View Full Version : Starting hand distribution

11-16-2003, 03:54 AM
Here's my question for the mega math junkies:

Discounting suited vs non suited, there are 91 different starting hands. Over the course of 100 hands, what is your expected # of those 91 hands to see? Stdev?

11-18-2003, 08:34 AM
There are 6 combinations (out of 1326) for each of the
13 pairs and 16 combinations for each of the unpaired
hands. Consider the chances that a hand is NOT found
in the 100 deals:

if C = combinations out of 1326, the odds are


which yield

0.6353905 for C=6 and
0.2970142 for C=16

Thus, the average number of pairs NOT represented
in the 100 deals is 13x0.6353905 = 8.26008 and
the number of nonpairs NOT represented is 78x
0.2970142 = 23.16710. Subtracting the sum of
these from 91 gives 59.572 of these or not quite
2/3 of them!