# Missing the flop with AK

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?

• .68 to power of 22
– WW.
Commented Nov 1, 2014 at 4:47
• @Steveg31 It is not an odds question, it is a Standard Deviation (SD) question. Search a little on SD and maybe answer your own question. SD happens and sometimes severely, understanding it does not help you figure out the game, it helps you stay sane while you go through those 90 degree drops, and widens your wisdom about bankroll. Why do you want to calculate the odds of loosing with AK 22 flops in a row?
– Jon
Commented Nov 1, 2014 at 5:18
• because it is currently happening to me and I was just curious how often this could occur Commented Nov 1, 2014 at 13:11
• @Jon: Totally disagree. It is a known and documented fact that there are rigged online poker websites out there (there are even companies advertising poker server software for which the "riggedness" is configurable at will). There's a 0.02% chance of not flopping at least a pair 22 times in a row when holding AK: if this happened to OP, he's totally right to ask such a question. To me if this happened to OP and if OP is playing on one of the lesser known and potentially shaddy site, this may be a good time to try one of the more legit site out there. Commented Nov 2, 2014 at 18:01
• @Jon: note by the way that this is StackExchange and comments like "do us a favor and delete this question" simply because you do not like it have zero place on StackExchange sites. If you don't like this question, vote to close it. Moreover theoretical questions like pure probabilities ones (say "How many different possible five cards boards exists?") which are in no way related to improving one's skills are totally fine here. Commented Nov 2, 2014 at 18:15

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.