probability of hands clashing....

[BruceZ]

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At the risk of BruceZ taking me to school for bad calculations [img]/images/graemlins/smile.gif[/img] I'll give this a shot.

The chances of two players with pocket pairs (any pocket pairs not of the same rank as opponent):

C(13,1)*(4,2)/C(52,2) = 78/1326 = 5.9%

times

C(12,1)*(4,2)/C(50,2) = 72/1225 = 5.9%

times chances that flop will give one player full house and the other quads:

C(2,1)*(2,2)/C(48,3) = 2/17296 = 0.01%

Total = 5.9% * 5.9% * 0.01% = 0.000003%, or 3.3 million to one.

This assumes only two players, so if other non-eights or non-nines were dealt to other players, the odds get better of this happening.

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All right except for final the arithmetic and round-off error. It's 2.5 million-to-1.