Sample Size

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.

Risk of ruin is the probability that a bettor will lose their entire bankroll. It depends on edge, variance, and bet sizing. Aggressive staking (high % of bankroll per bet) dramatically increases risk of ruin even with a positive edge. Proper bankroll management keeps risk of ruin acceptably low.