Where variance describes scatter in general, standard deviation puts a number on it in the same units as the bet. Roughly two thirds of results fall within one standard deviation of expectation, and about 95% within two.
The practical consequence is that expectation grows with the number of bets while the typical swing grows with the square root of it. Play four times as long and your expected loss quadruples while the size of a normal swing only doubles.
That is precisely why casinos are indifferent to individual winners and why players cannot outrun an edge by playing longer. The house is running the same arithmetic across millions of bets, where the swings have long since been swamped by the expectation.
The practical version worth carrying is this: to be reasonably confident an edge is real rather than a swing, you need far more hands than intuition suggests. Sessions and even months are samples small enough that a losing stretch tells you very little, which cuts both ways for anyone judging a system by how it has been running.
Where the numbers come from
Related terms in odds & money
- House edge — The average share of each bet the casino expects to keep over the long run.
- RTP — Return to player: the mirror of house edge, quoted as what comes back rather than what is kept.
- Expected value — The average result of a bet if it could be repeated indefinitely.
- Variance — How widely results scatter around their expected value.
- Bankroll — The money set aside for gambling, kept separate from money needed for anything else.
- Unit — One standard bet, used as the yardstick for measuring results and bankroll.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.