate bankroll ruin probability given variance\n4. **[Bankroll Growth Calculator](\u002Fbetting\u002Fbankroll-growth-calculator)** - Simulate long-term growth under different variance scenarios\n5. **[Staking Plan Calculator](\u002Fbetting\u002Fstaking-plan-calculator)** - Design staking plans that account for variance\n\n### Variance-Aware Strategy\n\n**For beginners:**\n- Start with small bet sizes (0.5-1% of bankroll)\n- Focus on lower variance markets (favorites, main markets)\n- Track every bet for minimum 500 bets\n- Never change strategy based on \u003C100 bet samples\n\n**For advanced bettors:**\n- Use fractional Kelly (25%-50%) to reduce variance\n- Diversify across multiple markets to smooth variance\n- Follow a disciplined [staking plan](\u002Fen\u002Fglossary\u002Fbetting\u002Fstaking-plan) consistently\n- Seek [closing line value](\u002Fen\u002Fglossary\u002Fbetting\u002Fclosing-line-value) and implement [sharp betting](\u002Fen\u002Fglossary\u002Fbetting\u002Fsharp-betting) principles\n- Accept that 20-30 bet losing streaks are **normal**\n\n---\n\n## Key Takeaways\n\n- ✅ **Variance is inevitable** - Even perfect betting experiences wild swings short-term\n- ✅ **Sample size matters** - Need 500+ bets to distinguish skill from luck\n- ✅ **Bankroll requirements** - Higher variance requires larger bankroll (100+ units)\n- ✅ **Mental game** - Understanding variance prevents tilt and emotional decisions\n- ✅ **Long-term thinking** - Focus on process, not short-term results\n- ✅ **Use Kelly Criterion** - Automatically accounts for variance in bet sizing\n\n**Remember:** Variance doesn't care about your edge. A profitable bettor can lose for months. An unprofitable bettor can win for weeks. Only sample size reveals truth.\n\n---\n\n## FAQ\n\n### How many bets until I know my true win rate?\n\n**Minimum 500 bets, ideally 1000+.** With 500 bets and 55% true win rate, you'll have 95% confidence interval of approximately 51%-59%. With only 50 bets, that interval becomes 40%-70% (essentially useless).\n\nUse the [Variance Analyzer](\u002Fbetting\u002Fvariance-analyzer) to calculate confidence intervals for your specific betting history.\n\n### Can I eliminate variance?\n\n**No.** Variance is fundamental to probability. You can **reduce** it by:\n- Betting lower odds (favorites)\n- Using proper bankroll management\n- Diversifying across multiple bets\n- Following Kelly Criterion\n\nBut you cannot eliminate it. Even professional bettors with 10-year track records experience multi-month losing streaks.\n\n### Is high variance bad?\n\n**Not necessarily.** High variance is fine **if**:\n- You have adequate bankroll (150+ units)\n- You use proper position sizing (fractional Kelly)\n- You have the mental fortitude to handle swings\n- Your edge justifies the variance\n\nHigh variance strategies (like longshot betting or parlays) can be profitable, but they require significantly larger bankrolls and stronger mental game.\n\n### What's the difference between variance and volatility?\n\n**They're the same concept, different contexts:**\n- **Variance\u002FStandard Deviation:** Technical statistical terms (mathematics)\n- **Volatility:** Casual term meaning \"swinginess\" (general usage)\n\nIn betting contexts, they're used interchangeably. \"High variance\" = \"High volatility\" = \"Results swing wildly.\"\n\n### How do I know if I'm experiencing variance or a losing strategy?\n\n**Use statistical analysis:**\n\n1. Calculate your confidence interval (use [Variance Analyzer](\u002Fbetting\u002Fvariance-analyzer))\n2. If your observed win rate **includes** your expected win rate within 95% confidence interval = **probably variance**\n3. If your observed win rate is **significantly below** expected even after 500+ bets = **strategy problem**\n\n**Example:** Expected 55% win rate, observed 51% after 500 bets\n- 95% CI: 47%-55%\n- Your 51% is within range → Keep going (likely variance)\n\n**Example 2:** Expected 55% win rate, observed 47% after 1000 bets\n- 95% CI: 50%-60%\n- Your 47% is below range → Strategy issue\n\n### Should I increase bet size during winning streaks?\n\n**No!** Winning streaks are often variance, not skill improvement. **Maintain consistent bet sizing** based on:\n- Your verified edge (500+ bet sample)\n- Your current bankroll\n- Kelly Criterion recommendations\n\nIncreasing stakes during hot streaks (positive variance) often leads to giving back all profits when variance normalizes. This is called **gambler's ruin via variance misattribution**.\n\nUse the [Kelly Calculator](\u002Fbetting\u002Fkelly-calculator) to determine optimal bet size regardless of recent results.\n\n---\n\n**Bottom Line:** Variance is the bettor's constant companion. Master it through proper bankroll management, large sample sizes, and emotional discipline - or let it master you through tilt, ruin, and abandoned +EV strategies. The choice is yours.",null,[],[31,32,33,34,35,36],"tr","en","pt","ru","de","es",[],{"data":39,"body":40},{},{"type":41,"children":42},"root",[43,52,456,467,481,487,616,634,638,644,649,682,689,694,727,737,740,746,750,758,1221,1226,1266,1274,1293,1509,1519,1522,1528,1534,1539,1638,2255,2261,2271,2275,2283,2301,2313,2319,2338,2346,2359,2369,2372,2378,2384,2394,2404,2414,2420,2429,2438,2447,2453,2623,3352,3361,3364,3370,3382,3388,3400,3831,3843,3849,3857,3870,3875,3881,3889,3922,3942,3948,3960,3963,3969,3974,4063,4073,4076,4082,4087,4154,4157,4163,4169,4174,4241,4247,4255,4278,4286,4342,4345,4351,4420,4430,4433,4439,4445,4455,4465,4471,4488,4511,4516,4522,4538,4561,4566,4572,4580,4603,4608,4614,4622,4669,4678,4691,4701,4714,4720,4737,4755,4766,4776,4779],{"type":44,"tag":45,"props":46,"children":48},"element","h2",{"id":47},"what-is-variance",[49],{"type":50,"value":51},"text","What is Variance?",{"type":44,"tag":53,"props":54,"children":55},"p",{},[56,58,454],{"type":50,"value":57},"Picture this: You've made 100 bets with a 55% win rate at -110 odds (genuinely profitable long-term), but you're down ",{"type":44,"tag":59,"props":60,"children":63},"span",{"className":61},[62],"katex",[64,259],{"type":44,"tag":59,"props":65,"children":68},{"className":66},[67],"katex-mathml",[69],{"type":44,"tag":70,"props":71,"children":73},"math",{"xmlns":72},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[74],{"type":44,"tag":75,"props":76,"children":77},"semantics",{},[78,252],{"type":44,"tag":79,"props":80,"children":81},"mrow",{},[82,88,94,99,104,109,114,119,124,129,133,140,145,150,155,160,165,169,173,177,181,186,191,195,199,203,208,213,217,222,227,231,235,239,243,247],{"type":44,"tag":83,"props":84,"children":85},"mn",{},[86],{"type":50,"value":87},"500.",{"type":44,"tag":89,"props":90,"children":91},"mi",{},[92],{"type":50,"value":93},"M",{"type":44,"tag":89,"props":95,"children":96},{},[97],{"type":50,"value":98},"e",{"type":44,"tag":89,"props":100,"children":101},{},[102],{"type":50,"value":103},"a",{"type":44,"tag":89,"props":105,"children":106},{},[107],{"type":50,"value":108},"n",{"type":44,"tag":89,"props":110,"children":111},{},[112],{"type":50,"value":113},"w",{"type":44,"tag":89,"props":115,"children":116},{},[117],{"type":50,"value":118},"h",{"type":44,"tag":89,"props":120,"children":121},{},[122],{"type":50,"value":123},"i",{"type":44,"tag":89,"props":125,"children":126},{},[127],{"type":50,"value":128},"l",{"type":44,"tag":89,"props":130,"children":131},{},[132],{"type":50,"value":98},{"type":44,"tag":134,"props":135,"children":137},"mo",{"separator":136},"true",[138],{"type":50,"value":139},",",{"type":44,"tag":89,"props":141,"children":142},{},[143],{"type":50,"value":144},"y",{"type":44,"tag":89,"props":146,"children":147},{},[148],{"type":50,"value":149},"o",{"type":44,"tag":89,"props":151,"children":152},{},[153],{"type":50,"value":154},"u",{"type":44,"tag":89,"props":156,"children":157},{},[158],{"type":50,"value":159},"r",{"type":44,"tag":89,"props":161,"children":162},{},[163],{"type":50,"value":164},"f",{"type":44,"tag":89,"props":166,"children":167},{},[168],{"type":50,"value":159},{"type":44,"tag":89,"props":170,"children":171},{},[172],{"type":50,"value":123},{"type":44,"tag":89,"props":174,"children":175},{},[176],{"type":50,"value":98},{"type":44,"tag":89,"props":178,"children":179},{},[180],{"type":50,"value":108},{"type":44,"tag":89,"props":182,"children":183},{},[184],{"type":50,"value":185},"d",{"type":44,"tag":89,"props":187,"children":188},{},[189],{"type":50,"value":190},"m",{"type":44,"tag":89,"props":192,"children":193},{},[194],{"type":50,"value":103},{"type":44,"tag":89,"props":196,"children":197},{},[198],{"type":50,"value":185},{"type":44,"tag":89,"props":200,"children":201},{},[202],{"type":50,"value":98},{"type":44,"tag":83,"props":204,"children":205},{},[206],{"type":50,"value":207},"100",{"type":44,"tag":89,"props":209,"children":210},{},[211],{"type":50,"value":212},"b",{"type":44,"tag":89,"props":214,"children":215},{},[216],{"type":50,"value":98},{"type":44,"tag":89,"props":218,"children":219},{},[220],{"type":50,"value":221},"t",{"type":44,"tag":89,"props":223,"children":224},{},[225],{"type":50,"value":226},"s",{"type":44,"tag":89,"props":228,"children":229},{},[230],{"type":50,"value":113},{"type":44,"tag":89,"props":232,"children":233},{},[234],{"type":50,"value":123},{"type":44,"tag":89,"props":236,"children":237},{},[238],{"type":50,"value":221},{"type":44,"tag":89,"props":240,"children":241},{},[242],{"type":50,"value":118},{"type":44,"tag":89,"props":244,"children":245},{},[246],{"type":50,"value":103},{"type":44,"tag":83,"props":248,"children":249},{},[250],{"type":50,"value":251},"48",{"type":44,"tag":253,"props":254,"children":256},"annotation",{"encoding":255},"application\u002Fx-tex",[257],{"type":50,"value":258},"500. Meanwhile, your friend made 100 bets with a 48% win rate (unprofitable long-term), but he's up ",{"type":44,"tag":59,"props":260,"children":263},{"className":261,"ariaHidden":136},[262],"katex-html",[264],{"type":44,"tag":59,"props":265,"children":268},{"className":266},[267],"base",[269,275,281,288,293,299,305,311,317,322,328,334,340,345,350,356,362,367,372,377,382,387,393,398,403,408,413,418,423,428,433,438,443,449],{"type":44,"tag":59,"props":270,"children":274},{"className":271,"style":273},[272],"strut","height:0.8889em;vertical-align:-0.1944em;",[],{"type":44,"tag":59,"props":276,"children":279},{"className":277},[278],"mord",[280],{"type":50,"value":87},{"type":44,"tag":59,"props":282,"children":286},{"className":283,"style":285},[278,284],"mathnormal","margin-right:0.109em;",[287],{"type":50,"value":93},{"type":44,"tag":59,"props":289,"children":291},{"className":290},[278,284],[292],{"type":50,"value":98},{"type":44,"tag":59,"props":294,"children":296},{"className":295},[278,284],[297],{"type":50,"value":298},"an",{"type":44,"tag":59,"props":300,"children":303},{"className":301,"style":302},[278,284],"margin-right:0.0269em;",[304],{"type":50,"value":113},{"type":44,"tag":59,"props":306,"children":308},{"className":307},[278,284],[309],{"type":50,"value":310},"hi",{"type":44,"tag":59,"props":312,"children":315},{"className":313,"style":314},[278,284],"margin-right:0.0197em;",[316],{"type":50,"value":128},{"type":44,"tag":59,"props":318,"children":320},{"className":319},[278,284],[321],{"type":50,"value":98},{"type":44,"tag":59,"props":323,"children":326},{"className":324},[325],"mpunct",[327],{"type":50,"value":139},{"type":44,"tag":59,"props":329,"children":333},{"className":330,"style":332},[331],"mspace","margin-right:0.1667em;",[],{"type":44,"tag":59,"props":335,"children":338},{"className":336,"style":337},[278,284],"margin-right:0.0359em;",[339],{"type":50,"value":144},{"type":44,"tag":59,"props":341,"children":343},{"className":342},[278,284],[344],{"type":50,"value":149},{"type":44,"tag":59,"props":346,"children":348},{"className":347},[278,284],[349],{"type":50,"value":154},{"type":44,"tag":59,"props":351,"children":354},{"className":352,"style":353},[278,284],"margin-right:0.0278em;",[355],{"type":50,"value":159},{"type":44,"tag":59,"props":357,"children":360},{"className":358,"style":359},[278,284],"margin-right:0.1076em;",[361],{"type":50,"value":164},{"type":44,"tag":59,"props":363,"children":365},{"className":364,"style":353},[278,284],[366],{"type":50,"value":159},{"type":44,"tag":59,"props":368,"children":370},{"className":369},[278,284],[371],{"type":50,"value":123},{"type":44,"tag":59,"props":373,"children":375},{"className":374},[278,284],[376],{"type":50,"value":98},{"type":44,"tag":59,"props":378,"children":380},{"className":379},[278,284],[381],{"type":50,"value":108},{"type":44,"tag":59,"props":383,"children":385},{"className":384},[278,284],[386],{"type":50,"value":185},{"type":44,"tag":59,"props":388,"children":390},{"className":389},[278,284],[391],{"type":50,"value":392},"ma",{"type":44,"tag":59,"props":394,"children":396},{"className":395},[278,284],[397],{"type":50,"value":185},{"type":44,"tag":59,"props":399,"children":401},{"className":400},[278,284],[402],{"type":50,"value":98},{"type":44,"tag":59,"props":404,"children":406},{"className":405},[278],[407],{"type":50,"value":207},{"type":44,"tag":59,"props":409,"children":411},{"className":410},[278,284],[412],{"type":50,"value":212},{"type":44,"tag":59,"props":414,"children":416},{"className":415},[278,284],[417],{"type":50,"value":98},{"type":44,"tag":59,"props":419,"children":421},{"className":420},[278,284],[422],{"type":50,"value":221},{"type":44,"tag":59,"props":424,"children":426},{"className":425},[278,284],[427],{"type":50,"value":226},{"type":44,"tag":59,"props":429,"children":431},{"className":430,"style":302},[278,284],[432],{"type":50,"value":113},{"type":44,"tag":59,"props":434,"children":436},{"className":435},[278,284],[437],{"type":50,"value":123},{"type":44,"tag":59,"props":439,"children":441},{"className":440},[278,284],[442],{"type":50,"value":221},{"type":44,"tag":59,"props":444,"children":446},{"className":445},[278,284],[447],{"type":50,"value":448},"ha",{"type":44,"tag":59,"props":450,"children":452},{"className":451},[278],[453],{"type":50,"value":251},{"type":50,"value":455},"300. Your bankroll graph looks like a rollercoaster, his looks like steady growth.",{"type":44,"tag":53,"props":457,"children":458},{},[459,461],{"type":50,"value":460},"What's happening? ",{"type":44,"tag":462,"props":463,"children":464},"strong",{},[465],{"type":50,"value":466},"Variance.",{"type":44,"tag":468,"props":469,"children":470},"blockquote",{},[471],{"type":44,"tag":53,"props":472,"children":473},{},[474,479],{"type":44,"tag":462,"props":475,"children":476},{},[477],{"type":50,"value":478},"In simple terms:",{"type":50,"value":480}," Variance is the mathematical way of saying \"results bounce around\" in the short run. Even perfect betting doesn't guarantee immediate profits - variance ensures that luck plays a role in short-term outcomes.",{"type":44,"tag":45,"props":482,"children":484},{"id":483},"tldr-quick-reference",[485],{"type":50,"value":486},"TL;DR - Quick Reference",{"type":44,"tag":488,"props":489,"children":490},"table",{},[491,509],{"type":44,"tag":492,"props":493,"children":494},"thead",{},[495],{"type":44,"tag":31,"props":496,"children":497},{},[498,504],{"type":44,"tag":499,"props":500,"children":501},"th",{},[502],{"type":50,"value":503},"Concept",{"type":44,"tag":499,"props":505,"children":506},{},[507],{"type":50,"value":508},"Explanation",{"type":44,"tag":510,"props":511,"children":512},"tbody",{},[513,530,546,568,584,600],{"type":44,"tag":31,"props":514,"children":515},{},[516,525],{"type":44,"tag":517,"props":518,"children":519},"td",{},[520],{"type":44,"tag":462,"props":521,"children":522},{},[523],{"type":50,"value":524},"What it is",{"type":44,"tag":517,"props":526,"children":527},{},[528],{"type":50,"value":529},"Natural randomness causing results to deviate from expected value",{"type":44,"tag":31,"props":531,"children":532},{},[533,541],{"type":44,"tag":517,"props":534,"children":535},{},[536],{"type":44,"tag":462,"props":537,"children":538},{},[539],{"type":50,"value":540},"Why it matters",{"type":44,"tag":517,"props":542,"children":543},{},[544],{"type":50,"value":545},"Your actual profit ≠ expected profit (short-term)",{"type":44,"tag":31,"props":547,"children":548},{},[549,557],{"type":44,"tag":517,"props":550,"children":551},{},[552],{"type":44,"tag":462,"props":553,"children":554},{},[555],{"type":50,"value":556},"Key metric",{"type":44,"tag":517,"props":558,"children":559},{},[560,566],{"type":44,"tag":103,"props":561,"children":563},{"href":562},"\u002Fen\u002Fglossary\u002Fbetting\u002Fstandard-deviation",[564],{"type":50,"value":565},"Standard deviation",{"type":50,"value":567}," (σ) measures swing size",{"type":44,"tag":31,"props":569,"children":570},{},[571,579],{"type":44,"tag":517,"props":572,"children":573},{},[574],{"type":44,"tag":462,"props":575,"children":576},{},[577],{"type":50,"value":578},"Sample size needed",{"type":44,"tag":517,"props":580,"children":581},{},[582],{"type":50,"value":583},"500+ bets to see true win rate with confidence",{"type":44,"tag":31,"props":585,"children":586},{},[587,595],{"type":44,"tag":517,"props":588,"children":589},{},[590],{"type":44,"tag":462,"props":591,"children":592},{},[593],{"type":50,"value":594},"Mental game",{"type":44,"tag":517,"props":596,"children":597},{},[598],{"type":50,"value":599},"Understanding variance prevents tilt and strategy changes",{"type":44,"tag":31,"props":601,"children":602},{},[603,611],{"type":44,"tag":517,"props":604,"children":605},{},[606],{"type":44,"tag":462,"props":607,"children":608},{},[609],{"type":50,"value":610},"Bankroll impact",{"type":44,"tag":517,"props":612,"children":613},{},[614],{"type":50,"value":615},"High variance requires larger bankroll (100+ units)",{"type":44,"tag":53,"props":617,"children":618},{},[619,624,626,632],{"type":44,"tag":462,"props":620,"children":621},{},[622],{"type":50,"value":623},"The bottom line:",{"type":50,"value":625}," Variance doesn't change your long-term edge, but it dramatically affects your short-term experience and ",{"type":44,"tag":103,"props":627,"children":629},{"href":628},"\u002Fen\u002Fglossary\u002Fbetting\u002Fbankroll-management",[630],{"type":50,"value":631},"bankroll management",{"type":50,"value":633}," requirements.",{"type":44,"tag":635,"props":636,"children":637},"hr",{},[],{"type":44,"tag":45,"props":639,"children":641},{"id":640},"understanding-variance-for-beginners",[642],{"type":50,"value":643},"Understanding Variance for Beginners",{"type":44,"tag":53,"props":645,"children":646},{},[647],{"type":50,"value":648},"Variance is why short-term results are unreliable. It's the reason:",{"type":44,"tag":650,"props":651,"children":652},"ul",{},[653,659,664,669],{"type":44,"tag":654,"props":655,"children":656},"li",{},[657],{"type":50,"value":658},"Profitable bettors experience losing streaks",{"type":44,"tag":654,"props":660,"children":661},{},[662],{"type":50,"value":663},"Poor bettors sometimes win big",{"type":44,"tag":654,"props":665,"children":666},{},[667],{"type":50,"value":668},"10 bets tell you almost nothing about skill",{"type":44,"tag":654,"props":670,"children":671},{},[672,674,680],{"type":50,"value":673},"Emotions and tilt destroy even ",{"type":44,"tag":103,"props":675,"children":677},{"href":676},"\u002Fen\u002Fglossary\u002Fbetting\u002Fvalue-betting",[678],{"type":50,"value":679},"value betting",{"type":50,"value":681}," strategies",{"type":44,"tag":683,"props":684,"children":686},"h3",{"id":685},"the-coin-flip-analogy",[687],{"type":50,"value":688},"The Coin Flip Analogy",{"type":44,"tag":53,"props":690,"children":691},{},[692],{"type":50,"value":693},"Imagine flipping a fair coin:",{"type":44,"tag":650,"props":695,"children":696},{},[697,707,717],{"type":44,"tag":654,"props":698,"children":699},{},[700,705],{"type":44,"tag":462,"props":701,"children":702},{},[703],{"type":50,"value":704},"10 flips:",{"type":50,"value":706}," You might get 7 heads (70%) - huge variance",{"type":44,"tag":654,"props":708,"children":709},{},[710,715],{"type":44,"tag":462,"props":711,"children":712},{},[713],{"type":50,"value":714},"100 flips:",{"type":50,"value":716}," You'll probably get 45-55 heads (reasonable variance)",{"type":44,"tag":654,"props":718,"children":719},{},[720,725],{"type":44,"tag":462,"props":721,"children":722},{},[723],{"type":50,"value":724},"10,000 flips:",{"type":50,"value":726}," You'll almost certainly get 49%-51% heads (variance minimized)",{"type":44,"tag":53,"props":728,"children":729},{},[730,735],{"type":44,"tag":462,"props":731,"children":732},{},[733],{"type":50,"value":734},"Betting works the same way.",{"type":50,"value":736}," Your true win rate emerges only after hundreds of bets. Before that? Variance dominates.",{"type":44,"tag":635,"props":738,"children":739},{},[],{"type":44,"tag":45,"props":741,"children":743},{"id":742},"the-mathematics-of-variance",[744],{"type":50,"value":745},"The Mathematics of Variance",{"type":44,"tag":747,"props":748,"children":749},"chart-variance-distribution",{},[],{"type":44,"tag":53,"props":751,"children":752},{},[753],{"type":44,"tag":462,"props":754,"children":755},{},[756],{"type":50,"value":757},"Standard deviation formula:",{"type":44,"tag":53,"props":759,"children":760},{},[761],{"type":44,"tag":59,"props":762,"children":764},{"className":763},[62],[765,856],{"type":44,"tag":59,"props":766,"children":768},{"className":767},[67],[769],{"type":44,"tag":70,"props":770,"children":771},{"xmlns":72},[772],{"type":44,"tag":75,"props":773,"children":774},{},[775,851],{"type":44,"tag":79,"props":776,"children":777},{},[778,783,788],{"type":44,"tag":89,"props":779,"children":780},{},[781],{"type":50,"value":782},"σ",{"type":44,"tag":134,"props":784,"children":785},{},[786],{"type":50,"value":787},"=",{"type":44,"tag":789,"props":790,"children":791},"msqrt",{},[792],{"type":44,"tag":793,"props":794,"children":795},"mfrac",{},[796,847],{"type":44,"tag":79,"props":797,"children":798},{},[799,804,810,823,828,833],{"type":44,"tag":134,"props":800,"children":801},{},[802],{"type":50,"value":803},"∑",{"type":44,"tag":134,"props":805,"children":807},{"stretchy":806},"false",[808],{"type":50,"value":809},"(",{"type":44,"tag":811,"props":812,"children":813},"msub",{},[814,819],{"type":44,"tag":89,"props":815,"children":816},{},[817],{"type":50,"value":818},"x",{"type":44,"tag":89,"props":820,"children":821},{},[822],{"type":50,"value":123},{"type":44,"tag":134,"props":824,"children":825},{},[826],{"type":50,"value":827},"−",{"type":44,"tag":89,"props":829,"children":830},{},[831],{"type":50,"value":832},"μ",{"type":44,"tag":834,"props":835,"children":836},"msup",{},[837,842],{"type":44,"tag":134,"props":838,"children":839},{"stretchy":806},[840],{"type":50,"value":841},")",{"type":44,"tag":83,"props":843,"children":844},{},[845],{"type":50,"value":846},"2",{"type":44,"tag":89,"props":848,"children":849},{},[850],{"type":50,"value":108},{"type":44,"tag":253,"props":852,"children":853},{"encoding":255},[854],{"type":50,"value":855},"\\sigma = \\sqrt{\\frac{\\sum(x_i - \\mu)^2}{n}}",{"type":44,"tag":59,"props":857,"children":859},{"className":858,"ariaHidden":136},[262],[860,889],{"type":44,"tag":59,"props":861,"children":863},{"className":862},[267],[864,869,874,879,885],{"type":44,"tag":59,"props":865,"children":868},{"className":866,"style":867},[272],"height:0.4306em;",[],{"type":44,"tag":59,"props":870,"children":872},{"className":871,"style":337},[278,284],[873],{"type":50,"value":782},{"type":44,"tag":59,"props":875,"children":878},{"className":876,"style":877},[331],"margin-right:0.2778em;",[],{"type":44,"tag":59,"props":880,"children":883},{"className":881},[882],"mrel",[884],{"type":50,"value":787},{"type":44,"tag":59,"props":886,"children":888},{"className":887,"style":877},[331],[],{"type":44,"tag":59,"props":890,"children":892},{"className":891},[267],[893,898],{"type":44,"tag":59,"props":894,"children":897},{"className":895,"style":896},[272],"height:1.84em;vertical-align:-0.5225em;",[],{"type":44,"tag":59,"props":899,"children":902},{"className":900},[278,901],"sqrt",[903],{"type":44,"tag":59,"props":904,"children":908},{"className":905},[906,907],"vlist-t","vlist-t2",[909,1209],{"type":44,"tag":59,"props":910,"children":913},{"className":911},[912],"vlist-r",[914,1204],{"type":44,"tag":59,"props":915,"children":919},{"className":916,"style":918},[917],"vlist","height:1.3175em;",[920,1176],{"type":44,"tag":59,"props":921,"children":925},{"className":922,"style":924},[923],"svg-align","top:-3.8em;",[926,932],{"type":44,"tag":59,"props":927,"children":931},{"className":928,"style":930},[929],"pstrut","height:3.8em;",[],{"type":44,"tag":59,"props":933,"children":936},{"className":934,"style":935},[278],"padding-left:1em;",[937],{"type":44,"tag":59,"props":938,"children":940},{"className":939},[278],[941,947,1172],{"type":44,"tag":59,"props":942,"children":946},{"className":943},[944,945],"mopen","nulldelimiter",[],{"type":44,"tag":59,"props":948,"children":950},{"className":949},[793],[951],{"type":44,"tag":59,"props":952,"children":954},{"className":953},[906,907],[955,1160],{"type":44,"tag":59,"props":956,"children":958},{"className":957},[912],[959,1155],{"type":44,"tag":59,"props":960,"children":963},{"className":961,"style":962},[917],"height:1.01em;",[964,990,1004],{"type":44,"tag":59,"props":965,"children":967},{"style":966},"top:-2.655em;",[968,973],{"type":44,"tag":59,"props":969,"children":972},{"className":970,"style":971},[929],"height:3em;",[],{"type":44,"tag":59,"props":974,"children":980},{"className":975},[976,977,978,979],"sizing","reset-size6","size3","mtight",[981],{"type":44,"tag":59,"props":982,"children":984},{"className":983},[278,979],[985],{"type":44,"tag":59,"props":986,"children":988},{"className":987},[278,284,979],[989],{"type":50,"value":108},{"type":44,"tag":59,"props":991,"children":993},{"style":992},"top:-3.23em;",[994,998],{"type":44,"tag":59,"props":995,"children":997},{"className":996,"style":971},[929],[],{"type":44,"tag":59,"props":999,"children":1003},{"className":1000,"style":1002},[1001],"frac-line","border-bottom-width:0.04em;",[],{"type":44,"tag":59,"props":1005,"children":1007},{"style":1006},"top:-3.485em;",[1008,1012],{"type":44,"tag":59,"props":1009,"children":1011},{"className":1010,"style":971},[929],[],{"type":44,"tag":59,"props":1013,"children":1015},{"className":1014},[976,977,978,979],[1016],{"type":44,"tag":59,"props":1017,"children":1019},{"className":1018},[278,979],[1020,1029,1034,1100,1106,1111],{"type":44,"tag":59,"props":1021,"children":1027},{"className":1022,"style":1026},[1023,1024,1025,979],"mop","op-symbol","small-op","position:relative;top:0em;",[1028],{"type":50,"value":803},{"type":44,"tag":59,"props":1030,"children":1032},{"className":1031},[944,979],[1033],{"type":50,"value":809},{"type":44,"tag":59,"props":1035,"children":1037},{"className":1036},[278,979],[1038,1043],{"type":44,"tag":59,"props":1039,"children":1041},{"className":1040},[278,284,979],[1042],{"type":50,"value":818},{"type":44,"tag":59,"props":1044,"children":1047},{"className":1045},[1046],"msupsub",[1048],{"type":44,"tag":59,"props":1049,"children":1051},{"className":1050},[906,907],[1052,1088],{"type":44,"tag":59,"props":1053,"children":1055},{"className":1054},[912],[1056,1081],{"type":44,"tag":59,"props":1057,"children":1060},{"className":1058,"style":1059},[917],"height:0.3281em;",[1061],{"type":44,"tag":59,"props":1062,"children":1064},{"style":1063},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1065,1070],{"type":44,"tag":59,"props":1066,"children":1069},{"className":1067,"style":1068},[929],"height:2.5em;",[],{"type":44,"tag":59,"props":1071,"children":1075},{"className":1072},[976,1073,1074,979],"reset-size3","size1",[1076],{"type":44,"tag":59,"props":1077,"children":1079},{"className":1078},[278,284,979],[1080],{"type":50,"value":123},{"type":44,"tag":59,"props":1082,"children":1085},{"className":1083},[1084],"vlist-s",[1086],{"type":50,"value":1087},"​",{"type":44,"tag":59,"props":1089,"children":1091},{"className":1090},[912],[1092],{"type":44,"tag":59,"props":1093,"children":1096},{"className":1094,"style":1095},[917],"height:0.143em;",[1097],{"type":44,"tag":59,"props":1098,"children":1099},{},[],{"type":44,"tag":59,"props":1101,"children":1104},{"className":1102},[1103,979],"mbin",[1105],{"type":50,"value":827},{"type":44,"tag":59,"props":1107,"children":1109},{"className":1108},[278,284,979],[1110],{"type":50,"value":832},{"type":44,"tag":59,"props":1112,"children":1115},{"className":1113},[1114,979],"mclose",[1116,1121],{"type":44,"tag":59,"props":1117,"children":1119},{"className":1118},[1114,979],[1120],{"type":50,"value":841},{"type":44,"tag":59,"props":1122,"children":1124},{"className":1123},[1046],[1125],{"type":44,"tag":59,"props":1126,"children":1128},{"className":1127},[906],[1129],{"type":44,"tag":59,"props":1130,"children":1132},{"className":1131},[912],[1133],{"type":44,"tag":59,"props":1134,"children":1137},{"className":1135,"style":1136},[917],"height:0.7463em;",[1138],{"type":44,"tag":59,"props":1139,"children":1141},{"style":1140},"top:-2.786em;margin-right:0.0714em;",[1142,1146],{"type":44,"tag":59,"props":1143,"children":1145},{"className":1144,"style":1068},[929],[],{"type":44,"tag":59,"props":1147,"children":1149},{"className":1148},[976,1073,1074,979],[1150],{"type":44,"tag":59,"props":1151,"children":1153},{"className":1152},[278,979],[1154],{"type":50,"value":846},{"type":44,"tag":59,"props":1156,"children":1158},{"className":1157},[1084],[1159],{"type":50,"value":1087},{"type":44,"tag":59,"props":1161,"children":1163},{"className":1162},[912],[1164],{"type":44,"tag":59,"props":1165,"children":1168},{"className":1166,"style":1167},[917],"height:0.345em;",[1169],{"type":44,"tag":59,"props":1170,"children":1171},{},[],{"type":44,"tag":59,"props":1173,"children":1175},{"className":1174},[1114,945],[],{"type":44,"tag":59,"props":1177,"children":1179},{"style":1178},"top:-3.2775em;",[1180,1184],{"type":44,"tag":59,"props":1181,"children":1183},{"className":1182,"style":930},[929],[],{"type":44,"tag":59,"props":1185,"children":1189},{"className":1186,"style":1188},[1187],"hide-tail","min-width:1.02em;height:1.88em;",[1190],{"type":44,"tag":1191,"props":1192,"children":1198},"svg",{"xmlns":1193,"width":1194,"height":1195,"viewBox":1196,"preserveAspectRatio":1197},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.88em","0 0 400000 1944","xMinYMin slice",[1199],{"type":44,"tag":1200,"props":1201,"children":1203},"path",{"d":1202},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[],{"type":44,"tag":59,"props":1205,"children":1207},{"className":1206},[1084],[1208],{"type":50,"value":1087},{"type":44,"tag":59,"props":1210,"children":1212},{"className":1211},[912],[1213],{"type":44,"tag":59,"props":1214,"children":1217},{"className":1215,"style":1216},[917],"height:0.5225em;",[1218],{"type":44,"tag":59,"props":1219,"children":1220},{},[],{"type":44,"tag":53,"props":1222,"children":1223},{},[1224],{"type":50,"value":1225},"Where:",{"type":44,"tag":650,"props":1227,"children":1228},{},[1229,1238,1248,1257],{"type":44,"tag":654,"props":1230,"children":1231},{},[1232,1236],{"type":44,"tag":462,"props":1233,"children":1234},{},[1235],{"type":50,"value":782},{"type":50,"value":1237}," = Standard deviation (measure of variance)",{"type":44,"tag":654,"props":1239,"children":1240},{},[1241,1246],{"type":44,"tag":462,"props":1242,"children":1243},{},[1244],{"type":50,"value":1245},"x_i",{"type":50,"value":1247}," = Individual result (win\u002Floss for each bet)",{"type":44,"tag":654,"props":1249,"children":1250},{},[1251,1255],{"type":44,"tag":462,"props":1252,"children":1253},{},[1254],{"type":50,"value":832},{"type":50,"value":1256}," = Expected value (mean result)",{"type":44,"tag":654,"props":1258,"children":1259},{},[1260,1264],{"type":44,"tag":462,"props":1261,"children":1262},{},[1263],{"type":50,"value":108},{"type":50,"value":1265}," = Number of bets",{"type":44,"tag":53,"props":1267,"children":1268},{},[1269],{"type":44,"tag":462,"props":1270,"children":1271},{},[1272],{"type":50,"value":1273},"What this means practically:",{"type":44,"tag":53,"props":1275,"children":1276},{},[1277,1279,1284,1286,1291],{"type":50,"value":1278},"If your expected ROI is ",{"type":44,"tag":462,"props":1280,"children":1281},{},[1282],{"type":50,"value":1283},"+5%",{"type":50,"value":1285}," with ",{"type":44,"tag":462,"props":1287,"children":1288},{},[1289],{"type":50,"value":1290},"20% standard deviation",{"type":50,"value":1292}," over 100 bets at $100 each:",{"type":44,"tag":650,"props":1294,"children":1295},{},[1296,1306,1372,1435],{"type":44,"tag":654,"props":1297,"children":1298},{},[1299,1304],{"type":44,"tag":462,"props":1300,"children":1301},{},[1302],{"type":50,"value":1303},"Expected profit:",{"type":50,"value":1305}," $500",{"type":44,"tag":654,"props":1307,"children":1308},{},[1309,1314,1316,1370],{"type":44,"tag":462,"props":1310,"children":1311},{},[1312],{"type":50,"value":1313},"68% of the time (±1σ):",{"type":50,"value":1315}," Between ",{"type":44,"tag":59,"props":1317,"children":1319},{"className":1318},[62],[1320,1347],{"type":44,"tag":59,"props":1321,"children":1323},{"className":1322},[67],[1324],{"type":44,"tag":70,"props":1325,"children":1326},{"xmlns":72},[1327],{"type":44,"tag":75,"props":1328,"children":1329},{},[1330,1342],{"type":44,"tag":79,"props":1331,"children":1332},{},[1333,1338],{"type":44,"tag":83,"props":1334,"children":1335},{},[1336],{"type":50,"value":1337},"300",{"type":44,"tag":134,"props":1339,"children":1340},{},[1341],{"type":50,"value":827},{"type":44,"tag":253,"props":1343,"children":1344},{"encoding":255},[1345],{"type":50,"value":1346},"300-",{"type":44,"tag":59,"props":1348,"children":1350},{"className":1349,"ariaHidden":136},[262],[1351],{"type":44,"tag":59,"props":1352,"children":1354},{"className":1353},[267],[1355,1360,1365],{"type":44,"tag":59,"props":1356,"children":1359},{"className":1357,"style":1358},[272],"height:0.7278em;vertical-align:-0.0833em;",[],{"type":44,"tag":59,"props":1361,"children":1363},{"className":1362},[278],[1364],{"type":50,"value":1337},{"type":44,"tag":59,"props":1366,"children":1368},{"className":1367},[278],[1369],{"type":50,"value":827},{"type":50,"value":1371},"700 profit",{"type":44,"tag":654,"props":1373,"children":1374},{},[1375,1380,1381,1433],{"type":44,"tag":462,"props":1376,"children":1377},{},[1378],{"type":50,"value":1379},"95% of the time (±2σ):",{"type":50,"value":1315},{"type":44,"tag":59,"props":1382,"children":1384},{"className":1383},[62],[1385,1411],{"type":44,"tag":59,"props":1386,"children":1388},{"className":1387},[67],[1389],{"type":44,"tag":70,"props":1390,"children":1391},{"xmlns":72},[1392],{"type":44,"tag":75,"props":1393,"children":1394},{},[1395,1406],{"type":44,"tag":79,"props":1396,"children":1397},{},[1398,1402],{"type":44,"tag":83,"props":1399,"children":1400},{},[1401],{"type":50,"value":207},{"type":44,"tag":134,"props":1403,"children":1404},{},[1405],{"type":50,"value":827},{"type":44,"tag":253,"props":1407,"children":1408},{"encoding":255},[1409],{"type":50,"value":1410},"100-",{"type":44,"tag":59,"props":1412,"children":1414},{"className":1413,"ariaHidden":136},[262],[1415],{"type":44,"tag":59,"props":1416,"children":1418},{"className":1417},[267],[1419,1423,1428],{"type":44,"tag":59,"props":1420,"children":1422},{"className":1421,"style":1358},[272],[],{"type":44,"tag":59,"props":1424,"children":1426},{"className":1425},[278],[1427],{"type":50,"value":207},{"type":44,"tag":59,"props":1429,"children":1431},{"className":1430},[278],[1432],{"type":50,"value":827},{"type":50,"value":1434},"900 profit",{"type":44,"tag":654,"props":1436,"children":1437},{},[1438,1443,1445,1507],{"type":44,"tag":462,"props":1439,"children":1440},{},[1441],{"type":50,"value":1442},"99.7% of the time (±3σ):",{"type":50,"value":1444}," Between -",{"type":44,"tag":59,"props":1446,"children":1448},{"className":1447},[62],[1449,1479],{"type":44,"tag":59,"props":1450,"children":1452},{"className":1451},[67],[1453],{"type":44,"tag":70,"props":1454,"children":1455},{"xmlns":72},[1456],{"type":44,"tag":75,"props":1457,"children":1458},{},[1459,1474],{"type":44,"tag":79,"props":1460,"children":1461},{},[1462,1466,1470],{"type":44,"tag":83,"props":1463,"children":1464},{},[1465],{"type":50,"value":207},{"type":44,"tag":89,"props":1467,"children":1468},{},[1469],{"type":50,"value":221},{"type":44,"tag":89,"props":1471,"children":1472},{},[1473],{"type":50,"value":149},{"type":44,"tag":253,"props":1475,"children":1476},{"encoding":255},[1477],{"type":50,"value":1478},"100 to ",{"type":44,"tag":59,"props":1480,"children":1482},{"className":1481,"ariaHidden":136},[262],[1483],{"type":44,"tag":59,"props":1484,"children":1486},{"className":1485},[267],[1487,1492,1497,1502],{"type":44,"tag":59,"props":1488,"children":1491},{"className":1489,"style":1490},[272],"height:0.6444em;",[],{"type":44,"tag":59,"props":1493,"children":1495},{"className":1494},[278],[1496],{"type":50,"value":207},{"type":44,"tag":59,"props":1498,"children":1500},{"className":1499},[278,284],[1501],{"type":50,"value":221},{"type":44,"tag":59,"props":1503,"children":1505},{"className":1504},[278,284],[1506],{"type":50,"value":149},{"type":50,"value":1508},"1,100 profit",{"type":44,"tag":53,"props":1510,"children":1511},{},[1512,1517],{"type":44,"tag":462,"props":1513,"children":1514},{},[1515],{"type":50,"value":1516},"Yes, you read that right",{"type":50,"value":1518}," - even with a +5% edge, there's a ~2.5% chance you'll be losing money after 100 bets. That's variance.",{"type":44,"tag":635,"props":1520,"children":1521},{},[],{"type":44,"tag":45,"props":1523,"children":1525},{"id":1524},"why-variance-matters-for-bettors",[1526],{"type":50,"value":1527},"Why Variance Matters for Bettors",{"type":44,"tag":683,"props":1529,"children":1531},{"id":1530},"_1-bankroll-requirements",[1532],{"type":50,"value":1533},"1. Bankroll Requirements",{"type":44,"tag":53,"props":1535,"children":1536},{},[1537],{"type":50,"value":1538},"Higher variance = need bigger bankroll to survive swings.",{"type":44,"tag":488,"props":1540,"children":1541},{},[1542,1563],{"type":44,"tag":492,"props":1543,"children":1544},{},[1545],{"type":44,"tag":31,"props":1546,"children":1547},{},[1548,1553,1558],{"type":44,"tag":499,"props":1549,"children":1550},{},[1551],{"type":50,"value":1552},"Bet Type",{"type":44,"tag":499,"props":1554,"children":1555},{},[1556],{"type":50,"value":1557},"Typical Variance",{"type":44,"tag":499,"props":1559,"children":1560},{},[1561],{"type":50,"value":1562},"Recommended Bankroll",{"type":44,"tag":510,"props":1564,"children":1565},{},[1566,1584,1602,1620],{"type":44,"tag":31,"props":1567,"children":1568},{},[1569,1574,1579],{"type":44,"tag":517,"props":1570,"children":1571},{},[1572],{"type":50,"value":1573},"Favorites (-200+)",{"type":44,"tag":517,"props":1575,"children":1576},{},[1577],{"type":50,"value":1578},"Low",{"type":44,"tag":517,"props":1580,"children":1581},{},[1582],{"type":50,"value":1583},"50-75 units",{"type":44,"tag":31,"props":1585,"children":1586},{},[1587,1592,1597],{"type":44,"tag":517,"props":1588,"children":1589},{},[1590],{"type":50,"value":1591},"Standard bets (-110)",{"type":44,"tag":517,"props":1593,"children":1594},{},[1595],{"type":50,"value":1596},"Medium",{"type":44,"tag":517,"props":1598,"children":1599},{},[1600],{"type":50,"value":1601},"75-100 units",{"type":44,"tag":31,"props":1603,"children":1604},{},[1605,1610,1615],{"type":44,"tag":517,"props":1606,"children":1607},{},[1608],{"type":50,"value":1609},"Underdogs (+150+)",{"type":44,"tag":517,"props":1611,"children":1612},{},[1613],{"type":50,"value":1614},"High",{"type":44,"tag":517,"props":1616,"children":1617},{},[1618],{"type":50,"value":1619},"100-150 units",{"type":44,"tag":31,"props":1621,"children":1622},{},[1623,1628,1633],{"type":44,"tag":517,"props":1624,"children":1625},{},[1626],{"type":50,"value":1627},"Parlays\u002FAccumulators",{"type":44,"tag":517,"props":1629,"children":1630},{},[1631],{"type":50,"value":1632},"Very High",{"type":44,"tag":517,"props":1634,"children":1635},{},[1636],{"type":50,"value":1637},"150-200 units",{"type":44,"tag":53,"props":1639,"children":1640},{},[1641,1646,1648,1949,1951,2253],{"type":44,"tag":462,"props":1642,"children":1643},{},[1644],{"type":50,"value":1645},"Example:",{"type":50,"value":1647}," If you bet ",{"type":44,"tag":59,"props":1649,"children":1651},{"className":1650},[62],[1652,1805],{"type":44,"tag":59,"props":1653,"children":1655},{"className":1654},[67],[1656],{"type":44,"tag":70,"props":1657,"children":1658},{"xmlns":72},[1659],{"type":44,"tag":75,"props":1660,"children":1661},{},[1662,1800],{"type":44,"tag":79,"props":1663,"children":1664},{},[1665,1669,1673,1677,1681,1686,1690,1694,1698,1702,1706,1710,1714,1719,1723,1727,1731,1735,1739,1743,1747,1751,1755,1759,1763,1767,1771,1775,1779,1783,1788,1792,1796],{"type":44,"tag":83,"props":1666,"children":1667},{},[1668],{"type":50,"value":207},{"type":44,"tag":89,"props":1670,"children":1671},{},[1672],{"type":50,"value":53},{"type":44,"tag":89,"props":1674,"children":1675},{},[1676],{"type":50,"value":98},{"type":44,"tag":89,"props":1678,"children":1679},{},[1680],{"type":50,"value":159},{"type":44,"tag":89,"props":1682,"children":1683},{},[1684],{"type":50,"value":1685},"g",{"type":44,"tag":89,"props":1687,"children":1688},{},[1689],{"type":50,"value":103},{"type":44,"tag":89,"props":1691,"children":1692},{},[1693],{"type":50,"value":190},{"type":44,"tag":89,"props":1695,"children":1696},{},[1697],{"type":50,"value":98},{"type":44,"tag":89,"props":1699,"children":1700},{},[1701],{"type":50,"value":149},{"type":44,"tag":89,"props":1703,"children":1704},{},[1705],{"type":50,"value":108},{"type":44,"tag":89,"props":1707,"children":1708},{},[1709],{"type":50,"value":164},{"type":44,"tag":89,"props":1711,"children":1712},{},[1713],{"type":50,"value":103},{"type":44,"tag":89,"props":1715,"children":1716},{},[1717],{"type":50,"value":1718},"v",{"type":44,"tag":89,"props":1720,"children":1721},{},[1722],{"type":50,"value":149},{"type":44,"tag":89,"props":1724,"children":1725},{},[1726],{"type":50,"value":159},{"type":44,"tag":89,"props":1728,"children":1729},{},[1730],{"type":50,"value":123},{"type":44,"tag":89,"props":1732,"children":1733},{},[1734],{"type":50,"value":221},{"type":44,"tag":89,"props":1736,"children":1737},{},[1738],{"type":50,"value":98},{"type":44,"tag":89,"props":1740,"children":1741},{},[1742],{"type":50,"value":226},{"type":44,"tag":134,"props":1744,"children":1745},{"stretchy":806},[1746],{"type":50,"value":809},{"type":44,"tag":89,"props":1748,"children":1749},{},[1750],{"type":50,"value":128},{"type":44,"tag":89,"props":1752,"children":1753},{},[1754],{"type":50,"value":149},{"type":44,"tag":89,"props":1756,"children":1757},{},[1758],{"type":50,"value":113},{"type":44,"tag":89,"props":1760,"children":1761},{},[1762],{"type":50,"value":1718},{"type":44,"tag":89,"props":1764,"children":1765},{},[1766],{"type":50,"value":103},{"type":44,"tag":89,"props":1768,"children":1769},{},[1770],{"type":50,"value":159},{"type":44,"tag":89,"props":1772,"children":1773},{},[1774],{"type":50,"value":123},{"type":44,"tag":89,"props":1776,"children":1777},{},[1778],{"type":50,"value":103},{"type":44,"tag":89,"props":1780,"children":1781},{},[1782],{"type":50,"value":108},{"type":44,"tag":89,"props":1784,"children":1785},{},[1786],{"type":50,"value":1787},"c",{"type":44,"tag":89,"props":1789,"children":1790},{},[1791],{"type":50,"value":98},{"type":44,"tag":134,"props":1793,"children":1794},{"stretchy":806},[1795],{"type":50,"value":841},{"type":44,"tag":134,"props":1797,"children":1798},{"separator":136},[1799],{"type":50,"value":139},{"type":44,"tag":253,"props":1801,"children":1802},{"encoding":255},[1803],{"type":50,"value":1804},"100 per game on favorites (low variance), ",{"type":44,"tag":59,"props":1806,"children":1808},{"className":1807,"ariaHidden":136},[262],[1809],{"type":44,"tag":59,"props":1810,"children":1812},{"className":1811},[267],[1813,1818,1823,1828,1834,1839,1845,1851,1856,1861,1866,1871,1877,1882,1887,1892,1897,1902,1907,1912,1917,1922,1927,1933,1939,1944],{"type":44,"tag":59,"props":1814,"children":1817},{"className":1815,"style":1816},[272],"height:1em;vertical-align:-0.25em;",[],{"type":44,"tag":59,"props":1819,"children":1821},{"className":1820},[278],[1822],{"type":50,"value":207},{"type":44,"tag":59,"props":1824,"children":1826},{"className":1825},[278,284],[1827],{"type":50,"value":53},{"type":44,"tag":59,"props":1829,"children":1831},{"className":1830,"style":353},[278,284],[1832],{"type":50,"value":1833},"er",{"type":44,"tag":59,"props":1835,"children":1837},{"className":1836,"style":337},[278,284],[1838],{"type":50,"value":1685},{"type":44,"tag":59,"props":1840,"children":1842},{"className":1841},[278,284],[1843],{"type":50,"value":1844},"am",{"type":44,"tag":59,"props":1846,"children":1848},{"className":1847},[278,284],[1849],{"type":50,"value":1850},"eo",{"type":44,"tag":59,"props":1852,"children":1854},{"className":1853},[278,284],[1855],{"type":50,"value":108},{"type":44,"tag":59,"props":1857,"children":1859},{"className":1858,"style":359},[278,284],[1860],{"type":50,"value":164},{"type":44,"tag":59,"props":1862,"children":1864},{"className":1863},[278,284],[1865],{"type":50,"value":103},{"type":44,"tag":59,"props":1867,"children":1869},{"className":1868,"style":337},[278,284],[1870],{"type":50,"value":1718},{"type":44,"tag":59,"props":1872,"children":1874},{"className":1873,"style":353},[278,284],[1875],{"type":50,"value":1876},"or",{"type":44,"tag":59,"props":1878,"children":1880},{"className":1879},[278,284],[1881],{"type":50,"value":123},{"type":44,"tag":59,"props":1883,"children":1885},{"className":1884},[278,284],[1886],{"type":50,"value":221},{"type":44,"tag":59,"props":1888,"children":1890},{"className":1889},[278,284],[1891],{"type":50,"value":36},{"type":44,"tag":59,"props":1893,"children":1895},{"className":1894},[944],[1896],{"type":50,"value":809},{"type":44,"tag":59,"props":1898,"children":1900},{"className":1899,"style":314},[278,284],[1901],{"type":50,"value":128},{"type":44,"tag":59,"props":1903,"children":1905},{"className":1904},[278,284],[1906],{"type":50,"value":149},{"type":44,"tag":59,"props":1908,"children":1910},{"className":1909,"style":302},[278,284],[1911],{"type":50,"value":113},{"type":44,"tag":59,"props":1913,"children":1915},{"className":1914,"style":337},[278,284],[1916],{"type":50,"value":1718},{"type":44,"tag":59,"props":1918,"children":1920},{"className":1919},[278,284],[1921],{"type":50,"value":103},{"type":44,"tag":59,"props":1923,"children":1925},{"className":1924,"style":353},[278,284],[1926],{"type":50,"value":159},{"type":44,"tag":59,"props":1928,"children":1930},{"className":1929},[278,284],[1931],{"type":50,"value":1932},"ian",{"type":44,"tag":59,"props":1934,"children":1936},{"className":1935},[278,284],[1937],{"type":50,"value":1938},"ce",{"type":44,"tag":59,"props":1940,"children":1942},{"className":1941},[1114],[1943],{"type":50,"value":841},{"type":44,"tag":59,"props":1945,"children":1947},{"className":1946},[325],[1948],{"type":50,"value":139},{"type":50,"value":1950},"5,000 bankroll is sufficient. But if you bet ",{"type":44,"tag":59,"props":1952,"children":1954},{"className":1953},[62],[1955,2101],{"type":44,"tag":59,"props":1956,"children":1958},{"className":1957},[67],[1959],{"type":44,"tag":70,"props":1960,"children":1961},{"xmlns":72},[1962],{"type":44,"tag":75,"props":1963,"children":1964},{},[1965,2096],{"type":44,"tag":79,"props":1966,"children":1967},{},[1968,1972,1976,1980,1984,1988,1992,1996,2000,2004,2008,2012,2016,2020,2024,2028,2032,2036,2040,2044,2048,2052,2056,2060,2064,2068,2072,2076,2080,2084,2088,2092],{"type":44,"tag":83,"props":1969,"children":1970},{},[1971],{"type":50,"value":207},{"type":44,"tag":89,"props":1973,"children":1974},{},[1975],{"type":50,"value":149},{"type":44,"tag":89,"props":1977,"children":1978},{},[1979],{"type":50,"value":108},{"type":44,"tag":89,"props":1981,"children":1982},{},[1983],{"type":50,"value":53},{"type":44,"tag":89,"props":1985,"children":1986},{},[1987],{"type":50,"value":103},{"type":44,"tag":89,"props":1989,"children":1990},{},[1991],{"type":50,"value":159},{"type":44,"tag":89,"props":1993,"children":1994},{},[1995],{"type":50,"value":128},{"type":44,"tag":89,"props":1997,"children":1998},{},[1999],{"type":50,"value":103},{"type":44,"tag":89,"props":2001,"children":2002},{},[2003],{"type":50,"value":144},{"type":44,"tag":89,"props":2005,"children":2006},{},[2007],{"type":50,"value":226},{"type":44,"tag":134,"props":2009,"children":2010},{"stretchy":806},[2011],{"type":50,"value":809},{"type":44,"tag":89,"props":2013,"children":2014},{},[2015],{"type":50,"value":118},{"type":44,"tag":89,"props":2017,"children":2018},{},[2019],{"type":50,"value":123},{"type":44,"tag":89,"props":2021,"children":2022},{},[2023],{"type":50,"value":1685},{"type":44,"tag":89,"props":2025,"children":2026},{},[2027],{"type":50,"value":118},{"type":44,"tag":89,"props":2029,"children":2030},{},[2031],{"type":50,"value":1718},{"type":44,"tag":89,"props":2033,"children":2034},{},[2035],{"type":50,"value":103},{"type":44,"tag":89,"props":2037,"children":2038},{},[2039],{"type":50,"value":159},{"type":44,"tag":89,"props":2041,"children":2042},{},[2043],{"type":50,"value":123},{"type":44,"tag":89,"props":2045,"children":2046},{},[2047],{"type":50,"value":103},{"type":44,"tag":89,"props":2049,"children":2050},{},[2051],{"type":50,"value":108},{"type":44,"tag":89,"props":2053,"children":2054},{},[2055],{"type":50,"value":1787},{"type":44,"tag":89,"props":2057,"children":2058},{},[2059],{"type":50,"value":98},{"type":44,"tag":134,"props":2061,"children":2062},{"stretchy":806},[2063],{"type":50,"value":841},{"type":44,"tag":134,"props":2065,"children":2066},{"separator":136},[2067],{"type":50,"value":139},{"type":44,"tag":89,"props":2069,"children":2070},{},[2071],{"type":50,"value":144},{"type":44,"tag":89,"props":2073,"children":2074},{},[2075],{"type":50,"value":149},{"type":44,"tag":89,"props":2077,"children":2078},{},[2079],{"type":50,"value":154},{"type":44,"tag":89,"props":2081,"children":2082},{},[2083],{"type":50,"value":108},{"type":44,"tag":89,"props":2085,"children":2086},{},[2087],{"type":50,"value":98},{"type":44,"tag":89,"props":2089,"children":2090},{},[2091],{"type":50,"value":98},{"type":44,"tag":89,"props":2093,"children":2094},{},[2095],{"type":50,"value":185},{"type":44,"tag":253,"props":2097,"children":2098},{"encoding":255},[2099],{"type":50,"value":2100},"100 on parlays (high variance), you need ",{"type":44,"tag":59,"props":2102,"children":2104},{"className":2103,"ariaHidden":136},[262],[2105],{"type":44,"tag":59,"props":2106,"children":2108},{"className":2107},[267],[2109,2113,2118,2123,2128,2133,2138,2143,2148,2153,2158,2163,2168,2173,2178,2183,2188,2193,2198,2203,2208,2213,2218,2222,2227,2232,2237,2242,2248],{"type":44,"tag":59,"props":2110,"children":2112},{"className":2111,"style":1816},[272],[],{"type":44,"tag":59,"props":2114,"children":2116},{"className":2115},[278],[2117],{"type":50,"value":207},{"type":44,"tag":59,"props":2119,"children":2121},{"className":2120},[278,284],[2122],{"type":50,"value":149},{"type":44,"tag":59,"props":2124,"children":2126},{"className":2125},[278,284],[2127],{"type":50,"value":108},{"type":44,"tag":59,"props":2129,"children":2131},{"className":2130},[278,284],[2132],{"type":50,"value":53},{"type":44,"tag":59,"props":2134,"children":2136},{"className":2135},[278,284],[2137],{"type":50,"value":103},{"type":44,"tag":59,"props":2139,"children":2141},{"className":2140,"style":353},[278,284],[2142],{"type":50,"value":159},{"type":44,"tag":59,"props":2144,"children":2146},{"className":2145,"style":314},[278,284],[2147],{"type":50,"value":128},{"type":44,"tag":59,"props":2149,"children":2151},{"className":2150},[278,284],[2152],{"type":50,"value":103},{"type":44,"tag":59,"props":2154,"children":2156},{"className":2155,"style":337},[278,284],[2157],{"type":50,"value":144},{"type":44,"tag":59,"props":2159,"children":2161},{"className":2160},[278,284],[2162],{"type":50,"value":226},{"type":44,"tag":59,"props":2164,"children":2166},{"className":2165},[944],[2167],{"type":50,"value":809},{"type":44,"tag":59,"props":2169,"children":2171},{"className":2170},[278,284],[2172],{"type":50,"value":310},{"type":44,"tag":59,"props":2174,"children":2176},{"className":2175,"style":337},[278,284],[2177],{"type":50,"value":1685},{"type":44,"tag":59,"props":2179,"children":2181},{"className":2180},[278,284],[2182],{"type":50,"value":118},{"type":44,"tag":59,"props":2184,"children":2186},{"className":2185,"style":337},[278,284],[2187],{"type":50,"value":1718},{"type":44,"tag":59,"props":2189,"children":2191},{"className":2190},[278,284],[2192],{"type":50,"value":103},{"type":44,"tag":59,"props":2194,"children":2196},{"className":2195,"style":353},[278,284],[2197],{"type":50,"value":159},{"type":44,"tag":59,"props":2199,"children":2201},{"className":2200},[278,284],[2202],{"type":50,"value":1932},{"type":44,"tag":59,"props":2204,"children":2206},{"className":2205},[278,284],[2207],{"type":50,"value":1938},{"type":44,"tag":59,"props":2209,"children":2211},{"className":2210},[1114],[2212],{"type":50,"value":841},{"type":44,"tag":59,"props":2214,"children":2216},{"className":2215},[325],[2217],{"type":50,"value":139},{"type":44,"tag":59,"props":2219,"children":2221},{"className":2220,"style":332},[331],[],{"type":44,"tag":59,"props":2223,"children":2225},{"className":2224,"style":337},[278,284],[2226],{"type":50,"value":144},{"type":44,"tag":59,"props":2228,"children":2230},{"className":2229},[278,284],[2231],{"type":50,"value":149},{"type":44,"tag":59,"props":2233,"children":2235},{"className":2234},[278,284],[2236],{"type":50,"value":154},{"type":44,"tag":59,"props":2238,"children":2240},{"className":2239},[278,284],[2241],{"type":50,"value":108},{"type":44,"tag":59,"props":2243,"children":2245},{"className":2244},[278,284],[2246],{"type":50,"value":2247},"ee",{"type":44,"tag":59,"props":2249,"children":2251},{"className":2250},[278,284],[2252],{"type":50,"value":185},{"type":50,"value":2254},"15,000-$20,000 to have the same risk of ruin.",{"type":44,"tag":683,"props":2256,"children":2258},{"id":2257},"_2-mental-game-protection",[2259],{"type":50,"value":2260},"2. Mental Game Protection",{"type":44,"tag":53,"props":2262,"children":2263},{},[2264,2269],{"type":44,"tag":462,"props":2265,"children":2266},{},[2267],{"type":50,"value":2268},"The Variance Trap:",{"type":50,"value":2270}," After 20 losing bets, your brain screams \"the strategy doesn't work!\" But statistically, a 55% bettor will experience 20-bet losing streaks regularly.",{"type":44,"tag":2272,"props":2273,"children":2274},"chart-variance-losing-streaks",{},[],{"type":44,"tag":53,"props":2276,"children":2277},{},[2278],{"type":44,"tag":462,"props":2279,"children":2280},{},[2281],{"type":50,"value":2282},"Reality check:",{"type":44,"tag":650,"props":2284,"children":2285},{},[2286,2291,2296],{"type":44,"tag":654,"props":2287,"children":2288},{},[2289],{"type":50,"value":2290},"50% win rate: Expect 8-bet losing streak every 256 bets",{"type":44,"tag":654,"props":2292,"children":2293},{},[2294],{"type":50,"value":2295},"55% win rate: Expect 6-bet losing streak every 128 bets",{"type":44,"tag":654,"props":2297,"children":2298},{},[2299],{"type":50,"value":2300},"60% win rate: Expect 5-bet losing streak every 64 bets",{"type":44,"tag":53,"props":2302,"children":2303},{},[2304,2306,2311],{"type":50,"value":2305},"Understanding this ",{"type":44,"tag":462,"props":2307,"children":2308},{},[2309],{"type":50,"value":2310},"prevents emotional betting decisions",{"type":50,"value":2312}," during downswings.",{"type":44,"tag":683,"props":2314,"children":2316},{"id":2315},"_3-true-roi-assessment",[2317],{"type":50,"value":2318},"3. True ROI Assessment",{"type":44,"tag":53,"props":2320,"children":2321},{},[2322,2324,2329,2331,2336],{"type":50,"value":2323},"You need ",{"type":44,"tag":462,"props":2325,"children":2326},{},[2327],{"type":50,"value":2328},"minimum 500 bets",{"type":50,"value":2330}," to assess your true ",{"type":44,"tag":103,"props":2332,"children":2334},{"href":2333},"\u002Fen\u002Fglossary\u002Fbetting\u002Froi",[2335],{"type":50,"value":16},{"type":50,"value":2337}," with statistical confidence.",{"type":44,"tag":53,"props":2339,"children":2340},{},[2341],{"type":44,"tag":462,"props":2342,"children":2343},{},[2344],{"type":50,"value":2345},"Why 500?",{"type":44,"tag":650,"props":2347,"children":2348},{},[2349,2354],{"type":44,"tag":654,"props":2350,"children":2351},{},[2352],{"type":50,"value":2353},"With 55% win rate, after 50 bets: 95% confidence interval = 40%-70% (useless!)",{"type":44,"tag":654,"props":2355,"children":2356},{},[2357],{"type":50,"value":2358},"After 500 bets: 95% confidence interval = 51%-59% (meaningful)",{"type":44,"tag":53,"props":2360,"children":2361},{},[2362,2367],{"type":44,"tag":462,"props":2363,"children":2364},{},[2365],{"type":50,"value":2366},"Never evaluate a betting strategy on less than 500 bets.",{"type":50,"value":2368}," You're just measuring variance, not skill.",{"type":44,"tag":635,"props":2370,"children":2371},{},[],{"type":44,"tag":45,"props":2373,"children":2375},{"id":2374},"common-variance-mistakes",[2376],{"type":50,"value":2377},"Common Variance Mistakes",{"type":44,"tag":683,"props":2379,"children":2381},{"id":2380},"mistake-1-changing-strategy-mid-variance",[2382],{"type":50,"value":2383},"Mistake #1: Changing Strategy Mid-Variance",{"type":44,"tag":53,"props":2385,"children":2386},{},[2387,2392],{"type":44,"tag":462,"props":2388,"children":2389},{},[2390],{"type":50,"value":2391},"❌ Wrong:",{"type":50,"value":2393}," \"I'm down $1,000 after 30 bets. This system doesn't work. Switching to a different model.\"",{"type":44,"tag":53,"props":2395,"children":2396},{},[2397,2402],{"type":44,"tag":462,"props":2398,"children":2399},{},[2400],{"type":50,"value":2401},"✅ Right:",{"type":50,"value":2403}," \"I'm down $1,000 after 30 bets. Expected variance for my bet size. Continuing with the plan until I have 500+ bet sample.\"",{"type":44,"tag":53,"props":2405,"children":2406},{},[2407,2412],{"type":44,"tag":462,"props":2408,"children":2409},{},[2410],{"type":50,"value":2411},"Why it's wrong:",{"type":50,"value":2413}," You might be abandoning a winning strategy during normal variance. Most bettors quit right before variance swings positive.",{"type":44,"tag":683,"props":2415,"children":2417},{"id":2416},"mistake-2-overconfidence-during-upswings",[2418],{"type":50,"value":2419},"Mistake #2: Overconfidence During Upswings",{"type":44,"tag":53,"props":2421,"children":2422},{},[2423,2427],{"type":44,"tag":462,"props":2424,"children":2425},{},[2426],{"type":50,"value":2391},{"type":50,"value":2428}," \"I'm up $5,000 in 2 weeks! I'm a genius. Doubling my bet size!\"",{"type":44,"tag":53,"props":2430,"children":2431},{},[2432,2436],{"type":44,"tag":462,"props":2433,"children":2434},{},[2435],{"type":50,"value":2401},{"type":50,"value":2437}," \"I'm up $5,000 in 2 weeks. Might be skill, might be variance. Maintaining bet size until I have larger sample.\"",{"type":44,"tag":53,"props":2439,"children":2440},{},[2441,2445],{"type":44,"tag":462,"props":2442,"children":2443},{},[2444],{"type":50,"value":2411},{"type":50,"value":2446}," Increasing stakes during a hot streak (possibly just positive variance) leads to catastrophic losses when variance normalizes.",{"type":44,"tag":683,"props":2448,"children":2450},{"id":2449},"mistake-3-ignoring-variance-in-bankroll-management",[2451],{"type":50,"value":2452},"Mistake #3: Ignoring Variance in Bankroll Management",{"type":44,"tag":53,"props":2454,"children":2455},{},[2456,2460,2462,2621],{"type":44,"tag":462,"props":2457,"children":2458},{},[2459],{"type":50,"value":2391},{"type":50,"value":2461}," \"I have ",{"type":44,"tag":59,"props":2463,"children":2465},{"className":2464},[62],[2466,2548],{"type":44,"tag":59,"props":2467,"children":2469},{"className":2468},[67],[2470],{"type":44,"tag":70,"props":2471,"children":2472},{"xmlns":72},[2473],{"type":44,"tag":75,"props":2474,"children":2475},{},[2476,2543],{"type":44,"tag":79,"props":2477,"children":2478},{},[2479,2484,2488,2493,2497,2501,2505,2510,2514,2518,2522,2526,2530,2534,2538],{"type":44,"tag":83,"props":2480,"children":2481},{},[2482],{"type":50,"value":2483},"1",{"type":44,"tag":134,"props":2485,"children":2486},{"separator":136},[2487],{"type":50,"value":139},{"type":44,"tag":83,"props":2489,"children":2490},{},[2491],{"type":50,"value":2492},"000",{"type":44,"tag":89,"props":2494,"children":2495},{},[2496],{"type":50,"value":212},{"type":44,"tag":89,"props":2498,"children":2499},{},[2500],{"type":50,"value":103},{"type":44,"tag":89,"props":2502,"children":2503},{},[2504],{"type":50,"value":108},{"type":44,"tag":89,"props":2506,"children":2507},{},[2508],{"type":50,"value":2509},"k",{"type":44,"tag":89,"props":2511,"children":2512},{},[2513],{"type":50,"value":159},{"type":44,"tag":89,"props":2515,"children":2516},{},[2517],{"type":50,"value":149},{"type":44,"tag":89,"props":2519,"children":2520},{},[2521],{"type":50,"value":128},{"type":44,"tag":89,"props":2523,"children":2524},{},[2525],{"type":50,"value":128},{"type":44,"tag":89,"props":2527,"children":2528},{},[2529],{"type":50,"value":103},{"type":44,"tag":89,"props":2531,"children":2532},{},[2533],{"type":50,"value":108},{"type":44,"tag":89,"props":2535,"children":2536},{},[2537],{"type":50,"value":185},{"type":44,"tag":83,"props":2539,"children":2540},{},[2541],{"type":50,"value":2542},"5",{"type":44,"tag":253,"props":2544,"children":2545},{"encoding":255},[2546],{"type":50,"value":2547},"1,000 bankroll and 5% edge. I can bet ",{"type":44,"tag":59,"props":2549,"children":2551},{"className":2550,"ariaHidden":136},[262],[2552],{"type":44,"tag":59,"props":2553,"children":2555},{"className":2554},[267],[2556,2560,2565,2570,2574,2579,2586,2591,2596,2601,2606,2611,2616],{"type":44,"tag":59,"props":2557,"children":2559},{"className":2558,"style":273},[272],[],{"type":44,"tag":59,"props":2561,"children":2563},{"className":2562},[278],[2564],{"type":50,"value":2483},{"type":44,"tag":59,"props":2566,"children":2568},{"className":2567},[325],[2569],{"type":50,"value":139},{"type":44,"tag":59,"props":2571,"children":2573},{"className":2572,"style":332},[331],[],{"type":44,"tag":59,"props":2575,"children":2577},{"className":2576},[278],[2578],{"type":50,"value":2492},{"type":44,"tag":59,"props":2580,"children":2583},{"className":2581,"style":2582},[278,284],"margin-right:0.0315em;",[2584],{"type":50,"value":2585},"bank",{"type":44,"tag":59,"props":2587,"children":2589},{"className":2588,"style":353},[278,284],[2590],{"type":50,"value":159},{"type":44,"tag":59,"props":2592,"children":2594},{"className":2593},[278,284],[2595],{"type":50,"value":149},{"type":44,"tag":59,"props":2597,"children":2599},{"className":2598,"style":314},[278,284],[2600],{"type":50,"value":128},{"type":44,"tag":59,"props":2602,"children":2604},{"className":2603,"style":314},[278,284],[2605],{"type":50,"value":128},{"type":44,"tag":59,"props":2607,"children":2609},{"className":2608},[278,284],[2610],{"type":50,"value":298},{"type":44,"tag":59,"props":2612,"children":2614},{"className":2613},[278,284],[2615],{"type":50,"value":185},{"type":44,"tag":59,"props":2617,"children":2619},{"className":2618},[278],[2620],{"type":50,"value":2542},{"type":50,"value":2622},"50 per game (5% of bankroll).\"",{"type":44,"tag":53,"props":2624,"children":2625},{},[2626,2630,2631,3350],{"type":44,"tag":462,"props":2627,"children":2628},{},[2629],{"type":50,"value":2401},{"type":50,"value":2461},{"type":44,"tag":59,"props":2632,"children":2634},{"className":2633},[62],[2635,2977],{"type":44,"tag":59,"props":2636,"children":2638},{"className":2637},[67],[2639],{"type":44,"tag":70,"props":2640,"children":2641},{"xmlns":72},[2642],{"type":44,"tag":75,"props":2643,"children":2644},{},[2645,2972],{"type":44,"tag":79,"props":2646,"children":2647},{},[2648,2652,2656,2660,2664,2668,2672,2676,2680,2684,2688,2692,2698,2703,2707,2711,2715,2719,2723,2727,2731,2735,2739,2743,2747,2751,2755,2759,2764,2769,2773,2777,2781,2785,2790,2794,2798,2802,2806,2810,2814,2818,2822,2826,2831,2835,2840,2844,2848,2852,2856,2860,2864,2868,2872,2876,2880,2884,2888,2892,2896,2900,2904,2908,2912,2916,2920,2924,2928,2932,2936,2940,2944,2948,2952,2956,2960,2964,2968],{"type":44,"tag":83,"props":2649,"children":2650},{},[2651],{"type":50,"value":2483},{"type":44,"tag":134,"props":2653,"children":2654},{"separator":136},[2655],{"type":50,"value":139},{"type":44,"tag":83,"props":2657,"children":2658},{},[2659],{"type":50,"value":2492},{"type":44,"tag":89,"props":2661,"children":2662},{},[2663],{"type":50,"value":212},{"type":44,"tag":89,"props":2665,"children":2666},{},[2667],{"type":50,"value":103},{"type":44,"tag":89,"props":2669,"children":2670},{},[2671],{"type":50,"value":108},{"type":44,"tag":89,"props":2673,"children":2674},{},[2675],{"type":50,"value":2509},{"type":44,"tag":89,"props":2677,"children":2678},{},[2679],{"type":50,"value":159},{"type":44,"tag":89,"props":2681,"children":2682},{},[2683],{"type":50,"value":149},{"type":44,"tag":89,"props":2685,"children":2686},{},[2687],{"type":50,"value":128},{"type":44,"tag":89,"props":2689,"children":2690},{},[2691],{"type":50,"value":128},{"type":44,"tag":89,"props":2693,"children":2695},{"mathvariant":2694},"normal",[2696],{"type":50,"value":2697},".",{"type":44,"tag":89,"props":2699,"children":2700},{},[2701],{"type":50,"value":2702},"W",{"type":44,"tag":89,"props":2704,"children":2705},{},[2706],{"type":50,"value":123},{"type":44,"tag":89,"props":2708,"children":2709},{},[2710],{"type":50,"value":221},{"type":44,"tag":89,"props":2712,"children":2713},{},[2714],{"type":50,"value":118},{"type":44,"tag":89,"props":2716,"children":2717},{},[2718],{"type":50,"value":190},{"type":44,"tag":89,"props":2720,"children":2721},{},[2722],{"type":50,"value":144},{"type":44,"tag":89,"props":2724,"children":2725},{},[2726],{"type":50,"value":1718},{"type":44,"tag":89,"props":2728,"children":2729},{},[2730],{"type":50,"value":103},{"type":44,"tag":89,"props":2732,"children":2733},{},[2734],{"type":50,"value":159},{"type":44,"tag":89,"props":2736,"children":2737},{},[2738],{"type":50,"value":123},{"type":44,"tag":89,"props":2740,"children":2741},{},[2742],{"type":50,"value":103},{"type":44,"tag":89,"props":2744,"children":2745},{},[2746],{"type":50,"value":108},{"type":44,"tag":89,"props":2748,"children":2749},{},[2750],{"type":50,"value":1787},{"type":44,"tag":89,"props":2752,"children":2753},{},[2754],{"type":50,"value":98},{"type":44,"tag":134,"props":2756,"children":2757},{"separator":136},[2758],{"type":50,"value":139},{"type":44,"tag":134,"props":2760,"children":2761},{"stretchy":806},[2762],{"type":50,"value":2763},"[",{"type":44,"tag":89,"props":2765,"children":2766},{},[2767],{"type":50,"value":2768},"K",{"type":44,"tag":89,"props":2770,"children":2771},{},[2772],{"type":50,"value":98},{"type":44,"tag":89,"props":2774,"children":2775},{},[2776],{"type":50,"value":128},{"type":44,"tag":89,"props":2778,"children":2779},{},[2780],{"type":50,"value":128},{"type":44,"tag":89,"props":2782,"children":2783},{},[2784],{"type":50,"value":144},{"type":44,"tag":89,"props":2786,"children":2787},{},[2788],{"type":50,"value":2789},"C",{"type":44,"tag":89,"props":2791,"children":2792},{},[2793],{"type":50,"value":103},{"type":44,"tag":89,"props":2795,"children":2796},{},[2797],{"type":50,"value":128},{"type":44,"tag":89,"props":2799,"children":2800},{},[2801],{"type":50,"value":1787},{"type":44,"tag":89,"props":2803,"children":2804},{},[2805],{"type":50,"value":154},{"type":44,"tag":89,"props":2807,"children":2808},{},[2809],{"type":50,"value":128},{"type":44,"tag":89,"props":2811,"children":2812},{},[2813],{"type":50,"value":103},{"type":44,"tag":89,"props":2815,"children":2816},{},[2817],{"type":50,"value":221},{"type":44,"tag":89,"props":2819,"children":2820},{},[2821],{"type":50,"value":149},{"type":44,"tag":89,"props":2823,"children":2824},{},[2825],{"type":50,"value":159},{"type":44,"tag":134,"props":2827,"children":2828},{"stretchy":806},[2829],{"type":50,"value":2830},"]",{"type":44,"tag":134,"props":2832,"children":2833},{"stretchy":806},[2834],{"type":50,"value":809},{"type":44,"tag":89,"props":2836,"children":2837},{"mathvariant":2694},[2838],{"type":50,"value":2839},"\u002F",{"type":44,"tag":89,"props":2841,"children":2842},{},[2843],{"type":50,"value":212},{"type":44,"tag":89,"props":2845,"children":2846},{},[2847],{"type":50,"value":98},{"type":44,"tag":89,"props":2849,"children":2850},{},[2851],{"type":50,"value":221},{"type":44,"tag":89,"props":2853,"children":2854},{},[2855],{"type":50,"value":221},{"type":44,"tag":89,"props":2857,"children":2858},{},[2859],{"type":50,"value":123},{"type":44,"tag":89,"props":2861,"children":2862},{},[2863],{"type":50,"value":108},{"type":44,"tag":89,"props":2865,"children":2866},{},[2867],{"type":50,"value":1685},{"type":44,"tag":89,"props":2869,"children":2870},{"mathvariant":2694},[2871],{"type":50,"value":2839},{"type":44,"tag":89,"props":2873,"children":2874},{},[2875],{"type":50,"value":2509},{"type":44,"tag":89,"props":2877,"children":2878},{},[2879],{"type":50,"value":98},{"type":44,"tag":89,"props":2881,"children":2882},{},[2883],{"type":50,"value":128},{"type":44,"tag":89,"props":2885,"children":2886},{},[2887],{"type":50,"value":128},{"type":44,"tag":89,"props":2889,"children":2890},{},[2891],{"type":50,"value":144},{"type":44,"tag":134,"props":2893,"children":2894},{},[2895],{"type":50,"value":827},{"type":44,"tag":89,"props":2897,"children":2898},{},[2899],{"type":50,"value":1787},{"type":44,"tag":89,"props":2901,"children":2902},{},[2903],{"type":50,"value":103},{"type":44,"tag":89,"props":2905,"children":2906},{},[2907],{"type":50,"value":128},{"type":44,"tag":89,"props":2909,"children":2910},{},[2911],{"type":50,"value":1787},{"type":44,"tag":89,"props":2913,"children":2914},{},[2915],{"type":50,"value":154},{"type":44,"tag":89,"props":2917,"children":2918},{},[2919],{"type":50,"value":128},{"type":44,"tag":89,"props":2921,"children":2922},{},[2923],{"type":50,"value":103},{"type":44,"tag":89,"props":2925,"children":2926},{},[2927],{"type":50,"value":221},{"type":44,"tag":89,"props":2929,"children":2930},{},[2931],{"type":50,"value":149},{"type":44,"tag":89,"props":2933,"children":2934},{},[2935],{"type":50,"value":159},{"type":44,"tag":134,"props":2937,"children":2938},{"stretchy":806},[2939],{"type":50,"value":841},{"type":44,"tag":89,"props":2941,"children":2942},{},[2943],{"type":50,"value":226},{"type":44,"tag":89,"props":2945,"children":2946},{},[2947],{"type":50,"value":154},{"type":44,"tag":89,"props":2949,"children":2950},{},[2951],{"type":50,"value":1685},{"type":44,"tag":89,"props":2953,"children":2954},{},[2955],{"type":50,"value":1685},{"type":44,"tag":89,"props":2957,"children":2958},{},[2959],{"type":50,"value":98},{"type":44,"tag":89,"props":2961,"children":2962},{},[2963],{"type":50,"value":226},{"type":44,"tag":89,"props":2965,"children":2966},{},[2967],{"type":50,"value":221},{"type":44,"tag":89,"props":2969,"children":2970},{},[2971],{"type":50,"value":226},{"type":44,"tag":253,"props":2973,"children":2974},{"encoding":255},[2975],{"type":50,"value":2976},"1,000 bankroll. With my variance, [Kelly Calculator](\u002Fbetting\u002Fkelly-calculator) suggests ",{"type":44,"tag":59,"props":2978,"children":2980},{"className":2979,"ariaHidden":136},[262],[2981,3261],{"type":44,"tag":59,"props":2982,"children":2984},{"className":2983},[267],[2985,2989,2994,2999,3003,3008,3013,3018,3023,3028,3033,3038,3044,3049,3054,3060,3065,3070,3075,3080,3085,3090,3095,3099,3104,3110,3115,3120,3125,3130,3135,3140,3145,3150,3155,3160,3165,3170,3175,3180,3185,3190,3195,3200,3206,3212,3217,3222,3227,3232,3237,3242,3247,3252,3257],{"type":44,"tag":59,"props":2986,"children":2988},{"className":2987,"style":1816},[272],[],{"type":44,"tag":59,"props":2990,"children":2992},{"className":2991},[278],[2993],{"type":50,"value":2483},{"type":44,"tag":59,"props":2995,"children":2997},{"className":2996},[325],[2998],{"type":50,"value":139},{"type":44,"tag":59,"props":3000,"children":3002},{"className":3001,"style":332},[331],[],{"type":44,"tag":59,"props":3004,"children":3006},{"className":3005},[278],[3007],{"type":50,"value":2492},{"type":44,"tag":59,"props":3009,"children":3011},{"className":3010,"style":2582},[278,284],[3012],{"type":50,"value":2585},{"type":44,"tag":59,"props":3014,"children":3016},{"className":3015,"style":353},[278,284],[3017],{"type":50,"value":159},{"type":44,"tag":59,"props":3019,"children":3021},{"className":3020},[278,284],[3022],{"type":50,"value":149},{"type":44,"tag":59,"props":3024,"children":3026},{"className":3025,"style":314},[278,284],[3027],{"type":50,"value":128},{"type":44,"tag":59,"props":3029,"children":3031},{"className":3030,"style":314},[278,284],[3032],{"type":50,"value":128},{"type":44,"tag":59,"props":3034,"children":3036},{"className":3035},[278],[3037],{"type":50,"value":2697},{"type":44,"tag":59,"props":3039,"children":3042},{"className":3040,"style":3041},[278,284],"margin-right:0.1389em;",[3043],{"type":50,"value":2702},{"type":44,"tag":59,"props":3045,"children":3047},{"className":3046},[278,284],[3048],{"type":50,"value":123},{"type":44,"tag":59,"props":3050,"children":3052},{"className":3051},[278,284],[3053],{"type":50,"value":221},{"type":44,"tag":59,"props":3055,"children":3057},{"className":3056},[278,284],[3058],{"type":50,"value":3059},"hm",{"type":44,"tag":59,"props":3061,"children":3063},{"className":3062,"style":337},[278,284],[3064],{"type":50,"value":144},{"type":44,"tag":59,"props":3066,"children":3068},{"className":3067,"style":337},[278,284],[3069],{"type":50,"value":1718},{"type":44,"tag":59,"props":3071,"children":3073},{"className":3072},[278,284],[3074],{"type":50,"value":103},{"type":44,"tag":59,"props":3076,"children":3078},{"className":3077,"style":353},[278,284],[3079],{"type":50,"value":159},{"type":44,"tag":59,"props":3081,"children":3083},{"className":3082},[278,284],[3084],{"type":50,"value":1932},{"type":44,"tag":59,"props":3086,"children":3088},{"className":3087},[278,284],[3089],{"type":50,"value":1938},{"type":44,"tag":59,"props":3091,"children":3093},{"className":3092},[325],[3094],{"type":50,"value":139},{"type":44,"tag":59,"props":3096,"children":3098},{"className":3097,"style":332},[331],[],{"type":44,"tag":59,"props":3100,"children":3102},{"className":3101},[944],[3103],{"type":50,"value":2763},{"type":44,"tag":59,"props":3105,"children":3108},{"className":3106,"style":3107},[278,284],"margin-right:0.0715em;",[3109],{"type":50,"value":2768},{"type":44,"tag":59,"props":3111,"children":3113},{"className":3112},[278,284],[3114],{"type":50,"value":98},{"type":44,"tag":59,"props":3116,"children":3118},{"className":3117,"style":314},[278,284],[3119],{"type":50,"value":128},{"type":44,"tag":59,"props":3121,"children":3123},{"className":3122,"style":314},[278,284],[3124],{"type":50,"value":128},{"type":44,"tag":59,"props":3126,"children":3128},{"className":3127,"style":337},[278,284],[3129],{"type":50,"value":144},{"type":44,"tag":59,"props":3131,"children":3133},{"className":3132,"style":3107},[278,284],[3134],{"type":50,"value":2789},{"type":44,"tag":59,"props":3136,"children":3138},{"className":3137},[278,284],[3139],{"type":50,"value":103},{"type":44,"tag":59,"props":3141,"children":3143},{"className":3142,"style":314},[278,284],[3144],{"type":50,"value":128},{"type":44,"tag":59,"props":3146,"children":3148},{"className":3147},[278,284],[3149],{"type":50,"value":1787},{"type":44,"tag":59,"props":3151,"children":3153},{"className":3152},[278,284],[3154],{"type":50,"value":154},{"type":44,"tag":59,"props":3156,"children":3158},{"className":3157,"style":314},[278,284],[3159],{"type":50,"value":128},{"type":44,"tag":59,"props":3161,"children":3163},{"className":3162},[278,284],[3164],{"type":50,"value":103},{"type":44,"tag":59,"props":3166,"children":3168},{"className":3167},[278,284],[3169],{"type":50,"value":221},{"type":44,"tag":59,"props":3171,"children":3173},{"className":3172,"style":353},[278,284],[3174],{"type":50,"value":1876},{"type":44,"tag":59,"props":3176,"children":3178},{"className":3177},[1114],[3179],{"type":50,"value":2830},{"type":44,"tag":59,"props":3181,"children":3183},{"className":3182},[944],[3184],{"type":50,"value":809},{"type":44,"tag":59,"props":3186,"children":3188},{"className":3187},[278],[3189],{"type":50,"value":2839},{"type":44,"tag":59,"props":3191,"children":3193},{"className":3192},[278,284],[3194],{"type":50,"value":212},{"type":44,"tag":59,"props":3196,"children":3198},{"className":3197},[278,284],[3199],{"type":50,"value":98},{"type":44,"tag":59,"props":3201,"children":3203},{"className":3202},[278,284],[3204],{"type":50,"value":3205},"tt",{"type":44,"tag":59,"props":3207,"children":3209},{"className":3208},[278,284],[3210],{"type":50,"value":3211},"in",{"type":44,"tag":59,"props":3213,"children":3215},{"className":3214,"style":337},[278,284],[3216],{"type":50,"value":1685},{"type":44,"tag":59,"props":3218,"children":3220},{"className":3219},[278],[3221],{"type":50,"value":2839},{"type":44,"tag":59,"props":3223,"children":3225},{"className":3224,"style":2582},[278,284],[3226],{"type":50,"value":2509},{"type":44,"tag":59,"props":3228,"children":3230},{"className":3229},[278,284],[3231],{"type":50,"value":98},{"type":44,"tag":59,"props":3233,"children":3235},{"className":3234,"style":314},[278,284],[3236],{"type":50,"value":128},{"type":44,"tag":59,"props":3238,"children":3240},{"className":3239,"style":314},[278,284],[3241],{"type":50,"value":128},{"type":44,"tag":59,"props":3243,"children":3245},{"className":3244,"style":337},[278,284],[3246],{"type":50,"value":144},{"type":44,"tag":59,"props":3248,"children":3251},{"className":3249,"style":3250},[331],"margin-right:0.2222em;",[],{"type":44,"tag":59,"props":3253,"children":3255},{"className":3254},[1103],[3256],{"type":50,"value":827},{"type":44,"tag":59,"props":3258,"children":3260},{"className":3259,"style":3250},[331],[],{"type":44,"tag":59,"props":3262,"children":3264},{"className":3263},[267],[3265,3269,3274,3279,3284,3289,3294,3299,3304,3309,3314,3319,3324,3330,3335,3340,3345],{"type":44,"tag":59,"props":3266,"children":3268},{"className":3267,"style":1816},[272],[],{"type":44,"tag":59,"props":3270,"children":3272},{"className":3271},[278,284],[3273],{"type":50,"value":1787},{"type":44,"tag":59,"props":3275,"children":3277},{"className":3276},[278,284],[3278],{"type":50,"value":103},{"type":44,"tag":59,"props":3280,"children":3282},{"className":3281,"style":314},[278,284],[3283],{"type":50,"value":128},{"type":44,"tag":59,"props":3285,"children":3287},{"className":3286},[278,284],[3288],{"type":50,"value":1787},{"type":44,"tag":59,"props":3290,"children":3292},{"className":3291},[278,284],[3293],{"type":50,"value":154},{"type":44,"tag":59,"props":3295,"children":3297},{"className":3296,"style":314},[278,284],[3298],{"type":50,"value":128},{"type":44,"tag":59,"props":3300,"children":3302},{"className":3301},[278,284],[3303],{"type":50,"value":103},{"type":44,"tag":59,"props":3305,"children":3307},{"className":3306},[278,284],[3308],{"type":50,"value":221},{"type":44,"tag":59,"props":3310,"children":3312},{"className":3311,"style":353},[278,284],[3313],{"type":50,"value":1876},{"type":44,"tag":59,"props":3315,"children":3317},{"className":3316},[1114],[3318],{"type":50,"value":841},{"type":44,"tag":59,"props":3320,"children":3322},{"className":3321},[278,284],[3323],{"type":50,"value":226},{"type":44,"tag":59,"props":3325,"children":3327},{"className":3326,"style":337},[278,284],[3328],{"type":50,"value":3329},"ug",{"type":44,"tag":59,"props":3331,"children":3333},{"className":3332,"style":337},[278,284],[3334],{"type":50,"value":1685},{"type":44,"tag":59,"props":3336,"children":3338},{"className":3337},[278,284],[3339],{"type":50,"value":36},{"type":44,"tag":59,"props":3341,"children":3343},{"className":3342},[278,284],[3344],{"type":50,"value":221},{"type":44,"tag":59,"props":3346,"children":3348},{"className":3347},[278,284],[3349],{"type":50,"value":226},{"type":50,"value":3351},"12-15 per bet to survive swings.\"",{"type":44,"tag":53,"props":3353,"children":3354},{},[3355,3359],{"type":44,"tag":462,"props":3356,"children":3357},{},[3358],{"type":50,"value":2411},{"type":50,"value":3360}," Ignoring variance causes bankroll ruin even with positive expectation.",{"type":44,"tag":635,"props":3362,"children":3363},{},[],{"type":44,"tag":45,"props":3365,"children":3367},{"id":3366},"reducing-variance-impact",[3368],{"type":50,"value":3369},"Reducing Variance Impact",{"type":44,"tag":53,"props":3371,"children":3372},{},[3373,3375,3380],{"type":50,"value":3374},"While you ",{"type":44,"tag":462,"props":3376,"children":3377},{},[3378],{"type":50,"value":3379},"can't eliminate variance",{"type":50,"value":3381},", you can reduce its impact on your bankroll and psychology:",{"type":44,"tag":683,"props":3383,"children":3385},{"id":3384},"_1-use-kelly-criterion-for-bet-sizing",[3386],{"type":50,"value":3387},"1. Use Kelly Criterion for Bet Sizing",{"type":44,"tag":53,"props":3389,"children":3390},{},[3391,3393,3398],{"type":50,"value":3392},"The ",{"type":44,"tag":103,"props":3394,"children":3396},{"href":3395},"\u002Fen\u002Fglossary\u002Fbetting\u002Fkelly-criterion",[3397],{"type":50,"value":18},{"type":50,"value":3399}," automatically accounts for variance. It recommends smaller bets for high-variance situations and larger bets for low-variance edges.",{"type":44,"tag":53,"props":3401,"children":3402},{},[3403,3408],{"type":44,"tag":462,"props":3404,"children":3405},{},[3406],{"type":50,"value":3407},"Formula:",{"type":44,"tag":59,"props":3409,"children":3411},{"className":3410},[62],[3412,3573],{"type":44,"tag":59,"props":3413,"children":3415},{"className":3414},[67],[3416],{"type":44,"tag":70,"props":3417,"children":3418},{"xmlns":72},[3419],{"type":44,"tag":75,"props":3420,"children":3421},{},[3422,3568],{"type":44,"tag":79,"props":3423,"children":3424},{},[3425,3429,3433,3437,3441,3445,3450,3454],{"type":44,"tag":89,"props":3426,"children":3427},{},[3428],{"type":50,"value":2768},{"type":44,"tag":89,"props":3430,"children":3431},{},[3432],{"type":50,"value":98},{"type":44,"tag":89,"props":3434,"children":3435},{},[3436],{"type":50,"value":128},{"type":44,"tag":89,"props":3438,"children":3439},{},[3440],{"type":50,"value":128},{"type":44,"tag":89,"props":3442,"children":3443},{},[3444],{"type":50,"value":144},{"type":44,"tag":89,"props":3446,"children":3447},{"mathvariant":2694},[3448],{"type":50,"value":3449},"%",{"type":44,"tag":134,"props":3451,"children":3452},{},[3453],{"type":50,"value":787},{"type":44,"tag":793,"props":3455,"children":3456},{},[3457,3541],{"type":44,"tag":79,"props":3458,"children":3459},{},[3460,3464,3468,3472,3476,3480,3485,3489,3493,3497,3501,3505,3509,3513,3517,3521,3525,3529,3533,3537],{"type":44,"tag":134,"props":3461,"children":3462},{"stretchy":806},[3463],{"type":50,"value":809},{"type":44,"tag":89,"props":3465,"children":3466},{},[3467],{"type":50,"value":149},{"type":44,"tag":89,"props":3469,"children":3470},{},[3471],{"type":50,"value":185},{"type":44,"tag":89,"props":3473,"children":3474},{},[3475],{"type":50,"value":185},{"type":44,"tag":89,"props":3477,"children":3478},{},[3479],{"type":50,"value":226},{"type":44,"tag":134,"props":3481,"children":3482},{},[3483],{"type":50,"value":3484},"×",{"type":44,"tag":89,"props":3486,"children":3487},{},[3488],{"type":50,"value":53},{"type":44,"tag":89,"props":3490,"children":3491},{},[3492],{"type":50,"value":159},{"type":44,"tag":89,"props":3494,"children":3495},{},[3496],{"type":50,"value":149},{"type":44,"tag":89,"props":3498,"children":3499},{},[3500],{"type":50,"value":212},{"type":44,"tag":89,"props":3502,"children":3503},{},[3504],{"type":50,"value":103},{"type":44,"tag":89,"props":3506,"children":3507},{},[3508],{"type":50,"value":212},{"type":44,"tag":89,"props":3510,"children":3511},{},[3512],{"type":50,"value":123},{"type":44,"tag":89,"props":3514,"children":3515},{},[3516],{"type":50,"value":128},{"type":44,"tag":89,"props":3518,"children":3519},{},[3520],{"type":50,"value":123},{"type":44,"tag":89,"props":3522,"children":3523},{},[3524],{"type":50,"value":221},{"type":44,"tag":89,"props":3526,"children":3527},{},[3528],{"type":50,"value":144},{"type":44,"tag":134,"props":3530,"children":3531},{"stretchy":806},[3532],{"type":50,"value":841},{"type":44,"tag":134,"props":3534,"children":3535},{},[3536],{"type":50,"value":827},{"type":44,"tag":83,"props":3538,"children":3539},{},[3540],{"type":50,"value":2483},{"type":44,"tag":79,"props":3542,"children":3543},{},[3544,3548,3552,3556,3560,3564],{"type":44,"tag":89,"props":3545,"children":3546},{},[3547],{"type":50,"value":149},{"type":44,"tag":89,"props":3549,"children":3550},{},[3551],{"type":50,"value":185},{"type":44,"tag":89,"props":3553,"children":3554},{},[3555],{"type":50,"value":185},{"type":44,"tag":89,"props":3557,"children":3558},{},[3559],{"type":50,"value":226},{"type":44,"tag":134,"props":3561,"children":3562},{},[3563],{"type":50,"value":827},{"type":44,"tag":83,"props":3565,"children":3566},{},[3567],{"type":50,"value":2483},{"type":44,"tag":253,"props":3569,"children":3570},{"encoding":255},[3571],{"type":50,"value":3572},"Kelly\\% = \\frac{(odds \\times probability) - 1}{odds - 1}",{"type":44,"tag":59,"props":3574,"children":3576},{"className":3575,"ariaHidden":136},[262],[3577,3629],{"type":44,"tag":59,"props":3578,"children":3580},{"className":3579},[267],[3581,3586,3591,3596,3601,3606,3611,3616,3620,3625],{"type":44,"tag":59,"props":3582,"children":3585},{"className":3583,"style":3584},[272],"height:0.9444em;vertical-align:-0.1944em;",[],{"type":44,"tag":59,"props":3587,"children":3589},{"className":3588,"style":3107},[278,284],[3590],{"type":50,"value":2768},{"type":44,"tag":59,"props":3592,"children":3594},{"className":3593},[278,284],[3595],{"type":50,"value":98},{"type":44,"tag":59,"props":3597,"children":3599},{"className":3598,"style":314},[278,284],[3600],{"type":50,"value":128},{"type":44,"tag":59,"props":3602,"children":3604},{"className":3603,"style":314},[278,284],[3605],{"type":50,"value":128},{"type":44,"tag":59,"props":3607,"children":3609},{"className":3608,"style":337},[278,284],[3610],{"type":50,"value":144},{"type":44,"tag":59,"props":3612,"children":3614},{"className":3613},[278],[3615],{"type":50,"value":3449},{"type":44,"tag":59,"props":3617,"children":3619},{"className":3618,"style":877},[331],[],{"type":44,"tag":59,"props":3621,"children":3623},{"className":3622},[882],[3624],{"type":50,"value":787},{"type":44,"tag":59,"props":3626,"children":3628},{"className":3627,"style":877},[331],[],{"type":44,"tag":59,"props":3630,"children":3632},{"className":3631},[267],[3633,3638],{"type":44,"tag":59,"props":3634,"children":3637},{"className":3635,"style":3636},[272],"height:1.4133em;vertical-align:-0.4033em;",[],{"type":44,"tag":59,"props":3639,"children":3641},{"className":3640},[278],[3642,3646,3827],{"type":44,"tag":59,"props":3643,"children":3645},{"className":3644},[944,945],[],{"type":44,"tag":59,"props":3647,"children":3649},{"className":3648},[793],[3650],{"type":44,"tag":59,"props":3651,"children":3653},{"className":3652},[906,907],[3654,3815],{"type":44,"tag":59,"props":3655,"children":3657},{"className":3656},[912],[3658,3810],{"type":44,"tag":59,"props":3659,"children":3661},{"className":3660,"style":962},[917],[3662,3703,3714],{"type":44,"tag":59,"props":3663,"children":3664},{"style":966},[3665,3669],{"type":44,"tag":59,"props":3666,"children":3668},{"className":3667,"style":971},[929],[],{"type":44,"tag":59,"props":3670,"children":3672},{"className":3671},[976,977,978,979],[3673],{"type":44,"tag":59,"props":3674,"children":3676},{"className":3675},[278,979],[3677,3682,3688,3693,3698],{"type":44,"tag":59,"props":3678,"children":3680},{"className":3679},[278,284,979],[3681],{"type":50,"value":149},{"type":44,"tag":59,"props":3683,"children":3685},{"className":3684},[278,284,979],[3686],{"type":50,"value":3687},"dd",{"type":44,"tag":59,"props":3689,"children":3691},{"className":3690},[278,284,979],[3692],{"type":50,"value":226},{"type":44,"tag":59,"props":3694,"children":3696},{"className":3695},[1103,979],[3697],{"type":50,"value":827},{"type":44,"tag":59,"props":3699,"children":3701},{"className":3700},[278,979],[3702],{"type":50,"value":2483},{"type":44,"tag":59,"props":3704,"children":3705},{"style":992},[3706,3710],{"type":44,"tag":59,"props":3707,"children":3709},{"className":3708,"style":971},[929],[],{"type":44,"tag":59,"props":3711,"children":3713},{"className":3712,"style":1002},[1001],[],{"type":44,"tag":59,"props":3715,"children":3716},{"style":1006},[3717,3721],{"type":44,"tag":59,"props":3718,"children":3720},{"className":3719,"style":971},[929],[],{"type":44,"tag":59,"props":3722,"children":3724},{"className":3723},[976,977,978,979],[3725],{"type":44,"tag":59,"props":3726,"children":3728},{"className":3727},[278,979],[3729,3734,3739,3744,3749,3754,3759,3764,3769,3775,3780,3785,3790,3795,3800,3805],{"type":44,"tag":59,"props":3730,"children":3732},{"className":3731},[944,979],[3733],{"type":50,"value":809},{"type":44,"tag":59,"props":3735,"children":3737},{"className":3736},[278,284,979],[3738],{"type":50,"value":149},{"type":44,"tag":59,"props":3740,"children":3742},{"className":3741},[278,284,979],[3743],{"type":50,"value":3687},{"type":44,"tag":59,"props":3745,"children":3747},{"className":3746},[278,284,979],[3748],{"type":50,"value":226},{"type":44,"tag":59,"props":3750,"children":3752},{"className":3751},[1103,979],[3753],{"type":50,"value":3484},{"type":44,"tag":59,"props":3755,"children":3757},{"className":3756},[278,284,979],[3758],{"type":50,"value":53},{"type":44,"tag":59,"props":3760,"children":3762},{"className":3761,"style":353},[278,284,979],[3763],{"type":50,"value":159},{"type":44,"tag":59,"props":3765,"children":3767},{"className":3766},[278,284,979],[3768],{"type":50,"value":149},{"type":44,"tag":59,"props":3770,"children":3772},{"className":3771},[278,284,979],[3773],{"type":50,"value":3774},"babi",{"type":44,"tag":59,"props":3776,"children":3778},{"className":3777,"style":314},[278,284,979],[3779],{"type":50,"value":128},{"type":44,"tag":59,"props":3781,"children":3783},{"className":3782},[278,284,979],[3784],{"type":50,"value":123},{"type":44,"tag":59,"props":3786,"children":3788},{"className":3787},[278,284,979],[3789],{"type":50,"value":221},{"type":44,"tag":59,"props":3791,"children":3793},{"className":3792,"style":337},[278,284,979],[3794],{"type":50,"value":144},{"type":44,"tag":59,"props":3796,"children":3798},{"className":3797},[1114,979],[3799],{"type":50,"value":841},{"type":44,"tag":59,"props":3801,"children":3803},{"className":3802},[1103,979],[3804],{"type":50,"value":827},{"type":44,"tag":59,"props":3806,"children":3808},{"className":3807},[278,979],[3809],{"type":50,"value":2483},{"type":44,"tag":59,"props":3811,"children":3813},{"className":3812},[1084],[3814],{"type":50,"value":1087},{"type":44,"tag":59,"props":3816,"children":3818},{"className":3817},[912],[3819],{"type":44,"tag":59,"props":3820,"children":3823},{"className":3821,"style":3822},[917],"height:0.4033em;",[3824],{"type":44,"tag":59,"props":3825,"children":3826},{},[],{"type":44,"tag":59,"props":3828,"children":3830},{"className":3829},[1114,945],[],{"type":44,"tag":53,"props":3832,"children":3833},{},[3834,3836,3841],{"type":50,"value":3835},"Then apply ",{"type":44,"tag":462,"props":3837,"children":3838},{},[3839],{"type":50,"value":3840},"fractional Kelly",{"type":50,"value":3842}," (25%-50% of full Kelly) to further reduce variance.",{"type":44,"tag":683,"props":3844,"children":3846},{"id":3845},"_2-bet-lower-odds-higher-probability",[3847],{"type":50,"value":3848},"2. Bet Lower Odds (Higher Probability)",{"type":44,"tag":53,"props":3850,"children":3851},{},[3852],{"type":44,"tag":462,"props":3853,"children":3854},{},[3855],{"type":50,"value":3856},"Lower odds = lower variance:",{"type":44,"tag":650,"props":3858,"children":3859},{},[3860,3865],{"type":44,"tag":654,"props":3861,"children":3862},{},[3863],{"type":50,"value":3864},"Betting -200 favorites: Win 66.7% of the time (predictable)",{"type":44,"tag":654,"props":3866,"children":3867},{},[3868],{"type":50,"value":3869},"Betting +200 underdogs: Win 33.3% of the time (high swings)",{"type":44,"tag":53,"props":3871,"children":3872},{},[3873],{"type":50,"value":3874},"If you have the same edge on both, favorites give smoother bankroll growth.",{"type":44,"tag":683,"props":3876,"children":3878},{"id":3877},"_3-maintain-adequate-bankroll",[3879],{"type":50,"value":3880},"3. Maintain Adequate Bankroll",{"type":44,"tag":53,"props":3882,"children":3883},{},[3884],{"type":44,"tag":462,"props":3885,"children":3886},{},[3887],{"type":50,"value":3888},"Rule of thumb:",{"type":44,"tag":650,"props":3890,"children":3891},{},[3892,3902,3912],{"type":44,"tag":654,"props":3893,"children":3894},{},[3895,3900],{"type":44,"tag":462,"props":3896,"children":3897},{},[3898],{"type":50,"value":3899},"Minimum:",{"type":50,"value":3901}," 50 units for low variance",{"type":44,"tag":654,"props":3903,"children":3904},{},[3905,3910],{"type":44,"tag":462,"props":3906,"children":3907},{},[3908],{"type":50,"value":3909},"Recommended:",{"type":50,"value":3911}," 100 units for medium variance",{"type":44,"tag":654,"props":3913,"children":3914},{},[3915,3920],{"type":44,"tag":462,"props":3916,"children":3917},{},[3918],{"type":50,"value":3919},"Conservative:",{"type":50,"value":3921}," 150 units for high variance",{"type":44,"tag":53,"props":3923,"children":3924},{},[3925,3927,3932,3934,3940],{"type":50,"value":3926},"Use the ",{"type":44,"tag":103,"props":3928,"children":3929},{"href":21},[3930],{"type":50,"value":3931},"Risk of Ruin Calculator",{"type":50,"value":3933}," to determine your specific ",{"type":44,"tag":103,"props":3935,"children":3937},{"href":3936},"\u002Fen\u002Fglossary\u002Fbetting\u002Frisk-of-ruin",[3938],{"type":50,"value":3939},"risk of ruin",{"type":50,"value":3941}," probability.",{"type":44,"tag":683,"props":3943,"children":3945},{"id":3944},"_4-track-minimum-500-bets",[3946],{"type":50,"value":3947},"4. Track Minimum 500 Bets",{"type":44,"tag":53,"props":3949,"children":3950},{},[3951,3953,3958],{"type":50,"value":3952},"Don't assess performance until you have meaningful sample size. Use ",{"type":44,"tag":103,"props":3954,"children":3955},{"href":20},[3956],{"type":50,"value":3957},"Variance Analyzer",{"type":50,"value":3959}," to understand if you're winning due to skill or just experiencing positive variance.",{"type":44,"tag":635,"props":3961,"children":3962},{},[],{"type":44,"tag":45,"props":3964,"children":3966},{"id":3965},"variance-vs-volatility-vs-standard-deviation",[3967],{"type":50,"value":3968},"Variance vs Volatility vs Standard Deviation",{"type":44,"tag":53,"props":3970,"children":3971},{},[3972],{"type":50,"value":3973},"These terms are often confused:",{"type":44,"tag":488,"props":3975,"children":3976},{},[3977,3998],{"type":44,"tag":492,"props":3978,"children":3979},{},[3980],{"type":44,"tag":31,"props":3981,"children":3982},{},[3983,3988,3993],{"type":44,"tag":499,"props":3984,"children":3985},{},[3986],{"type":50,"value":3987},"Term",{"type":44,"tag":499,"props":3989,"children":3990},{},[3991],{"type":50,"value":3992},"Definition",{"type":44,"tag":499,"props":3994,"children":3995},{},[3996],{"type":50,"value":3997},"Usage",{"type":44,"tag":510,"props":3999,"children":4000},{},[4001,4021,4042],{"type":44,"tag":31,"props":4002,"children":4003},{},[4004,4011,4016],{"type":44,"tag":517,"props":4005,"children":4006},{},[4007],{"type":44,"tag":462,"props":4008,"children":4009},{},[4010],{"type":50,"value":25},{"type":44,"tag":517,"props":4012,"children":4013},{},[4014],{"type":50,"value":4015},"Statistical measure (σ²)",{"type":44,"tag":517,"props":4017,"children":4018},{},[4019],{"type":50,"value":4020},"Formal mathematical term",{"type":44,"tag":31,"props":4022,"children":4023},{},[4024,4032,4037],{"type":44,"tag":517,"props":4025,"children":4026},{},[4027],{"type":44,"tag":462,"props":4028,"children":4029},{},[4030],{"type":50,"value":4031},"Standard Deviation (σ)",{"type":44,"tag":517,"props":4033,"children":4034},{},[4035],{"type":50,"value":4036},"Square root of variance",{"type":44,"tag":517,"props":4038,"children":4039},{},[4040],{"type":50,"value":4041},"More intuitive measure",{"type":44,"tag":31,"props":4043,"children":4044},{},[4045,4053,4058],{"type":44,"tag":517,"props":4046,"children":4047},{},[4048],{"type":44,"tag":462,"props":4049,"children":4050},{},[4051],{"type":50,"value":4052},"Volatility",{"type":44,"tag":517,"props":4054,"children":4055},{},[4056],{"type":50,"value":4057},"General term for \"swinginess\"",{"type":44,"tag":517,"props":4059,"children":4060},{},[4061],{"type":50,"value":4062},"Casual usage",{"type":44,"tag":53,"props":4064,"children":4065},{},[4066,4071],{"type":44,"tag":462,"props":4067,"children":4068},{},[4069],{"type":50,"value":4070},"They all measure the same concept:",{"type":50,"value":4072}," How much results bounce around the expected value.",{"type":44,"tag":635,"props":4074,"children":4075},{},[],{"type":44,"tag":45,"props":4077,"children":4079},{"id":4078},"related-concepts",[4080],{"type":50,"value":4081},"Related Concepts",{"type":44,"tag":53,"props":4083,"children":4084},{},[4085],{"type":50,"value":4086},"Understanding variance connects to several critical betting concepts:",{"type":44,"tag":650,"props":4088,"children":4089},{},[4090,4106,4121,4140],{"type":44,"tag":654,"props":4091,"children":4092},{},[4093,4104],{"type":44,"tag":462,"props":4094,"children":4095},{},[4096,4102],{"type":44,"tag":103,"props":4097,"children":4099},{"href":4098},"\u002Fbetting\u002Fexpected-value",[4100],{"type":50,"value":4101},"Expected Value (EV)",{"type":50,"value":4103},":",{"type":50,"value":4105}," Variance doesn't change your EV, but it determines how reliably you reach it. High variance = long wait to realize EV.",{"type":44,"tag":654,"props":4107,"children":4108},{},[4109,4119],{"type":44,"tag":462,"props":4110,"children":4111},{},[4112,4118],{"type":44,"tag":103,"props":4113,"children":4115},{"href":4114},"\u002Fbetting\u002Froi",[4116],{"type":50,"value":4117},"ROI (Return on Investment)",{"type":50,"value":4103},{"type":50,"value":4120}," Your measured ROI includes both edge and variance. True ROI only emerges after hundreds of bets.",{"type":44,"tag":654,"props":4122,"children":4123},{},[4124,4132,4134,4138],{"type":44,"tag":462,"props":4125,"children":4126},{},[4127,4131],{"type":44,"tag":103,"props":4128,"children":4129},{"href":628},[4130],{"type":50,"value":17},{"type":50,"value":4103},{"type":50,"value":4133}," Proper bankroll sizing accounts for variance. The ",{"type":44,"tag":103,"props":4135,"children":4136},{"href":3395},[4137],{"type":50,"value":18},{"type":50,"value":4139}," explicitly balances edge vs. variance.",{"type":44,"tag":654,"props":4141,"children":4142},{},[4143,4152],{"type":44,"tag":462,"props":4144,"children":4145},{},[4146,4151],{"type":44,"tag":103,"props":4147,"children":4148},{"href":3936},[4149],{"type":50,"value":4150},"Risk of Ruin",{"type":50,"value":4103},{"type":50,"value":4153}," Variance is the primary driver of ruin risk. Higher variance = higher probability of going broke even with positive EV.",{"type":44,"tag":635,"props":4155,"children":4156},{},[],{"type":44,"tag":45,"props":4158,"children":4160},{"id":4159},"practical-tools",[4161],{"type":50,"value":4162},"Practical Tools",{"type":44,"tag":683,"props":4164,"children":4166},{"id":4165},"calculators-for-variance-management",[4167],{"type":50,"value":4168},"Calculators for Variance Management",{"type":44,"tag":53,"props":4170,"children":4171},{},[4172],{"type":50,"value":4173},"Use these tools to manage variance effectively:",{"type":44,"tag":4175,"props":4176,"children":4177},"ol",{},[4178,4190,4203,4215,4228],{"type":44,"tag":654,"props":4179,"children":4180},{},[4181,4188],{"type":44,"tag":462,"props":4182,"children":4183},{},[4184],{"type":44,"tag":103,"props":4185,"children":4186},{"href":20},[4187],{"type":50,"value":3957},{"type":50,"value":4189}," - Analyze your betting history to separate skill from luck",{"type":44,"tag":654,"props":4191,"children":4192},{},[4193,4201],{"type":44,"tag":462,"props":4194,"children":4195},{},[4196],{"type":44,"tag":103,"props":4197,"children":4198},{"href":23},[4199],{"type":50,"value":4200},"Kelly Calculator",{"type":50,"value":4202}," - Optimal bet sizing accounting for variance",{"type":44,"tag":654,"props":4204,"children":4205},{},[4206,4213],{"type":44,"tag":462,"props":4207,"children":4208},{},[4209],{"type":44,"tag":103,"props":4210,"children":4211},{"href":21},[4212],{"type":50,"value":3931},{"type":50,"value":4214}," - Calculate bankroll ruin probability given variance",{"type":44,"tag":654,"props":4216,"children":4217},{},[4218,4226],{"type":44,"tag":462,"props":4219,"children":4220},{},[4221],{"type":44,"tag":103,"props":4222,"children":4223},{"href":22},[4224],{"type":50,"value":4225},"Bankroll Growth Calculator",{"type":50,"value":4227}," - Simulate long-term growth under different variance scenarios",{"type":44,"tag":654,"props":4229,"children":4230},{},[4231,4239],{"type":44,"tag":462,"props":4232,"children":4233},{},[4234],{"type":44,"tag":103,"props":4235,"children":4236},{"href":24},[4237],{"type":50,"value":4238},"Staking Plan Calculator",{"type":50,"value":4240}," - Design staking plans that account for variance",{"type":44,"tag":683,"props":4242,"children":4244},{"id":4243},"variance-aware-strategy",[4245],{"type":50,"value":4246},"Variance-Aware Strategy",{"type":44,"tag":53,"props":4248,"children":4249},{},[4250],{"type":44,"tag":462,"props":4251,"children":4252},{},[4253],{"type":50,"value":4254},"For beginners:",{"type":44,"tag":650,"props":4256,"children":4257},{},[4258,4263,4268,4273],{"type":44,"tag":654,"props":4259,"children":4260},{},[4261],{"type":50,"value":4262},"Start with small bet sizes (0.5-1% of bankroll)",{"type":44,"tag":654,"props":4264,"children":4265},{},[4266],{"type":50,"value":4267},"Focus on lower variance markets (favorites, main markets)",{"type":44,"tag":654,"props":4269,"children":4270},{},[4271],{"type":50,"value":4272},"Track every bet for minimum 500 bets",{"type":44,"tag":654,"props":4274,"children":4275},{},[4276],{"type":50,"value":4277},"Never change strategy based on \u003C100 bet samples",{"type":44,"tag":53,"props":4279,"children":4280},{},[4281],{"type":44,"tag":462,"props":4282,"children":4283},{},[4284],{"type":50,"value":4285},"For advanced bettors:",{"type":44,"tag":650,"props":4287,"children":4288},{},[4289,4294,4299,4312,4333],{"type":44,"tag":654,"props":4290,"children":4291},{},[4292],{"type":50,"value":4293},"Use fractional Kelly (25%-50%) to reduce variance",{"type":44,"tag":654,"props":4295,"children":4296},{},[4297],{"type":50,"value":4298},"Diversify across multiple markets to smooth variance",{"type":44,"tag":654,"props":4300,"children":4301},{},[4302,4304,4310],{"type":50,"value":4303},"Follow a disciplined ",{"type":44,"tag":103,"props":4305,"children":4307},{"href":4306},"\u002Fen\u002Fglossary\u002Fbetting\u002Fstaking-plan",[4308],{"type":50,"value":4309},"staking plan",{"type":50,"value":4311}," consistently",{"type":44,"tag":654,"props":4313,"children":4314},{},[4315,4317,4323,4325,4331],{"type":50,"value":4316},"Seek ",{"type":44,"tag":103,"props":4318,"children":4320},{"href":4319},"\u002Fen\u002Fglossary\u002Fbetting\u002Fclosing-line-value",[4321],{"type":50,"value":4322},"closing line value",{"type":50,"value":4324}," and implement ",{"type":44,"tag":103,"props":4326,"children":4328},{"href":4327},"\u002Fen\u002Fglossary\u002Fbetting\u002Fsharp-betting",[4329],{"type":50,"value":4330},"sharp betting",{"type":50,"value":4332}," principles",{"type":44,"tag":654,"props":4334,"children":4335},{},[4336,4338],{"type":50,"value":4337},"Accept that 20-30 bet losing streaks are ",{"type":44,"tag":462,"props":4339,"children":4340},{},[4341],{"type":50,"value":2694},{"type":44,"tag":635,"props":4343,"children":4344},{},[],{"type":44,"tag":45,"props":4346,"children":4348},{"id":4347},"key-takeaways",[4349],{"type":50,"value":4350},"Key Takeaways",{"type":44,"tag":650,"props":4352,"children":4353},{},[4354,4366,4377,4388,4398,4409],{"type":44,"tag":654,"props":4355,"children":4356},{},[4357,4359,4364],{"type":50,"value":4358},"✅ ",{"type":44,"tag":462,"props":4360,"children":4361},{},[4362],{"type":50,"value":4363},"Variance is inevitable",{"type":50,"value":4365}," - Even perfect betting experiences wild swings short-term",{"type":44,"tag":654,"props":4367,"children":4368},{},[4369,4370,4375],{"type":50,"value":4358},{"type":44,"tag":462,"props":4371,"children":4372},{},[4373],{"type":50,"value":4374},"Sample size matters",{"type":50,"value":4376}," - Need 500+ bets to distinguish skill from luck",{"type":44,"tag":654,"props":4378,"children":4379},{},[4380,4381,4386],{"type":50,"value":4358},{"type":44,"tag":462,"props":4382,"children":4383},{},[4384],{"type":50,"value":4385},"Bankroll requirements",{"type":50,"value":4387}," - Higher variance requires larger bankroll (100+ units)",{"type":44,"tag":654,"props":4389,"children":4390},{},[4391,4392,4396],{"type":50,"value":4358},{"type":44,"tag":462,"props":4393,"children":4394},{},[4395],{"type":50,"value":594},{"type":50,"value":4397}," - Understanding variance prevents tilt and emotional decisions",{"type":44,"tag":654,"props":4399,"children":4400},{},[4401,4402,4407],{"type":50,"value":4358},{"type":44,"tag":462,"props":4403,"children":4404},{},[4405],{"type":50,"value":4406},"Long-term thinking",{"type":50,"value":4408}," - Focus on process, not short-term results",{"type":44,"tag":654,"props":4410,"children":4411},{},[4412,4413,4418],{"type":50,"value":4358},{"type":44,"tag":462,"props":4414,"children":4415},{},[4416],{"type":50,"value":4417},"Use Kelly Criterion",{"type":50,"value":4419}," - Automatically accounts for variance in bet sizing",{"type":44,"tag":53,"props":4421,"children":4422},{},[4423,4428],{"type":44,"tag":462,"props":4424,"children":4425},{},[4426],{"type":50,"value":4427},"Remember:",{"type":50,"value":4429}," Variance doesn't care about your edge. A profitable bettor can lose for months. An unprofitable bettor can win for weeks. Only sample size reveals truth.",{"type":44,"tag":635,"props":4431,"children":4432},{},[],{"type":44,"tag":45,"props":4434,"children":4436},{"id":4435},"faq",[4437],{"type":50,"value":4438},"FAQ",{"type":44,"tag":683,"props":4440,"children":4442},{"id":4441},"how-many-bets-until-i-know-my-true-win-rate",[4443],{"type":50,"value":4444},"How many bets until I know my true win rate?",{"type":44,"tag":53,"props":4446,"children":4447},{},[4448,4453],{"type":44,"tag":462,"props":4449,"children":4450},{},[4451],{"type":50,"value":4452},"Minimum 500 bets, ideally 1000+.",{"type":50,"value":4454}," With 500 bets and 55% true win rate, you'll have 95% confidence interval of approximately 51%-59%. With only 50 bets, that interval becomes 40%-70% (essentially useless).",{"type":44,"tag":53,"props":4456,"children":4457},{},[4458,4459,4463],{"type":50,"value":3926},{"type":44,"tag":103,"props":4460,"children":4461},{"href":20},[4462],{"type":50,"value":3957},{"type":50,"value":4464}," to calculate confidence intervals for your specific betting history.",{"type":44,"tag":683,"props":4466,"children":4468},{"id":4467},"can-i-eliminate-variance",[4469],{"type":50,"value":4470},"Can I eliminate variance?",{"type":44,"tag":53,"props":4472,"children":4473},{},[4474,4479,4481,4486],{"type":44,"tag":462,"props":4475,"children":4476},{},[4477],{"type":50,"value":4478},"No.",{"type":50,"value":4480}," Variance is fundamental to probability. You can ",{"type":44,"tag":462,"props":4482,"children":4483},{},[4484],{"type":50,"value":4485},"reduce",{"type":50,"value":4487}," it by:",{"type":44,"tag":650,"props":4489,"children":4490},{},[4491,4496,4501,4506],{"type":44,"tag":654,"props":4492,"children":4493},{},[4494],{"type":50,"value":4495},"Betting lower odds (favorites)",{"type":44,"tag":654,"props":4497,"children":4498},{},[4499],{"type":50,"value":4500},"Using proper bankroll management",{"type":44,"tag":654,"props":4502,"children":4503},{},[4504],{"type":50,"value":4505},"Diversifying across multiple bets",{"type":44,"tag":654,"props":4507,"children":4508},{},[4509],{"type":50,"value":4510},"Following Kelly Criterion",{"type":44,"tag":53,"props":4512,"children":4513},{},[4514],{"type":50,"value":4515},"But you cannot eliminate it. Even professional bettors with 10-year track records experience multi-month losing streaks.",{"type":44,"tag":683,"props":4517,"children":4519},{"id":4518},"is-high-variance-bad",[4520],{"type":50,"value":4521},"Is high variance bad?",{"type":44,"tag":53,"props":4523,"children":4524},{},[4525,4530,4532,4537],{"type":44,"tag":462,"props":4526,"children":4527},{},[4528],{"type":50,"value":4529},"Not necessarily.",{"type":50,"value":4531}," High variance is fine ",{"type":44,"tag":462,"props":4533,"children":4534},{},[4535],{"type":50,"value":4536},"if",{"type":50,"value":4103},{"type":44,"tag":650,"props":4539,"children":4540},{},[4541,4546,4551,4556],{"type":44,"tag":654,"props":4542,"children":4543},{},[4544],{"type":50,"value":4545},"You have adequate bankroll (150+ units)",{"type":44,"tag":654,"props":4547,"children":4548},{},[4549],{"type":50,"value":4550},"You use proper position sizing (fractional Kelly)",{"type":44,"tag":654,"props":4552,"children":4553},{},[4554],{"type":50,"value":4555},"You have the mental fortitude to handle swings",{"type":44,"tag":654,"props":4557,"children":4558},{},[4559],{"type":50,"value":4560},"Your edge justifies the variance",{"type":44,"tag":53,"props":4562,"children":4563},{},[4564],{"type":50,"value":4565},"High variance strategies (like longshot betting or parlays) can be profitable, but they require significantly larger bankrolls and stronger mental game.",{"type":44,"tag":683,"props":4567,"children":4569},{"id":4568},"whats-the-difference-between-variance-and-volatility",[4570],{"type":50,"value":4571},"What's the difference between variance and volatility?",{"type":44,"tag":53,"props":4573,"children":4574},{},[4575],{"type":44,"tag":462,"props":4576,"children":4577},{},[4578],{"type":50,"value":4579},"They're the same concept, different contexts:",{"type":44,"tag":650,"props":4581,"children":4582},{},[4583,4593],{"type":44,"tag":654,"props":4584,"children":4585},{},[4586,4591],{"type":44,"tag":462,"props":4587,"children":4588},{},[4589],{"type":50,"value":4590},"Variance\u002FStandard Deviation:",{"type":50,"value":4592}," Technical statistical terms (mathematics)",{"type":44,"tag":654,"props":4594,"children":4595},{},[4596,4601],{"type":44,"tag":462,"props":4597,"children":4598},{},[4599],{"type":50,"value":4600},"Volatility:",{"type":50,"value":4602}," Casual term meaning \"swinginess\" (general usage)",{"type":44,"tag":53,"props":4604,"children":4605},{},[4606],{"type":50,"value":4607},"In betting contexts, they're used interchangeably. \"High variance\" = \"High volatility\" = \"Results swing wildly.\"",{"type":44,"tag":683,"props":4609,"children":4611},{"id":4610},"how-do-i-know-if-im-experiencing-variance-or-a-losing-strategy",[4612],{"type":50,"value":4613},"How do I know if I'm experiencing variance or a losing strategy?",{"type":44,"tag":53,"props":4615,"children":4616},{},[4617],{"type":44,"tag":462,"props":4618,"children":4619},{},[4620],{"type":50,"value":4621},"Use statistical analysis:",{"type":44,"tag":4175,"props":4623,"children":4624},{},[4625,4635,4652],{"type":44,"tag":654,"props":4626,"children":4627},{},[4628,4630,4634],{"type":50,"value":4629},"Calculate your confidence interval (use ",{"type":44,"tag":103,"props":4631,"children":4632},{"href":20},[4633],{"type":50,"value":3957},{"type":50,"value":841},{"type":44,"tag":654,"props":4636,"children":4637},{},[4638,4640,4645,4647],{"type":50,"value":4639},"If your observed win rate ",{"type":44,"tag":462,"props":4641,"children":4642},{},[4643],{"type":50,"value":4644},"includes",{"type":50,"value":4646}," your expected win rate within 95% confidence interval = ",{"type":44,"tag":462,"props":4648,"children":4649},{},[4650],{"type":50,"value":4651},"probably variance",{"type":44,"tag":654,"props":4653,"children":4654},{},[4655,4657,4662,4664],{"type":50,"value":4656},"If your observed win rate is ",{"type":44,"tag":462,"props":4658,"children":4659},{},[4660],{"type":50,"value":4661},"significantly below",{"type":50,"value":4663}," expected even after 500+ bets = ",{"type":44,"tag":462,"props":4665,"children":4666},{},[4667],{"type":50,"value":4668},"strategy problem",{"type":44,"tag":53,"props":4670,"children":4671},{},[4672,4676],{"type":44,"tag":462,"props":4673,"children":4674},{},[4675],{"type":50,"value":1645},{"type":50,"value":4677}," Expected 55% win rate, observed 51% after 500 bets",{"type":44,"tag":650,"props":4679,"children":4680},{},[4681,4686],{"type":44,"tag":654,"props":4682,"children":4683},{},[4684],{"type":50,"value":4685},"95% CI: 47%-55%",{"type":44,"tag":654,"props":4687,"children":4688},{},[4689],{"type":50,"value":4690},"Your 51% is within range → Keep going (likely variance)",{"type":44,"tag":53,"props":4692,"children":4693},{},[4694,4699],{"type":44,"tag":462,"props":4695,"children":4696},{},[4697],{"type":50,"value":4698},"Example 2:",{"type":50,"value":4700}," Expected 55% win rate, observed 47% after 1000 bets",{"type":44,"tag":650,"props":4702,"children":4703},{},[4704,4709],{"type":44,"tag":654,"props":4705,"children":4706},{},[4707],{"type":50,"value":4708},"95% CI: 50%-60%",{"type":44,"tag":654,"props":4710,"children":4711},{},[4712],{"type":50,"value":4713},"Your 47% is below range → Strategy issue",{"type":44,"tag":683,"props":4715,"children":4717},{"id":4716},"should-i-increase-bet-size-during-winning-streaks",[4718],{"type":50,"value":4719},"Should I increase bet size during winning streaks?",{"type":44,"tag":53,"props":4721,"children":4722},{},[4723,4728,4730,4735],{"type":44,"tag":462,"props":4724,"children":4725},{},[4726],{"type":50,"value":4727},"No!",{"type":50,"value":4729}," Winning streaks are often variance, not skill improvement. ",{"type":44,"tag":462,"props":4731,"children":4732},{},[4733],{"type":50,"value":4734},"Maintain consistent bet sizing",{"type":50,"value":4736}," based on:",{"type":44,"tag":650,"props":4738,"children":4739},{},[4740,4745,4750],{"type":44,"tag":654,"props":4741,"children":4742},{},[4743],{"type":50,"value":4744},"Your verified edge (500+ bet sample)",{"type":44,"tag":654,"props":4746,"children":4747},{},[4748],{"type":50,"value":4749},"Your current bankroll",{"type":44,"tag":654,"props":4751,"children":4752},{},[4753],{"type":50,"value":4754},"Kelly Criterion recommendations",{"type":44,"tag":53,"props":4756,"children":4757},{},[4758,4760,4765],{"type":50,"value":4759},"Increasing stakes during hot streaks (positive variance) often leads to giving back all profits when variance normalizes. This is called ",{"type":44,"tag":462,"props":4761,"children":4762},{},[4763],{"type":50,"value":4764},"gambler's ruin via variance misattribution",{"type":50,"value":2697},{"type":44,"tag":53,"props":4767,"children":4768},{},[4769,4770,4774],{"type":50,"value":3926},{"type":44,"tag":103,"props":4771,"children":4772},{"href":23},[4773],{"type":50,"value":4200},{"type":50,"value":4775}," to determine optimal bet size regardless of recent results.",{"type":44,"tag":635,"props":4777,"children":4778},{},[],{"type":44,"tag":53,"props":4780,"children":4781},{},[4782,4787],{"type":44,"tag":462,"props":4783,"children":4784},{},[4785],{"type":50,"value":4786},"Bottom Line:",{"type":50,"value":4788}," Variance is the bettor's constant companion. Master it through proper bankroll management, large sample sizes, and emotional discipline - or let it master you through tilt, ruin, and abandoned +EV strategies. The choice is yours."]