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Aug 31, 2018 at 18:09 comment added John @Addem Sorry I missed this for over a year. Your answer has a prime factorization of $2^3 \cdot 13 \cdot 1423$. I can't resolve the discrepancy between your answer and mine, but at the same time your answer seems a bit removed from a combinatorial counting argument.
Apr 1, 2017 at 4:40 comment added Addem I did a manual count of this using a computer script to run through all subsets of {1,2,3,...,52} associating cards with congruence classes mod 13. It gave me the result 147992 which is different from your answer of 123552. I've checked the script and am pretty sure it's right: It correctly counts all possible hands of cards, 52C5, and it correctly tests any hand for whether it contains two pair.
Nov 15, 2015 at 21:02 comment added LoMaPh Is this result for Texas Hold'em (where a player uses the best five-card poker hand out of seven cards)?
Jan 14, 2014 at 6:16 vote accept Curt
Jan 14, 2014 at 6:08 history edited John CC BY-SA 3.0
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Jan 14, 2014 at 5:56 history answered John CC BY-SA 3.0