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Variance & Bankroll Calculator
Enter your win rate, odds, and how many bets you're planning. This shows the realistic range of outcomes, including how often a genuinely winning strategy still looks like a loser over a small sample.
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How this is calculated
Each bet is treated as a two-outcome event: win with probabilityp (profit = stake × (odds − 1)), or lose with probability 1 − p (profit = −stake). From that, the expected profit and variance of a single bet follow directly from the standard formulas for a discrete random variable. Betting n independent bets multiplies the mean by n and the variance by n (not the standard deviation, which only scales by√n, which is the entire reason variance shrinks proportionally as a sample grows).
The "chance of being in the red" uses the normal approximation to this distribution (reasonably accurate once you're past ~30 bets; treat it as a rough guide, not an exact figure, for very smalln).
Why this matters: plug in a real, modest edge (say 55% at 1.91 odds, close to what a genuinely good process might sustain) and run it at n=50. The red-zone probability is uncomfortably high even though the strategy is profitable in expectation. This is the same variance that makes any single week or month a weak signal on its own. See is value betting profitableand why we default to flat stakingrather than sizing up on perceived edge.
Worked example: 55 % at 1.91, 50 bets of 1 unit
- Expected profit per bet: 0.55 × 0.91 − 0.45 = +0.0505 units, so +2.52 units over 50 bets.
- Standard deviation over 50 bets: about 6.72 units, almost three times the expected profit.
- Chance of being in the red after 50 bets: about 35 %, even though the strategy wins in the long run.
- Run the same numbers at 500 bets and that chance falls to about 12 %. Sample size matters more than any single week.
Common mistakes
- Judging a strategy after 20 or 50 bets. As the example shows, a third of the time a winning strategy is still behind.
- Assuming a losing run means the edge is gone. Check the expected range first.
- Raising stakes after a good run. Variance does not care about recent results.
In tennis
Tennis favourites win often but pay little, underdogs the reverse; both swing more than most bettors expect. Our track record publishes every loss for exactly this reason.
Read next: Public track record · Is value betting profitable? · Kelly & value calculator
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