If the SD for blackjack is 1.1 per hand, can you use this same figure for a higher odds game or does each casino game have a different SD per event? Putting it another way; does a game with higher odds deviate from what is expected MORE than a game with lower odds?
Thanks in advance.
North Wind,
The SD for other casino games is different than that for BJ.
To calculate the SD, use this formula:
SD = sqrt(var)
with
var = (sum((x_i - x_mean)^2))/(n-1)
As an example, let's calculate the SD for betting a single number at an American (38-spot) roulette table, where the payout is 35 if we hit, and 0 if we don't.
In the equations above, "SD" is the standard deviation, "var" is the variance, "x_i" is the result for number "i", so x_i = 35 for i=1, and x_i = 0 for i = 2, 3, 4, ..., 38, "sqrt" is the square root command, "sum" means sum over all results from i=1 to i=38, "n" is the number of results, so here n=38, and "x_mean" is the average (or mean) result, so for this bet x_mean = 35/38 = 0.921052632, since on average we'll hit once every 38 tries.
If you perform the above calculations, you'll find that the var = 32.23684211, so the SD = 5.67774974 units. Thus, we see that the SD for betting a single number at roulette is about 5 times the SD for a single hand of BJ.
Hope this helps!
Dog Hand
