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Old 08-26-2005, 10:20 AM
aloiz aloiz is offline
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Join Date: Feb 2004
Posts: 4
Default Re: flush over flush or set over set - which is rarer?

Given that two players have suited hole cards of the same suit and they both see the river, the odds that they both make the flush:

C(9,3)*C(39,2)/C(48,5) + C(9,4)*39/C(48,5) + C(9,5)/C(48,5) =~ 0.0393 or about 24.4:1

Given that two players have different pocket pairs, and they both stay to the river, the odds that both make at least a set including the possiblity that one or both hit quads:

2*2*C(44,3)/C(48,5) + 2*C(44,2)/C(48,5) + 44/C(48,5) =~ 0.0321 or about 30.2:1 against.

Please note that this is not a good way of comparing the frequency that you will observe these types of hands at a table, as you are starting off by assuming that you have two players with pocket pairs or two players with suited cards. The odds that you have two players with two pocket pairs is much less than the odds that you have two with suited cards. (Of course this is somewhat offset by the fact that people will play a lower percentage of suited hands compared to pocket pairs). Also you are assuming that the both players stay to the river. The best way to get accurate real-world results would be to query a large poker tracker database.

aloiz
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