How to use this betting tool
- Enter equal stake and decimal odds.
- Enter the assumed win probability.
- Choose the number of independent bets.
- Compare expected profit with standard deviation and the approximate range.
#096 · Bet Tracking & Performance Tool
Betting Variance Calculator
Quantify the spread around an expected betting result when each wager has the same stake, odds and win probability. This is a model of independent binary bets, not a promise that returns will be normally distributed.
Calculator
Enter assumptions$
x
%
bets
Ad space
What this tool calculates
Each bet has two net outcomes: stake × (odds−1) on a win and −stake on a loss. Variance measures squared dispersion around the expected profit.
Per-bet variance = p(win−μ)² + (1−p)(loss−μ)². Total variance = n × per-bet variance; SD = √variance.
The 95% range uses expected profit ±1.96 standard deviations and a normal approximation. It is not a confidence guarantee.
Worked example
For 100 independent $100 bets at odds 2.00 with a 52% win chance, expected profit is $400 while standard deviation is close to $999.
| Win outcome | +$100 |
|---|---|
| Loss outcome | −$100 |
| Expected wins | 52 of 100 |
| Expected profit | $400 |
Tips and limitations
- Correlation can make real variance higher than this independent-bet model.
- Changing stakes or odds require bet-level data rather than one common input.
- Variance is expressed in squared currency; standard deviation is easier to interpret.
FAQ
What is betting variance?
It is the probability-weighted squared spread of possible profit outcomes around their expected value.
Why is variance shown in squared dollars?
Squaring deviations prevents positive and negative differences from cancelling; standard deviation converts the result back to dollars.
Does a larger sample remove betting risk?
No. Relative fluctuations often shrink, but the absolute standard deviation generally grows with the square root of the number of bets.
What assumptions does this calculator make?
Bets are independent and share the same stake, decimal odds and win probability.
Is the 95% range exact?
No. It is a normal approximation and can be poor for small samples or extreme probabilities.
Related betting tools
Dispersion measures
| Expected profit | Probability-weighted average |
|---|---|
| Variance | Average squared deviation |
| Standard deviation | Square root of variance |
Browse more betting tools
Betting calculator hubsOdds & ProbabilityConvert odds formats, calculate implied probability, and remove bookmaker margin.View all
Payout & ProfitEstimate returns, profit, parlay payouts, and break-even outcomes.View all
Handicap ConversionCompare Asian, European, and Macau handicap lines and settlement rules.View all
Bankroll & RiskPlan stake sizes and understand variance, exposure, and expected value.View all