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Old 12-11-2002, 10:48 AM
PseudoPserious PseudoPserious is offline
Senior Member
Join Date: Oct 2002
Posts: 151
Default Re: Hold\'em Probability Puzzler

Hey Carl,

Okay, here's how I would figure out the average number deals it would take to be dealt every possible hold'em hand (1326 possible hands).

Call N the number of hands you haven't seen.

The probability of getting a hand you haven't seen is
P(N) = N / 1326

From the mean of the geometric distribution, the average number of deals it will take you to see a hand you haven't seen before is:
A(N) = 1326/N

The average to get from N=1326 (prior to the first deal) to N=0 (just after your dealt the final 1326th hand) is then
A = Sum [ 1326/N , N=1326 to 1]

This works out to, oh, quite a lot (just shy of 10300).

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