rec.gambling.poker FAQ - How many fundamentally different Omaha or Omaha-8 starting hands are there?

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Index > Poker games and rules > Odds and probabilities

How many fundamentally different Omaha or Omaha-8 starting hands are there?

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


16432___________________total