Model │ Math · Free tool
Monte Carlo
Expected value is what the bet is worth on average. Monte Carlo shows you the runs you actually have to live through. Set the scenario, run it thousands of times, see the envelope.
A percentage above 0 and below 100.
A price in any format, +120, 1.91 or 10/11.
A dollar amount greater than zero.
A whole number between 1 and 1,000.
A whole number between 100 and 50,000.
Edits re-run automatically. Re-roll draws fresh randomness with the same scenario.
- Probability of profit ,
- Expected (mean) ,
- 5th percentile (worst 5%) ,
- 95th percentile (best 5%) ,
- Worst drawdown across runs ,
- Longest losing streak ,
Final P&L distribution
Every bar is the count of runs that finished inside that P&L bucket. The gold lines mark the 5th, 50th and 95th percentiles. The dashed navy line is breakeven.
Why variance is the number that bites
Expected value tells you what a bet is worth on average. Average is a useful summary. It is not a path. A +EV bet placed enough times will win in the long run, but the runs in between can be vicious. A long losing streak, a deep drawdown, a stretch of months below break-even. Monte Carlo gives you the shape of those paths, not just the centre.
- Probability of profit
- The share of runs that ended positive. A +EV bet placed enough times has a high probability of profit; placed too few times, it can be a coin flip even when the math says otherwise.
- The 5th-percentile path
- The worst 1-in-20 outcome. If you cannot survive this path financially or emotionally, the stake is too large, even when the expected value is positive.
- Worst drawdown
- The largest peak-to-trough loss seen across every simulated run. A useful sanity check on bankroll sizing. If the worst drawdown wipes your bankroll, the strategy is too aggressive to deploy.
Pair this with the Kelly Stake calculator. Kelly tells you the size. Monte Carlo tells you what that size feels like across thousands of paths.