Standard Deviation

Standard deviation is the square root of variance and provides a more intuitive measure of result dispersion because it is expressed in the same units as the original data. In gambling, one standard deviation represents the typical range of fluctuation you can expect from the mathematical average.

For a single bet, the standard deviation depends on the payout structure. A bet paying even money (like red/black in roulette) has a standard deviation of approximately 1 unit per bet. After 100 such bets, your results will typically fall within two standard deviations of the expected loss. This means your actual results will usually be within a predictable range, though outliers always remain possible.

The standard deviation for a series of bets grows with the square root of the number of bets, not linearly. After 100 bets, the standard deviation is 10 times the per-bet deviation. After 10,000 bets, it is 100 times. This means that while absolute swings get larger as you play more, relative swings (as a percentage of total wagered) actually shrink. This is the mathematical foundation behind the certainty of casino profits over large volumes.

Professional gamblers use standard deviation to calculate confidence intervals for their expected results. Knowing that approximately 68% of outcomes fall within one standard deviation and 95% within two standard deviations helps with bankroll planning and deciding when a winning or losing streak is within normal bounds versus statistically unusual.