Statistics 25100
Poker hands

The various types of hands in poker, arranged from highest to lowest, are as follows:

An ace can be played in a straight or straight flush either high (A, K, Q, J, 10) or low (5, 4, 3, 2, A).

The following table gives the Number of (unordered) hands of each type, and the Chance to be dealt a hand of that type when all hands are equally likely. We worked out some of these entries in class. See if you can derive the others.

Hand Number Chance
Straight flush 40 0.0000154
Four of a kind 624 0.0002401
Full house 3,744 0.0014406
Flush 5,108 0.0019654
Straight 10,200 0.0039246
Three of a kind 54,912 0.0211285
Two pairs 123,552 0.0475390
One pair 1,098,240 0.4225690
No pair 1,302,540 0.5011774
Total 2,598,960 1.0000000


Michael J. Wichura
Last modified: Tuesday, March 27, 2007