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OFF TOPIC probabilities for poker dice full house and straight

Posted By: Stein Kulseth
Date: Sunday, 20 March 2011, at 5:11 p.m.

In Response To: OFF TOPIC probabilities for poker dice full house and straight (leobueno)

You have 2 small straigths (SS) where the last die differs from the others (12346 and 13456) For both of these any of 5 dice can be the lowest, any of the 4 remaining can be the second lowest, etc, for a total of 5! = 120 permutations for each, 240 total.

Then you have the SSs where the last die equals one of the other. You have 3 possible SSs (1234, 2345, 3456) and the duplicated die can be any one of the 4 for 12 distinct variants. For the permutations, any 2 dice can be the duplicated value, thats 5*4/2= 10 permutations, furthermore any of the 3 remaining can be the lowest of the remaining, and any of the 2 then remaining etc. That's 6 permutations of the remaing 3. That is 60 permutations per distinct variation, 12*60 in all that is 720. Plus the 240 mentioned above that is 960 in all, so exact probability is 960/7776 putting it between 3-of-a-kind and full house.

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