[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"blog-article-bankroll-risk-of-ruin-guide-en":3,"mdc-ke34rj-key":77},{"id":4,"slug":5,"status":6,"section":7,"category":8,"author":9,"publish_date":10,"read_time":11,"image":12,"embedded_components":13,"related_calculators":13,"related_articles":14,"title":15,"description":16,"keywords":17,"content":28,"faq":29,"availableLocales":72},"81ca21b5-9bfd-42d9-92b2-2900f5458761","bankroll-risk-of-ruin-guide","published","betting","strategies","Evgeniy Volkov","2026-04-25",13,"\u002Fimages\u002Fblog\u002Fbankroll-risk-of-ruin-guide.webp","[]",[],"How Risk of Ruin Works: A Bankroll Survival Guide (2026)","Risk of ruin explained: how bankroll size, edge, and variance combine to wipe out bettors. Worked examples plus survival math for 2026.",[18,19,20,21,22,23,24,25,26,27],"risk of ruin","bankroll risk of ruin","how risk of ruin works","ruin probability","bankroll survival","variance and ruin","kelly and risk of ruin","drawdown vs ruin","bankroll units","betting bankroll math","# How Risk of Ruin Works: A Bankroll Survival Guide (2026)\n\n**Picture this:** you've grinded a +1.5% edge on NFL underdogs across 600 bets. Your model is honest, your closing line value is real, your records are clean. And yet — six weeks into the season — your bankroll is at zero. Not because the edge disappeared. Because the bankroll was always too small for the variance you were taking.\n\nRisk of ruin is the math that explains why this keeps happening to bettors who \"do everything right.\" It is not a calculator interface or a number you punch into a tool — it is the underlying probability curve that decides whether you survive long enough to realize your edge. In 2026, with sharper books and thinner edges than ever, getting this math right is the difference between a long career and a short one.\n\nThis guide walks you through how ruin probability emerges from three numbers — bankroll size, edge per bet, variance — and why the formula is exponential rather than linear. We'll show why the popular \"1% rule\" usually works, where it breaks, and how variance amplifies ruin in markets like parlays and full-Kelly poker. By the end you'll be able to look at any betting strategy and tell, within a few percentage points, how likely it is to bust.\n\n## TL;DR — Bankroll Survival at a Glance\n\n### Key Numbers You Need to Know\n\n| Bankroll Units | Edge | Approx. Risk of Ruin | Survival Tier |\n|:--------------:|:----:|:--------------------:|:--------------|\n| 25  | +1% | ~60% | Unstable |\n| 50  | +1% | ~37% | High risk |\n| 100 | +1% | ~13.5% | Tolerable |\n| 100 | +2% | ~1.8% | Safe |\n| 200 | +1% | ~1.8% | Safe |\n| 500 | +1% | \u003C0.01% | Bulletproof |\n\n> 💡 Risk of ruin is one survival metric inside the larger **[bankroll management guide](\u002Fblog\u002Fbankroll-management-guide)** framework.\n\n\n**The pattern:** doubling units does not halve ruin — it squares the survival probability. Adding edge has the same compounding effect. That is why a 2%-edge bettor with 100 units is dramatically safer than a 1%-edge bettor with the same stack.\n\n## What Risk of Ruin Actually Means\n\nRisk of ruin is the **lifetime probability** that a sequence of losing bets will drive your bankroll to zero before you stop playing. It is not a forecast for the next session — it is the long-run number, assuming you keep betting at fixed unit size with the same edge and variance.\n\nThe phrase \"risk of ruin\" was popularized by professional blackjack players in the 1980s, but the underlying math comes from a 1965 paper by statisticians David R. Cox and H.D. Miller on stochastic processes — random walks with drift. The drift is your edge; the random walk is the bet-by-bet noise; ruin is the absorbing barrier at zero.\n\n### Drawdown vs Ruin: One Recovers, One Doesn't\n\nThis is the distinction most bettors miss. **Drawdown** is the maximum drop from a recent peak. It is temporary — variance pushes you down, then variance pushes you back up. A 40% drawdown across a season is normal for a flat-betting sports bettor with a 1.5% edge.\n\n**Ruin** is terminal. You hit zero, you cannot place another bet, the game ends. Ruin is not the worst case of drawdown — it is a different kind of event with its own probability calculation.\n\nYou can survive any drawdown that doesn't reach 100%. You cannot survive ruin. That asymmetry is why bankroll sizing focuses on ruin probability first, then accepts whatever drawdown comes. For deeper coverage of the full bankroll equation, our [universal bankroll calculator](\u002Fbetting\u002Fbankroll-calculator) bundles ruin and drawdown side by side.\n\n### Why Flat Betting Doesn't Save You\n\nA common myth: \"I bet flat units, so I can't go broke.\" The math says otherwise.\n\nFlat betting does prevent the suicide spiral of doubling-down systems like Martingale, where one bad streak compounds into total wipeout. But flat betting at a small unit size with a thin edge still has a real, calculable ruin probability. The formula doesn't care that you're betting flat — it cares about how many units of bankroll stand between you and zero.\n\nImagine flat betting 1 unit per bet at a true 50% win rate (zero edge). Your ruin probability over infinite time is exactly 100%. Flat betting at zero edge guarantees eventual ruin — it just delays it. Edge is what creates survival; flat betting only protects you from compounding mistakes on the way down.\n\n## The Math Behind Ruin Probability\n\nHere is the simplified formula for a binary win\u002Flose bet with equal stakes — the classic gambler's ruin equation:\n\n$$P(\\text{ruin}) = \\left( \\frac{1 - p_{\\text{edge}}}{1 + p_{\\text{edge}}} \\right)^{N}$$\n\nWhere `p_edge` is your edge per bet (e.g., 0.01 for 1%) and `N` is the number of bankroll units you can afford to lose before going broke.\n\n### The Core Formula in Plain English\n\nRead the formula like this: each unit of bankroll multiplies your survival odds by the same constant fraction. If `(1 - edge) \u002F (1 + edge)` is 0.98 (a 1% edge), then every additional unit of bankroll cuts ruin probability by 2%. That sounds linear, but it isn't — because each cut applies to the previous remaining ruin probability, not to the original 100%.\n\nA 100-unit bankroll at a 1% edge gives `0.98^100 = 0.1326` — roughly **13.5% ruin probability**. Add another 100 units and you get `0.98^200 = 0.0176` — about **1.76%**. Doubling the bankroll didn't halve ruin; it squared the survival fraction.\n\n### Why the Curve Is Exponential\n\nThe exponential shape is a direct consequence of independence. Each bet is its own coin flip with a tilt, and tilts compound multiplicatively, not additively. To go from 100 units to zero, you need a sequence of net losses worth 100 units — and the probability of that sequence is the product of all the individual probabilities, which is exponential in the count.\n\nThis is why ruin curves drop sharply at first, then flatten. The first 50 units of bankroll buy you most of the safety; the next 200 add comfort but rapidly diminishing returns. There is no point in stockpiling 1,000 units if 200 already gives you 1.8% ruin — the spare 800 units would be better deployed at higher stakes or held outside the bankroll.\n\n### Plain-English Translation You Can Use at the Table\n\n**Edge halves ruin faster than bankroll doubles it.** If you can find a way to push your edge from 1% to 2% (better closing line, less juice, sharper books), that single change cuts your ruin probability more than adding 100 units to your bankroll would. Hunting for edge dominates hunting for bankroll — once you have enough to play.\n\n::chart-ruin-probability-curve\n::\n\nThe curve above plots ruin probability vs bankroll size at four edge levels. Notice how the 0.5%-edge curve takes hundreds of units to reach safety, while the 5%-edge curve is essentially flat after 50 units. Edge is the leverage that makes everything else easier.\n\n## Variance, Streaks, and the Hidden Engine of Ruin\n\nThe simple formula treats every bet as binary — you win 1 unit or lose 1 unit. Real betting has **variance**, the spread of possible outcomes around the expected value. Variance is what makes ruin a real risk even at positive edge.\n\n### Why High-Variance Markets Need Bigger Bankrolls\n\nThe full ruin formula uses standard deviation explicitly:\n\n$$P(\\text{ruin}) = e^{-2 \\cdot WR \\cdot BR \u002F SD^2}$$\n\nWhere `WR` is win rate per bet, `BR` is bankroll in units, `SD` is standard deviation of bet outcome, and `e` is Euler's number (~2.718). The term that matters here: **SD is squared in the denominator**. Doubling the standard deviation roughly quadruples the bankroll needed to keep ruin constant.\n\nThis is why a parlay-heavy bettor goes broke faster than a singles bettor with the same edge. Same-game parlays at +800 have variance 4 to 6 times higher than -110 singles. To bet parlays at the same ruin tolerance, you need 4 to 6 times the bankroll. Most parlay bettors don't know this and use the same 50-unit stack they'd use for singles — which is why 50-unit parlay bankrolls regularly get wiped out inside a month.\n\nFor a clean low-variance comparison, video poker bankrolls follow a similar but lower-variance pattern — see our [video poker bankroll strategy guide](\u002Fblog\u002Fvideo-poker-bankroll-strategy) for the full breakdown of how SD changes the survival math in casino games versus sports.\n\n### Streak Math: Probability of N Losses in a Row\n\nVariance shows up as cold streaks. The probability of `n` consecutive losses at win rate `w` is simply `(1 - w)^n` — but that ignores the path. What actually matters is whether such a streak hits before the bankroll grows enough to absorb it.\n\n#### Single Streak Probabilities at -110\n\n| Streak Length | Probability (52.4% breakeven) | Probability (55% true win rate) |\n|:-------------:|:-----------------------------:|:-------------------------------:|\n| 5  in a row | 24.2% | 18.5% |\n| 7  in a row | 11.6% | 8.3% |\n| 10 in a row | 3.07% | 0.34% |\n| 15 in a row | 0.10% | 0.0008% |\n\nA 10-loss streak feels like a once-in-a-lifetime disaster. At a true 55% win rate, it has 0.34% probability per attempt — which sounds tiny, but across 1,000 bets you get hundreds of \"attempts\" at a 10-streak window. **You will see them.**\n\n#### Compounded Risk Across a Session\n\nThe probability that *some* 10-loss streak occurs in a 500-bet sample is roughly 1 - (1 - 0.0034)^491 ≈ 81%. Most bettors don't think in terms of \"across the season,\" and that's why a normal distribution of cold streaks feels like cosmic injustice.\n\nBankroll sizing has to assume these streaks will happen. The 5% ruin tolerance bakes in the expected worst streak across your expected bet count.\n\n## Three Worked Examples That Show the Pattern\n\nNumbers in isolation are abstract. Let's plug three realistic scenarios into the formula and see how small changes in unit size or edge swing ruin probability by an order of magnitude.\n\n### Scenario 1: The Conservative Path\n\n- **Bankroll:** \\$1,000\n- **Unit size:** 2% (\\$20 per bet)\n- **Edge:** +1%\n- **Bankroll units:** 50\n- **Approximate ruin probability over 1,000 bets:** ~3%\n\nA standard \"1-2% of bankroll\" approach with a thin but realistic edge. Ruin is low enough that any half-decent run lets variance work in your favor. This is the survival zone for most serious recreational bettors.\n\n### Scenario 2: The Compounding Trap\n\n- **Bankroll:** \\$1,000\n- **Unit size:** 5% (\\$50 per bet)\n- **Edge:** +1%\n- **Bankroll units:** 20\n- **Approximate ruin probability over 1,000 bets:** ~30%\n\nSame edge, same bankroll — but the unit size jumped from 2% to 5%. Ruin probability went from 3% to 30%, a 10x increase. This is the trap aggressive bettors fall into: they think 5% units \"don't seem that big\" because each bet is small. The math disagrees. **Unit size matters more than total bankroll.** Use the [betting bankroll calculator](\u002Fbetting\u002Fbankroll-calculator) to verify the unit size your edge can support.\n\n### Scenario 3: The Safe Zone\n\n- **Bankroll:** \\$5,000\n- **Unit size:** 1% (\\$50 per bet)\n- **Edge:** +2%\n- **Bankroll units:** 100\n- **Approximate ruin probability over 1,000 bets:** \u003C1%\n\nThe combination of more units, smaller percentage stakes, and a doubled edge produces a near-impervious bankroll. Even a brutal cold streak doesn't threaten ruin here. This is the configuration professional bettors aim for — and the one most amateurs never reach because they over-size their bets relative to their actual edge.\n\nFor the live computation of your own scenario, our [risk of ruin calculator](\u002Fbetting\u002Frisk-of-ruin-calculator) plugs your numbers into both the simple and SD-aware formulas side by side.\n\n::inline-ruin-probability-visualizer\n::\n\n## The Kelly Connection and Why It Solves Ruin\n\nThe Kelly Criterion isn't a separate concept from risk of ruin — it is the optimal answer to the ruin problem. Kelly tells you the unique bet size that maximizes long-run bankroll growth while keeping ruin probability mathematically zero across infinite play.\n\nThe formula is straightforward:\n\n$$f^* = \\frac{\\text{edge}}{\\text{odds}}$$\n\nFor a bet at decimal odds `b` with true win probability `p`, Kelly fraction is `f* = (bp - 1) \u002F (b - 1)`. At -110 with a 53% true win rate, that comes out to ~5.7% of bankroll — which is much higher than the 1-2% most bettors use.\n\n### How Kelly Minimizes Ruin While Maximizing Growth\n\nKelly works because under-betting wastes growth and over-betting amplifies ruin in proportion to the square of the over-bet. The peak of the growth curve is exactly the Kelly fraction; everything to the left grows slower; everything to the right grows slower *and* eventually goes negative. Full-Kelly is the unique point where growth is maximized.\n\n**The catch:** Kelly assumes you know your edge perfectly. In sports betting, you don't. If your true edge is 1.5% but you estimated 2%, you'll bet 33% more than Kelly recommends — and that puts you in the over-bet zone where growth slows and ruin rises.\n\n### Why Smart Bettors Use Half-Kelly or Quarter-Kelly\n\nThe standard professional adjustment is half-Kelly: bet 50% of what the formula recommends. This:\n\n- Costs about 25% of the long-run growth rate\n- Reduces drawdown variance by about 50%\n- Cuts realized ruin probability by orders of magnitude\n- Creates a buffer for edge-estimation error\n\nQuarter-Kelly is more conservative still — common among bettors who suspect their edge is overestimated. The trade-off is always the same: smaller fractions trade growth for survival. Survival usually wins. The deeper your edge-estimation uncertainty, the smaller the fraction you should bet — and the lower the resulting ruin probability.\n\n## Common Misconceptions That Wipe Out Bankrolls\n\nThe math of ruin is straightforward, but the intuition is counterintuitive. These three myths are the most common reasons bettors with real edges still go broke.\n\n### \"Flat Betting Means I'm Safe\"\n\nAlready covered, but worth repeating: flat betting reduces ruin compared to Martingale-style escalation, but flat betting **at the wrong unit size** with a thin edge still produces meaningful ruin probability. The unit size is the variable that matters most after edge — not whether you're flat or not.\n\n### \"I'll Just Stop When I'm Down\"\n\nThe \"stop-loss\" mental model assumes you can predict when a downswing is over. You can't. The reality is that bettors who plan to stop when they lose 30% usually push through that line during the dip (\"variance, just have to ride it out\"), and the ones who do stop often re-deposit the next week with a smaller, weaker bankroll — accelerating ruin.\n\nStop-losses work as **bankroll partitions**, not as in-session emotion controls. Set the stack you can afford to lose, treat the rest as off-limits, and let the math run. The pre-committed bankroll is the one the formula applies to; everything else is a future deposit decision, not part of the current ruin calculation.\n\n### \"Variance Always Evens Out\"\n\nIt does — over infinite trials. Over the 1,000 to 5,000 bets a recreational bettor places per year, variance does *not* reliably even out. The 95% confidence interval on a 1.5% edge across 1,000 bets is roughly -2% to +5%. You can play a full year of perfectly profitable bets and end up at -2% return. That's not bad luck; that's normal variance.\n\nThe bettors who survive understand this. The ones who don't conclude their edge \"stopped working,\" chase, and bust.\n\n## When Risk of Ruin Matters Most\n\nNot every betting context demands a 5% ruin target. The right ruin tolerance depends on whether the bankroll is replaceable, whether you're playing for income or recreation, and how thin your edge is.\n\n### Recreational vs Professional Stakes\n\nFor a recreational bettor playing with discretionary cash, a 15-20% ruin tolerance is reasonable — the bankroll is a hobby budget, not a livelihood. The cost of going broke is \"hobby ends,\" not \"rent unpaid.\"\n\nFor a professional or semi-pro relying on betting income, ruin must be near-zero. 1-2% ruin tolerance is standard, achieved through fractional Kelly, large unit counts (200+ units), and edge diversification across markets. Professionals who survive long-term treat ruin probability as a hard constraint, not a soft one.\n\n### When You Can Safely Ignore It\n\nThree contexts where ruin math matters less:\n\n1. **Single-event recreational betting.** If you're putting one Sunday wager on the Super Bowl with money you'd happily spend on a concert, ruin doesn't apply — there is no repeated game.\n2. **Negative-edge entertainment bankrolls.** If you know the edge is negative (slots, lotteries), ruin is a certainty across infinite play. Use a session budget instead — a number you're willing to lose and walk.\n3. **Very short horizons with large stacks.** If you can only play for 100 bets and your bankroll is 500 units, ruin is essentially zero regardless of strategy. Variance dominates.\n\nFor everyone in between — the bettors with a real edge who plan to keep playing — ruin is the metric that decides whether the edge ever pays off. Plug your edge, unit size, and bankroll into our [free bankroll tool](\u002Fbetting\u002Fbankroll-calculator) to stress-test the survival math before scaling up.\n\n## FAQ",[30,33,36,39,42,45,48,51,54,57,60,63,66,69],{"answer":31,"question":32},"Risk of ruin is the probability that a string of losses will wipe out your entire bankroll before your edge can grind out a profit. It is a single number — usually shown as a percentage — that depends on three inputs: the size of your bankroll, your edge per bet, and the variance of your outcomes. Lower is safer.","What is risk of ruin in betting?",{"answer":34,"question":35},"The standard closed-form formula is RoR = ((1 - edge) \u002F (1 + edge)) raised to the number of betting units in your bankroll. So a 1% edge with 100 units gives RoR of about 13.5%. Real games use a more general formula based on win rate and standard deviation, but the unit-based version is accurate enough for binary -110 betting.","How is risk of ruin calculated for a flat-staking bettor?",{"answer":37,"question":38},"Most professionals target 5% or lower for serious bankrolls. Recreational bettors who can reload tolerate 10 to 20%. Anything above 30% is unstable — even a slightly unlucky run breaks you before variance has time to work. The lower the number, the longer you survive across thousands of bets.","What is an acceptable risk of ruin percentage?",{"answer":40,"question":41},"The 1%-of-bankroll rule gives you 100 units. Plugging 100 units into the formula at a typical sports-betting edge of around 2% returns ruin probability of about 1.8%. At a thinner 1% edge it climbs near 13%. The 1% bet size is a reasonable target for typical edges; pure 5% RoR usually requires a bigger edge or fractional Kelly.","Why does the 1% rule produce roughly 5% risk of ruin?",{"answer":43,"question":44},"No. Drawdown is the deepest dip your bankroll takes before recovering — temporary and reversible. Ruin is terminal: you go to zero and cannot place another bet. A session can hit a 40% drawdown and still finish positive. The same session that hits 100% drawdown is bust. Always size for ruin, then expect the drawdown.","Is risk of ruin the same as drawdown?",{"answer":46,"question":47},"No. Flat betting only stops you from compounding losses by chasing — it does not eliminate ruin. If you keep betting the same flat unit, a long enough cold streak still pushes the stack to zero. Flat betting plus a positive edge plus enough units (usually 100 or more) is what controls ruin, not flat betting alone.","Does flat betting eliminate risk of ruin?",{"answer":49,"question":50},"Variance is the engine that drives ruin. Two bettors with identical edge and bankroll can have wildly different ruin probabilities if one plays a high-variance market like long parlays and the other plays low-variance singles. The standard deviation appears squared in the formula, so doubling variance roughly quadruples bankroll need at constant ruin.","How does variance affect ruin probability?",{"answer":52,"question":53},"Each additional unit of bankroll cuts ruin probability by a constant fraction, not a constant amount. Doubling units does not halve ruin — it squares the survival probability. That is why moving from 50 to 100 units shrinks ruin from about 37% to 13.5% at a 1% edge: the curve drops fast at first, then flattens past 200 units.","Why is the ruin formula exponential in bankroll size?",{"answer":55,"question":56},"Kelly is the bet size that maximizes long-run growth while keeping ruin probability technically zero in idealized math. In practice, full-Kelly produces large drawdowns that feel like ruin even if the formula says otherwise. Most pros use half-Kelly or quarter-Kelly to trade some growth for far gentler downswings and lower realized ruin risk.","How does Kelly Criterion relate to risk of ruin?",{"answer":58,"question":59},"Almost no one should. Full-Kelly assumes your edge estimate is exactly right, which is never true in betting. If you over-estimate your edge by 25%, full-Kelly behaves like 125% Kelly — which is over-betting and raises ruin sharply. Half-Kelly cuts growth by about 25% but lowers ruin and drawdown by far more. Stick to fractional Kelly.","Should I bet full-Kelly?",{"answer":61,"question":62},"At -110 odds you need to win about 52.4% to break even. If your true win rate is 55%, the chance of losing 10 bets in a row is 0.45 to the 10th = roughly 0.34%. That sounds small, but across 1,000 bets you will see runs of 10 losses several times — which is why bankroll math has to assume long streaks happen.","What is the probability of 10 losses in a row at -110 odds?",{"answer":64,"question":65},"Yes. Edge alone does not save you if your bankroll is too small relative to variance. A bettor with a 2% edge but only 25 units has roughly 36% risk of ruin — worse than coin flip survival. The combination of edge, units, and variance determines ruin. Edge without units is just slow bleeding with extra steps.","Can a positive-edge bettor still go bankrupt?",{"answer":67,"question":68},"The closed-form formula assumes infinite play. For a finite session, ruin probability is lower because you stop before a long downswing has time to develop. A 95% session-survival target uses different math than infinite-horizon ruin, and short sessions need smaller bankrolls. For overall lifetime bankroll, use the infinite-horizon formula.","How does session length affect risk of ruin?",{"answer":70,"question":71},"Standard deviation enters the bankroll formula squared. Same-game parlays at +800 have roughly 4 to 6 times the per-bet variance of straight singles at -110. To keep ruin probability constant when variance quadruples, your bankroll needs to roughly quadruple too. That is why parlay bettors who use single-bet bankrolls go broke fast.","Why do high-variance markets need bigger bankrolls?",[73,74,75,76],"en","ru","de","tr",{"data":78,"body":79},{},{"type":80,"children":81},"root",[82,90,102,107,112,118,125,295,316,326,332,344,349,355,367,377,390,396,401,406,411,417,422,964,985,991,1004,1039,1045,1050,1055,1061,1071,1075,1080,1086,1098,1104,1109,1421,1463,1468,1481,1487,1516,1523,1622,1632,1638,1651,1656,1662,1667,1673,1728,1733,1739,1785,1804,1810,1858,1863,1876,1880,1886,1891,1896,2134,2162,2168,2180,2190,2196,2201,2224,2229,2235,2240,2246,2258,2264,2269,2281,2287,2299,2304,2310,2315,2321,2326,2331,2337,2342,2376,2388],{"type":83,"tag":84,"props":85,"children":87},"element","h2",{"id":86},"how-risk-of-ruin-works-a-bankroll-survival-guide-2026",[88],{"type":89,"value":15},"text",{"type":83,"tag":91,"props":92,"children":93},"p",{},[94,100],{"type":83,"tag":95,"props":96,"children":97},"strong",{},[98],{"type":89,"value":99},"Picture this:",{"type":89,"value":101}," you've grinded a +1.5% edge on NFL underdogs across 600 bets. Your model is honest, your closing line value is real, your records are clean. And yet — six weeks into the season — your bankroll is at zero. Not because the edge disappeared. Because the bankroll was always too small for the variance you were taking.",{"type":83,"tag":91,"props":103,"children":104},{},[105],{"type":89,"value":106},"Risk of ruin is the math that explains why this keeps happening to bettors who \"do everything right.\" It is not a calculator interface or a number you punch into a tool — it is the underlying probability curve that decides whether you survive long enough to realize your edge. In 2026, with sharper books and thinner edges than ever, getting this math right is the difference between a long career and a short one.",{"type":83,"tag":91,"props":108,"children":109},{},[110],{"type":89,"value":111},"This guide walks you through how ruin probability emerges from three numbers — bankroll size, edge per bet, variance — and why the formula is exponential rather than linear. We'll show why the popular \"1% rule\" usually works, where it breaks, and how variance amplifies ruin in markets like parlays and full-Kelly poker. By the end you'll be able to look at any betting strategy and tell, within a few percentage points, how likely it is to bust.",{"type":83,"tag":84,"props":113,"children":115},{"id":114},"tldr-bankroll-survival-at-a-glance",[116],{"type":89,"value":117},"TL;DR — Bankroll Survival at a Glance",{"type":83,"tag":119,"props":120,"children":122},"h3",{"id":121},"key-numbers-you-need-to-know",[123],{"type":89,"value":124},"Key Numbers You Need to Know",{"type":83,"tag":126,"props":127,"children":128},"table",{},[129,159],{"type":83,"tag":130,"props":131,"children":132},"thead",{},[133],{"type":83,"tag":76,"props":134,"children":135},{},[136,143,148,153],{"type":83,"tag":137,"props":138,"children":140},"th",{"align":139},"center",[141],{"type":89,"value":142},"Bankroll Units",{"type":83,"tag":137,"props":144,"children":145},{"align":139},[146],{"type":89,"value":147},"Edge",{"type":83,"tag":137,"props":149,"children":150},{"align":139},[151],{"type":89,"value":152},"Approx. 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Add another 100 units and you get ",{"type":83,"tag":970,"props":1025,"children":1027},{"className":1026},[],[1028],{"type":89,"value":1029},"0.98^200 = 0.0176",{"type":89,"value":1031}," — about ",{"type":83,"tag":95,"props":1033,"children":1034},{},[1035],{"type":89,"value":1036},"1.76%",{"type":89,"value":1038},". Doubling the bankroll didn't halve ruin; it squared the survival fraction.",{"type":83,"tag":119,"props":1040,"children":1042},{"id":1041},"why-the-curve-is-exponential",[1043],{"type":89,"value":1044},"Why the Curve Is Exponential",{"type":83,"tag":91,"props":1046,"children":1047},{},[1048],{"type":89,"value":1049},"The exponential shape is a direct consequence of independence. Each bet is its own coin flip with a tilt, and tilts compound multiplicatively, not additively. To go from 100 units to zero, you need a sequence of net losses worth 100 units — and the probability of that sequence is the product of all the individual probabilities, which is exponential in the count.",{"type":83,"tag":91,"props":1051,"children":1052},{},[1053],{"type":89,"value":1054},"This is why ruin curves drop sharply at first, then flatten. The first 50 units of bankroll buy you most of the safety; the next 200 add comfort but rapidly diminishing returns. There is no point in stockpiling 1,000 units if 200 already gives you 1.8% ruin — the spare 800 units would be better deployed at higher stakes or held outside the bankroll.",{"type":83,"tag":119,"props":1056,"children":1058},{"id":1057},"plain-english-translation-you-can-use-at-the-table",[1059],{"type":89,"value":1060},"Plain-English Translation You Can Use at the Table",{"type":83,"tag":91,"props":1062,"children":1063},{},[1064,1069],{"type":83,"tag":95,"props":1065,"children":1066},{},[1067],{"type":89,"value":1068},"Edge halves ruin faster than bankroll doubles it.",{"type":89,"value":1070}," If you can find a way to push your edge from 1% to 2% (better closing line, less juice, sharper books), that single change cuts your ruin probability more than adding 100 units to your bankroll would. 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The term that matters here: ",{"type":83,"tag":95,"props":1457,"children":1458},{},[1459],{"type":89,"value":1460},"SD is squared in the denominator",{"type":89,"value":1462},". Doubling the standard deviation roughly quadruples the bankroll needed to keep ruin constant.",{"type":83,"tag":91,"props":1464,"children":1465},{},[1466],{"type":89,"value":1467},"This is why a parlay-heavy bettor goes broke faster than a singles bettor with the same edge. Same-game parlays at +800 have variance 4 to 6 times higher than -110 singles. To bet parlays at the same ruin tolerance, you need 4 to 6 times the bankroll. Most parlay bettors don't know this and use the same 50-unit stack they'd use for singles — which is why 50-unit parlay bankrolls regularly get wiped out inside a month.",{"type":83,"tag":91,"props":1469,"children":1470},{},[1471,1473,1479],{"type":89,"value":1472},"For a clean low-variance comparison, video poker bankrolls follow a similar but lower-variance pattern — see our ",{"type":83,"tag":308,"props":1474,"children":1476},{"href":1475},"\u002Fblog\u002Fvideo-poker-bankroll-strategy",[1477],{"type":89,"value":1478},"video poker bankroll strategy guide",{"type":89,"value":1480}," for the full breakdown of how SD changes the survival math in casino games versus sports.",{"type":83,"tag":119,"props":1482,"children":1484},{"id":1483},"streak-math-probability-of-n-losses-in-a-row",[1485],{"type":89,"value":1486},"Streak Math: Probability of N Losses in a Row",{"type":83,"tag":91,"props":1488,"children":1489},{},[1490,1492,1498,1500,1506,1508,1514],{"type":89,"value":1491},"Variance shows up as cold streaks. The probability of ",{"type":83,"tag":970,"props":1493,"children":1495},{"className":1494},[],[1496],{"type":89,"value":1497},"n",{"type":89,"value":1499}," consecutive losses at win rate ",{"type":83,"tag":970,"props":1501,"children":1503},{"className":1502},[],[1504],{"type":89,"value":1505},"w",{"type":89,"value":1507}," is simply ",{"type":83,"tag":970,"props":1509,"children":1511},{"className":1510},[],[1512],{"type":89,"value":1513},"(1 - w)^n",{"type":89,"value":1515}," — but that ignores the path. 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Most bettors don't think in terms of \"across the season,\" and that's why a normal distribution of cold streaks feels like cosmic injustice.",{"type":83,"tag":91,"props":1652,"children":1653},{},[1654],{"type":89,"value":1655},"Bankroll sizing has to assume these streaks will happen. The 5% ruin tolerance bakes in the expected worst streak across your expected bet count.",{"type":83,"tag":84,"props":1657,"children":1659},{"id":1658},"three-worked-examples-that-show-the-pattern",[1660],{"type":89,"value":1661},"Three Worked Examples That Show the Pattern",{"type":83,"tag":91,"props":1663,"children":1664},{},[1665],{"type":89,"value":1666},"Numbers in isolation are abstract. Let's plug three realistic scenarios into the formula and see how small changes in unit size or edge swing ruin probability by an order of magnitude.",{"type":83,"tag":119,"props":1668,"children":1670},{"id":1669},"scenario-1-the-conservative-path",[1671],{"type":89,"value":1672},"Scenario 1: The Conservative Path",{"type":83,"tag":1674,"props":1675,"children":1676},"ul",{},[1677,1688,1698,1708,1718],{"type":83,"tag":1678,"props":1679,"children":1680},"li",{},[1681,1686],{"type":83,"tag":95,"props":1682,"children":1683},{},[1684],{"type":89,"value":1685},"Bankroll:",{"type":89,"value":1687}," $1,000",{"type":83,"tag":1678,"props":1689,"children":1690},{},[1691,1696],{"type":83,"tag":95,"props":1692,"children":1693},{},[1694],{"type":89,"value":1695},"Unit size:",{"type":89,"value":1697}," 2% ($20 per bet)",{"type":83,"tag":1678,"props":1699,"children":1700},{},[1701,1706],{"type":83,"tag":95,"props":1702,"children":1703},{},[1704],{"type":89,"value":1705},"Edge:",{"type":89,"value":1707}," +1%",{"type":83,"tag":1678,"props":1709,"children":1710},{},[1711,1716],{"type":83,"tag":95,"props":1712,"children":1713},{},[1714],{"type":89,"value":1715},"Bankroll units:",{"type":89,"value":1717}," 50",{"type":83,"tag":1678,"props":1719,"children":1720},{},[1721,1726],{"type":83,"tag":95,"props":1722,"children":1723},{},[1724],{"type":89,"value":1725},"Approximate ruin probability over 1,000 bets:",{"type":89,"value":1727}," ~3%",{"type":83,"tag":91,"props":1729,"children":1730},{},[1731],{"type":89,"value":1732},"A standard \"1-2% of bankroll\" approach with a thin but realistic edge. Ruin is low enough that any half-decent run lets variance work in your favor. This is the survival zone for most serious recreational bettors.",{"type":83,"tag":119,"props":1734,"children":1736},{"id":1735},"scenario-2-the-compounding-trap",[1737],{"type":89,"value":1738},"Scenario 2: The Compounding Trap",{"type":83,"tag":1674,"props":1740,"children":1741},{},[1742,1750,1759,1767,1776],{"type":83,"tag":1678,"props":1743,"children":1744},{},[1745,1749],{"type":83,"tag":95,"props":1746,"children":1747},{},[1748],{"type":89,"value":1685},{"type":89,"value":1687},{"type":83,"tag":1678,"props":1751,"children":1752},{},[1753,1757],{"type":83,"tag":95,"props":1754,"children":1755},{},[1756],{"type":89,"value":1695},{"type":89,"value":1758}," 5% ($50 per bet)",{"type":83,"tag":1678,"props":1760,"children":1761},{},[1762,1766],{"type":83,"tag":95,"props":1763,"children":1764},{},[1765],{"type":89,"value":1705},{"type":89,"value":1707},{"type":83,"tag":1678,"props":1768,"children":1769},{},[1770,1774],{"type":83,"tag":95,"props":1771,"children":1772},{},[1773],{"type":89,"value":1715},{"type":89,"value":1775}," 20",{"type":83,"tag":1678,"props":1777,"children":1778},{},[1779,1783],{"type":83,"tag":95,"props":1780,"children":1781},{},[1782],{"type":89,"value":1725},{"type":89,"value":1784}," ~30%",{"type":83,"tag":91,"props":1786,"children":1787},{},[1788,1790,1795,1797,1802],{"type":89,"value":1789},"Same edge, same bankroll — but the unit size jumped from 2% to 5%. Ruin probability went from 3% to 30%, a 10x increase. This is the trap aggressive bettors fall into: they think 5% units \"don't seem that big\" because each bet is small. The math disagrees. ",{"type":83,"tag":95,"props":1791,"children":1792},{},[1793],{"type":89,"value":1794},"Unit size matters more than total bankroll.",{"type":89,"value":1796}," Use the ",{"type":83,"tag":308,"props":1798,"children":1799},{"href":384},[1800],{"type":89,"value":1801},"betting bankroll calculator",{"type":89,"value":1803}," to verify the unit size your edge can support.",{"type":83,"tag":119,"props":1805,"children":1807},{"id":1806},"scenario-3-the-safe-zone",[1808],{"type":89,"value":1809},"Scenario 3: The Safe Zone",{"type":83,"tag":1674,"props":1811,"children":1812},{},[1813,1822,1831,1840,1849],{"type":83,"tag":1678,"props":1814,"children":1815},{},[1816,1820],{"type":83,"tag":95,"props":1817,"children":1818},{},[1819],{"type":89,"value":1685},{"type":89,"value":1821}," $5,000",{"type":83,"tag":1678,"props":1823,"children":1824},{},[1825,1829],{"type":83,"tag":95,"props":1826,"children":1827},{},[1828],{"type":89,"value":1695},{"type":89,"value":1830}," 1% ($50 per bet)",{"type":83,"tag":1678,"props":1832,"children":1833},{},[1834,1838],{"type":83,"tag":95,"props":1835,"children":1836},{},[1837],{"type":89,"value":1705},{"type":89,"value":1839}," +2%",{"type":83,"tag":1678,"props":1841,"children":1842},{},[1843,1847],{"type":83,"tag":95,"props":1844,"children":1845},{},[1846],{"type":89,"value":1715},{"type":89,"value":1848}," 100",{"type":83,"tag":1678,"props":1850,"children":1851},{},[1852,1856],{"type":83,"tag":95,"props":1853,"children":1854},{},[1855],{"type":89,"value":1725},{"type":89,"value":1857}," \u003C1%",{"type":83,"tag":91,"props":1859,"children":1860},{},[1861],{"type":89,"value":1862},"The combination of more units, smaller percentage stakes, and a doubled edge produces a near-impervious bankroll. Even a brutal cold streak doesn't threaten ruin here. This is the configuration professional bettors aim for — and the one most amateurs never reach because they over-size their bets relative to their actual edge.",{"type":83,"tag":91,"props":1864,"children":1865},{},[1866,1868,1874],{"type":89,"value":1867},"For the live computation of your own scenario, our ",{"type":83,"tag":308,"props":1869,"children":1871},{"href":1870},"\u002Fbetting\u002Frisk-of-ruin-calculator",[1872],{"type":89,"value":1873},"risk of ruin calculator",{"type":89,"value":1875}," plugs your numbers into both the simple and SD-aware formulas side by side.",{"type":83,"tag":1877,"props":1878,"children":1879},"inline-ruin-probability-visualizer",{},[],{"type":83,"tag":84,"props":1881,"children":1883},{"id":1882},"the-kelly-connection-and-why-it-solves-ruin",[1884],{"type":89,"value":1885},"The Kelly Connection and Why It Solves Ruin",{"type":83,"tag":91,"props":1887,"children":1888},{},[1889],{"type":89,"value":1890},"The Kelly Criterion isn't a separate concept from risk of ruin — it is the optimal answer to the ruin problem. Kelly tells you the unique bet size that maximizes long-run bankroll growth while keeping ruin probability mathematically zero across infinite play.",{"type":83,"tag":91,"props":1892,"children":1893},{},[1894],{"type":89,"value":1895},"The formula is straightforward:",{"type":83,"tag":91,"props":1897,"children":1898},{},[1899],{"type":83,"tag":426,"props":1900,"children":1902},{"className":1901},[429],[1903,1950],{"type":83,"tag":426,"props":1904,"children":1906},{"className":1905},[434],[1907],{"type":83,"tag":437,"props":1908,"children":1909},{"xmlns":439},[1910],{"type":83,"tag":442,"props":1911,"children":1912},{},[1913,1945],{"type":83,"tag":446,"props":1914,"children":1915},{},[1916,1929,1933],{"type":83,"tag":479,"props":1917,"children":1918},{},[1919,1924],{"type":83,"tag":450,"props":1920,"children":1921},{},[1922],{"type":89,"value":1923},"f",{"type":83,"tag":456,"props":1925,"children":1926},{},[1927],{"type":89,"value":1928},"∗",{"type":83,"tag":456,"props":1930,"children":1931},{},[1932],{"type":89,"value":477},{"type":83,"tag":491,"props":1934,"children":1935},{},[1936,1940],{"type":83,"tag":463,"props":1937,"children":1938},{},[1939],{"type":89,"value":520},{"type":83,"tag":463,"props":1941,"children":1942},{},[1943],{"type":89,"value":1944},"odds",{"type":83,"tag":554,"props":1946,"children":1947},{"encoding":556},[1948],{"type":89,"value":1949},"f^* 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a bet at decimal odds ",{"type":83,"tag":970,"props":2140,"children":2142},{"className":2141},[],[2143],{"type":89,"value":2144},"b",{"type":89,"value":2146}," with true win probability ",{"type":83,"tag":970,"props":2148,"children":2150},{"className":2149},[],[2151],{"type":89,"value":91},{"type":89,"value":2153},", Kelly fraction is ",{"type":83,"tag":970,"props":2155,"children":2157},{"className":2156},[],[2158],{"type":89,"value":2159},"f* = (bp - 1) \u002F (b - 1)",{"type":89,"value":2161},". At -110 with a 53% true win rate, that comes out to ~5.7% of bankroll — which is much higher than the 1-2% most bettors use.",{"type":83,"tag":119,"props":2163,"children":2165},{"id":2164},"how-kelly-minimizes-ruin-while-maximizing-growth",[2166],{"type":89,"value":2167},"How Kelly Minimizes Ruin While Maximizing Growth",{"type":83,"tag":91,"props":2169,"children":2170},{},[2171,2173,2178],{"type":89,"value":2172},"Kelly works because under-betting wastes growth and over-betting amplifies ruin in proportion to the square of the over-bet. The peak of the growth curve is exactly the Kelly fraction; everything to the left grows slower; everything to the right grows slower ",{"type":83,"tag":1644,"props":2174,"children":2175},{},[2176],{"type":89,"value":2177},"and",{"type":89,"value":2179}," eventually goes negative. Full-Kelly is the unique point where growth is maximized.",{"type":83,"tag":91,"props":2181,"children":2182},{},[2183,2188],{"type":83,"tag":95,"props":2184,"children":2185},{},[2186],{"type":89,"value":2187},"The catch:",{"type":89,"value":2189}," Kelly assumes you know your edge perfectly. In sports betting, you don't. If your true edge is 1.5% but you estimated 2%, you'll bet 33% more than Kelly recommends — and that puts you in the over-bet zone where growth slows and ruin rises.",{"type":83,"tag":119,"props":2191,"children":2193},{"id":2192},"why-smart-bettors-use-half-kelly-or-quarter-kelly",[2194],{"type":89,"value":2195},"Why Smart Bettors Use Half-Kelly or Quarter-Kelly",{"type":83,"tag":91,"props":2197,"children":2198},{},[2199],{"type":89,"value":2200},"The standard professional adjustment is half-Kelly: bet 50% of what the formula recommends. This:",{"type":83,"tag":1674,"props":2202,"children":2203},{},[2204,2209,2214,2219],{"type":83,"tag":1678,"props":2205,"children":2206},{},[2207],{"type":89,"value":2208},"Costs about 25% of the long-run growth rate",{"type":83,"tag":1678,"props":2210,"children":2211},{},[2212],{"type":89,"value":2213},"Reduces drawdown variance by about 50%",{"type":83,"tag":1678,"props":2215,"children":2216},{},[2217],{"type":89,"value":2218},"Cuts realized ruin probability by orders of magnitude",{"type":83,"tag":1678,"props":2220,"children":2221},{},[2222],{"type":89,"value":2223},"Creates a buffer for edge-estimation error",{"type":83,"tag":91,"props":2225,"children":2226},{},[2227],{"type":89,"value":2228},"Quarter-Kelly is more conservative still — common among bettors who suspect their edge is overestimated. The trade-off is always the same: smaller fractions trade growth for survival. Survival usually wins. The deeper your edge-estimation uncertainty, the smaller the fraction you should bet — and the lower the resulting ruin probability.",{"type":83,"tag":84,"props":2230,"children":2232},{"id":2231},"common-misconceptions-that-wipe-out-bankrolls",[2233],{"type":89,"value":2234},"Common Misconceptions That Wipe Out Bankrolls",{"type":83,"tag":91,"props":2236,"children":2237},{},[2238],{"type":89,"value":2239},"The math of ruin is straightforward, but the intuition is counterintuitive. These three myths are the most common reasons bettors with real edges still go broke.",{"type":83,"tag":119,"props":2241,"children":2243},{"id":2242},"flat-betting-means-im-safe",[2244],{"type":89,"value":2245},"\"Flat Betting Means I'm Safe\"",{"type":83,"tag":91,"props":2247,"children":2248},{},[2249,2251,2256],{"type":89,"value":2250},"Already covered, but worth repeating: flat betting reduces ruin compared to Martingale-style escalation, but flat betting ",{"type":83,"tag":95,"props":2252,"children":2253},{},[2254],{"type":89,"value":2255},"at the wrong unit size",{"type":89,"value":2257}," with a thin edge still produces meaningful ruin probability. The unit size is the variable that matters most after edge — not whether you're flat or not.",{"type":83,"tag":119,"props":2259,"children":2261},{"id":2260},"ill-just-stop-when-im-down",[2262],{"type":89,"value":2263},"\"I'll Just Stop When I'm Down\"",{"type":83,"tag":91,"props":2265,"children":2266},{},[2267],{"type":89,"value":2268},"The \"stop-loss\" mental model assumes you can predict when a downswing is over. You can't. The reality is that bettors who plan to stop when they lose 30% usually push through that line during the dip (\"variance, just have to ride it out\"), and the ones who do stop often re-deposit the next week with a smaller, weaker bankroll — accelerating ruin.",{"type":83,"tag":91,"props":2270,"children":2271},{},[2272,2274,2279],{"type":89,"value":2273},"Stop-losses work as ",{"type":83,"tag":95,"props":2275,"children":2276},{},[2277],{"type":89,"value":2278},"bankroll partitions",{"type":89,"value":2280},", not as in-session emotion controls. Set the stack you can afford to lose, treat the rest as off-limits, and let the math run. The pre-committed bankroll is the one the formula applies to; everything else is a future deposit decision, not part of the current ruin calculation.",{"type":83,"tag":119,"props":2282,"children":2284},{"id":2283},"variance-always-evens-out",[2285],{"type":89,"value":2286},"\"Variance Always Evens Out\"",{"type":83,"tag":91,"props":2288,"children":2289},{},[2290,2292,2297],{"type":89,"value":2291},"It does — over infinite trials. Over the 1,000 to 5,000 bets a recreational bettor places per year, variance does ",{"type":83,"tag":1644,"props":2293,"children":2294},{},[2295],{"type":89,"value":2296},"not",{"type":89,"value":2298}," reliably even out. The 95% confidence interval on a 1.5% edge across 1,000 bets is roughly -2% to +5%. You can play a full year of perfectly profitable bets and end up at -2% return. That's not bad luck; that's normal variance.",{"type":83,"tag":91,"props":2300,"children":2301},{},[2302],{"type":89,"value":2303},"The bettors who survive understand this. The ones who don't conclude their edge \"stopped working,\" chase, and bust.",{"type":83,"tag":84,"props":2305,"children":2307},{"id":2306},"when-risk-of-ruin-matters-most",[2308],{"type":89,"value":2309},"When Risk of Ruin Matters Most",{"type":83,"tag":91,"props":2311,"children":2312},{},[2313],{"type":89,"value":2314},"Not every betting context demands a 5% ruin target. The right ruin tolerance depends on whether the bankroll is replaceable, whether you're playing for income or recreation, and how thin your edge is.",{"type":83,"tag":119,"props":2316,"children":2318},{"id":2317},"recreational-vs-professional-stakes",[2319],{"type":89,"value":2320},"Recreational vs Professional Stakes",{"type":83,"tag":91,"props":2322,"children":2323},{},[2324],{"type":89,"value":2325},"For a recreational bettor playing with discretionary cash, a 15-20% ruin tolerance is reasonable — the bankroll is a hobby budget, not a livelihood. The cost of going broke is \"hobby ends,\" not \"rent unpaid.\"",{"type":83,"tag":91,"props":2327,"children":2328},{},[2329],{"type":89,"value":2330},"For a professional or semi-pro relying on betting income, ruin must be near-zero. 1-2% ruin tolerance is standard, achieved through fractional Kelly, large unit counts (200+ units), and edge diversification across markets. Professionals who survive long-term treat ruin probability as a hard constraint, not a soft one.",{"type":83,"tag":119,"props":2332,"children":2334},{"id":2333},"when-you-can-safely-ignore-it",[2335],{"type":89,"value":2336},"When You Can Safely Ignore It",{"type":83,"tag":91,"props":2338,"children":2339},{},[2340],{"type":89,"value":2341},"Three contexts where ruin math matters less:",{"type":83,"tag":2343,"props":2344,"children":2345},"ol",{},[2346,2356,2366],{"type":83,"tag":1678,"props":2347,"children":2348},{},[2349,2354],{"type":83,"tag":95,"props":2350,"children":2351},{},[2352],{"type":89,"value":2353},"Single-event recreational betting.",{"type":89,"value":2355}," If you're putting one Sunday wager on the Super Bowl with money you'd happily spend on a concert, ruin doesn't apply — there is no repeated game.",{"type":83,"tag":1678,"props":2357,"children":2358},{},[2359,2364],{"type":83,"tag":95,"props":2360,"children":2361},{},[2362],{"type":89,"value":2363},"Negative-edge entertainment bankrolls.",{"type":89,"value":2365}," If you know the edge is negative (slots, lotteries), ruin is a certainty across infinite play. Use a session budget instead — a number you're willing to lose and walk.",{"type":83,"tag":1678,"props":2367,"children":2368},{},[2369,2374],{"type":83,"tag":95,"props":2370,"children":2371},{},[2372],{"type":89,"value":2373},"Very short horizons with large stacks.",{"type":89,"value":2375}," If you can only play for 100 bets and your bankroll is 500 units, ruin is essentially zero regardless of strategy. Variance dominates.",{"type":83,"tag":91,"props":2377,"children":2378},{},[2379,2381,2386],{"type":89,"value":2380},"For everyone in between — the bettors with a real edge who plan to keep playing — ruin is the metric that decides whether the edge ever pays off. Plug your edge, unit size, and bankroll into our ",{"type":83,"tag":308,"props":2382,"children":2383},{"href":384},[2384],{"type":89,"value":2385},"free bankroll tool",{"type":89,"value":2387}," to stress-test the survival math before scaling up.",{"type":83,"tag":84,"props":2389,"children":2391},{"id":2390},"faq",[2392],{"type":89,"value":2393},"FAQ"]