What are the chances of missing the flop 22 straight hands with AK? I mean when you don't flop at least one pair, two pair, straight, or a flush. I've read the chances of flopping a pair or better is around 32%. But how would you calculate your chances of missing 22 flops in a row?
This is a binomial distribution: either you miss the flop or you don't.
If your probability to NOT miss is .32, then your probability to miss is 1 - .32 = .68.
Your number of trials is 22. The expected number of missing is 22 * .68 = 14.96.
The variance of the binomial distribution is np(1-p). In your case, 22*.68*(1-.68) = 4.7872. The standard deviation is the square root of variance, 2.188.
Anyway, you don't need standard deviation to answer your question. This answer was already given in the comment by @WW. as .68^22 = .0002 or 0.02%. You don't need statistics or sd to get that.