Risk of Ruin

Monte Carlo simulation is a computational technique that uses random sampling to model the probability of different outcomes. In betting, it simulates thousands of possible bankroll trajectories based on your historical edge and variance to estimate risk of ruin, expected growth, and confidence intervals.

Variance measures how widely your betting results spread around the expected value. High variance means large swings (common with longshot bets at high odds), while low variance means more predictable results. Understanding variance helps set realistic expectations and avoid tilt.

Standard deviation is the square root of variance and quantifies the typical size of swings in your betting results. It is expressed in the same units as your returns (dollars or units), making it more intuitive than variance for assessing risk.

Sample size refers to the number of bets in your track record. In sports betting, small samples are dominated by variance and tell you very little about true skill. Statisticians generally recommend at least 500-1,000 bets at similar odds ranges before drawing conclusions about edge.