My question is math related, specifically how do you calculate
variance for a video poker payline?
The variance for a game is the sum of variances for each pay line.
Calculating the variance for a pay line is the piece I'm missing.
I have searched a few stats books that I own and the internet for a
formula to do this but have found only the following equations
regarding variance:
var = (x-u)^2 * p(x)
var = (x^2 * p(x)) - u^2
The examples given for variance calculations always seem to be based
on coin flipping or dice rolling and do not seem to work for video
poker. I would guess that's because these equations are used for
random events that have a normal distribution and video poker does not
have a normal distribution (or video poker is not random!).
If I use the above formula to calculate the variance of a royal flush
in a 9/6 Jacks+ game I get the following:
u = (493,512,264 * 800) / 19,933,230,517,200 = 0.0198 (I'm assuming
here that u = ev(x))
p(x) = 493,512,264 / 19,933,230,517,200 = 0.000024758
var = (800-0.0198)^2 * 0.000024758 = 15.84434
Every source I've found that states variance for paylines states the
variance for a royal flush as 15.8059.
I'm obviously missing something here, probably something very obvious
but I just can't seem to put my finger on it.
If anyone can help or point me to a source that explains it, I'd be
very grateful!