What is standard deviation in casino games?
Standard deviation is the usual size of the gap between one round's result and the game's average result, measured in the same units as the stake. It is the square root of the variance. A larger figure means wider swings; it does not change the average cost set by the house edge.
Definition
Standard deviation measures spread. For one round of a game, you take each possible result, find its distance from the average result, square it, weigh it by its probability and add the lot up. That total is the variance, and its square root is the standard deviation.
It is stated in the same unit as the stake, so a figure of 5.84 means a typical round lands about 5.84 stakes away from the average. The idea behind it is covered in the guide to volatility.
Worked example: two roulette bets
Take a European wheel with 37 pockets and a stake of 1 unit. A straight bet on one number returns a profit of 35 units with probability 1/37 and a loss of 1 unit with probability 36/37.
Average result: (35 x 1 + (-1) x 36) / 37 = -1/37, about -0.027 units. Average of the squared results: (35 x 35 + 1 x 36) / 37 = 1261/37. Variance: 1261/37 - 1/1369 = 46656/1369. Square root: 216/37, about 5.84 units.
An even-money bet on 18 pockets wins 1 unit with probability 18/37 and loses 1 unit with probability 19/37. Its average is also -1/37, but its squared results are always 1, so the variance is 1 - 1/1369 and the standard deviation is about 1.00 unit.
Both bets cost the same on average. The straight bet simply spreads its results about 5.8 times wider.
Over many rounds
Across n independent rounds the average loss grows in proportion to n, while the standard deviation grows only with the square root of n. After 100 rounds of the straight bet, the average result is about -2.70 units and the standard deviation is about 58.4 units. The spread dwarfs the average, which is why short sessions say little about the house edge, as explained in the guide to theoretical RTP and short-session results.
Questions and answers
Is standard deviation the same as volatility?
They are closely linked. Variance is the mathematical quantity, standard deviation is its square root, and volatility is the everyday word for how large that spread is. Game descriptions rarely print the number.
Does a high standard deviation change the house edge?
No. The house edge comes from the average result per stake. Standard deviation only describes how far single rounds and short sessions stray from that average.
Do licensed operators have to show the standard deviation?
Regulation 20(2) of the Conduct of Gambling Operations Regulations, 2026 lists rules of games, odds, house edge and average return to the player as items to display. Standard deviation is not named in that list.