Gambling Mathematics Academy
Monte Carlo Simulation for Bettors, Without the Calculus
How sampling-based simulation gives a realistic picture of variance, drawdowns, and risk of ruin.
Direct Answer
Monte Carlo simulation runs thousands of randomized trials of a betting strategy to estimate the distribution of outcomes. It produces realistic estimates of expected return, drawdown, and risk of ruin that no closed-form formula can match.
Key Takeaways
- 01Closed-form risk formulas underestimate real-world tail outcomes.
- 02Monte Carlo gives a full distribution, not just a point estimate.
- 03A spreadsheet is enough to run useful simulations.
- 04The output is most useful for bet sizing, not picking winners.
What Monte Carlo does
You specify an edge, an odds price, a bet size rule, and a starting bankroll. The simulation draws random wager outcomes consistent with the edge thousands of times, recording the path of the bankroll. The distribution of final outcomes tells you what to expect.
What it reveals
Real strategies that look profitable on paper often show meaningful risk of ruin once volatility is simulated. Even a 5% edge at heavy stakes will bankrupt some realistic fraction of bankrolls.
A minimal example
A bettor with a 53% true win rate at -110, betting 5% of bankroll flat, has a substantially lower long-run growth rate than the same bettor at 2%. Simulation makes the trade-off visible in a way intuition cannot.
Frequently asked questions
Do I need to code to run Monte Carlo?+
No. Spreadsheets with RAND() functions can run useful simulations. Python or R unlock larger sample sizes and faster iteration.
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