rec.gambling.poker FAQ
|
| Unlawful Internet Gambling Enforcement
Act - full analysis for
poker players. |
|
|
|
|
|
|
|
|
|
|
| The FAQ is a volunteer effort. Join us by submitting updates,
or let us help you learn about online poker. Details. |
|
|
Index > Poker games and rules >
Odds and
probabilities
How many fundamentally different Omaha or Omaha-8 starting
hands are there?
Author: Frank Jerome
Last updated: Mar 2010
Copyright © 2009 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
858 13*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
2574 13*3*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
(Thanks to storkk for a correction submitted Mar 2010).
Copyright © 2009 Frank Jerome.
Unauthorized copying prohibited. Contact
info@rgpfaq.com for
permission to redistribute.