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How many fundamentally different Omaha or Omaha-8 starting
hands are there?
Author: Frank Jerome
Last updated: Jul 2002
Copyright © 2004 Frank Jerome
The official and up-to-date version of this answer is here
Although there are C(52,4) = 270,725 different 4-card hands,
many of them are indistinguishible as starting hands because they
differ only in suit. For example, AhTh9c8c is equivalent to
AsTs9d8d. How many distinct starting hands are there? A total of
16,432, as follows:
715_____C(13,4)_______all four cards in same suit
2860_____4*C(13,4)_____two suits (3,1), no pairs
2145_____3*C(13,4)_____two suits (2,2), no pairs
858_____13*C(12,2)____two suits (3,1), one pair
1716_____13*2*C(12,2)__two suits (2,2), one pair
78_____C(13,2)_______two suits (2,2), two pairs
4290_____6*C(13,4)_____three suits, no pairs
1716_____13*2*C(12,2)__three suits, one pair
78_____C(13,2)_______three suits, two pairs
156_____13*12_________three suits, triplets
715_____C(13,4)_______four suits, no pairs
858_____13*C(12,2)____four suits, one pair
78_____C(13,2)_______four suits, two pairs
156_____13*12_________four suits, triplets
13_____13____________four suits, quads
Copyright © 2004 Frank Jerome.
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