Betting Variance Calculator: See Your Bankroll Swings (2026)
A real edge does not stop you having brutal losing runs. Enter your win probability, price, stake, number of bets and bankroll, and this tool shows the whole spread: your chance of finishing in profit, the size of the swings, the risk of ruin and the worst drawdown to expect. Closed-form plus a Monte Carlo simulation, free and in your browser.
Everything runs in your browser. Nothing is uploaded and no account is needed. The simulation is seeded, so the same inputs always give the same result.
Variance analyzer
Your betting plan
This is the probability your total profit is above zero at the end of the run. Even a genuine edge can land below a coin flip over a small number of bets.
Distribution of final results
2000 simulated runsEach bar is how often the simulation finished in that profit range. The dashed line is break-even: bars to its left are losing runs, to its right are winning ones.
Betting variance: why a winning edge still comes with brutal swings
Having an edge tells you where you end up in the long run. It says nothing about the ride. As of 2026 this free ToolsGambling variance calculator shows that ride: how likely you are to be up after a run, how big the swings will be, how much of your bankroll a bad streak can eat, and how often it wipes you out entirely. It uses exact maths and a Monte Carlo simulation, in your browser.
Why use the ToolsGambling variance calculator
Most variance tools give you a single number and stop. This one runs two engines: the exact closed-form spread for instant confidence bands, and a seeded Monte Carlo simulation that plays out thousands of runs to reveal the true, path-dependent risk of ruin and the worst drawdown you should expect. And it is honest: it never dresses variance up as a hot or cold streak you can act on.
Two engines: exact maths and simulation
The formula gives your expected result and confidence bands the instant you type. The simulation plays out thousands of full runs to show the whole distribution, including the outcomes a formula alone cannot capture.
True risk of ruin, not a rough guess
Because the simulation walks bet by bet, it catches the runs where your bankroll hits zero partway through, even if the final result would have recovered. That path-dependent ruin is the number that actually matters.
The worst drawdown you must survive
It reports the deepest peak-to-trough fall across the runs, not just the average. Bankrolls and nerves are broken by the worst drawdown, so sizing your bankroll to survive it is the whole point.
Honest about what variance is
Every spin is independent and this tool treats it that way. No hot or cold gauges, no due bets, just the real spread of results your edge and stakes produce. Any odds format, no account, and a shareable link.
What is variance in betting?
Variance is the spread of your results around their expected value. Two bettors with the same edge can have wildly different seasons: one drifts smoothly upward, the other survives a stomach-churning drawdown before ending in the same place. Variance measures how wide that range of outcomes is.
It matters because you bet in the short run, where variance dominates, not the long run, where edge does. A positive edge is no protection against a losing month, and underestimating variance is how bettors with a real edge still go broke. Modelling it is how you set a bankroll that survives the swings.
The betting variance formula
The standard deviation of a single level-stake bet comes from its two outcomes, win or lose, around the expected value. Over many independent bets, the total standard deviation grows with the square root of the number of bets, not the number itself:
SD(total) = √N × SD(one bet)That square-root law is why swings feel smaller as a share of turnover over a long run, but the absolute swings still grow. Your expected profit grows with N while your standard deviation grows only with the square root of N, so a real edge does win out eventually, just far more slowly than most bettors expect.
I once had a 3% edge on a season of bets and still spent six weeks underwater, down almost forty units at the low. Nothing was wrong with the model; it was ordinary variance. Having simulated the range beforehand was the only reason I held my stake sizing instead of panicking and blowing the bankroll.
How to calculate your betting variance
Three inputs, and the tool models the whole range for you.
- 01
Estimate your edge honestly
Enter your true win probability and the price you get. If the probability is only a hopeful guess, the variance is real but the edge may not be.
- 02
Describe your stake plan
Add your stake per bet, how many bets you plan to place, and the bankroll you are risking. These set the scale of the swings.
- 03
Read the risk, then size to survive it
Look at the risk of ruin and the worst drawdown, not just the expected profit. If ruin is more than a few percent, your stake is too big for your bankroll.
How to read the results
Four numbers tell you whether your plan is survivable, not just profitable in theory.
| Metric | What it tells you |
|---|---|
| Chance of profit | Your odds of finishing up after the run. Even a real edge can be near a coin flip over a small sample. |
| Standard deviation | The typical size of your swings. Bigger means a rougher ride to the same expected profit. |
| Risk of ruin | The chance your bankroll hits zero before the run ends. Above a few percent is dangerous. |
| Worst drawdown | The deepest fall from a high to a low. Your bankroll and your nerves both have to survive it. |
Variance terms
- The spread of your results around their expected value; wider variance means bigger swings.
- The square root of variance, in the same units as your profit, a direct measure of swing size.
- The probability your bankroll is wiped out before the end of a run.
- A fall from a bankroll peak to a later low, the depth of a losing stretch.
- Simulating many random runs to estimate a distribution that is hard to solve by formula.
- Your average result per bet; the centre that variance spreads your outcomes around.
Variance
Standard deviation
Risk of ruin
Drawdown
Monte Carlo
Expected value (EV)
More free betting tools on ToolsGambling.com
Variance pairs with the tools that size your bankroll and stakes to survive it. These free calculators help.
Bet responsibly
Modelling variance is about respecting how badly a run can go, not beating it. Only stake what you can afford to lose and take a break if it stops being fun. Free, confidential help is at BeGambleAware.org.
Evgeniy Volkov
Verified ExpertFullstack developer with a background in mathematics. I build the calculators and game-style tools on ToolsGambling with Pixi.js and modern web tech, and every result uses transparent probability formulas you can verify yourself.
Variance calculator FAQ
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Zero in on the single number this tool surfaces: the chance a losing run wipes out your bankroll.
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