Please compute the probability of the following event which actually occurred at our local club card game:

Game --- 7-card stud poker, standard 52 card deck, eight active players at the beginning of each hand. Some players dropping out during the play of each hand. In no case did we run out of cards.

My question is: What are the odds against the same person holding all four eights in three consecutive hands.

I am not at all sure that this can be calculated. but my card player's instinct tells me that the answer would be well into the " millions to one". I will eagerly await your reply.

Blair

The probability of being dealt quad eights for a particular hand in 7-card stud is  ¹/₇₇₃₅. Thus, the probability of being dealt quad eights for a particular set of three consecutive hands is ( ¹/₇₇₃₅) ³.

However, if asking the probability of it happening over a session of several hours you have to make the appopriate adjustment where it can start at any time for a segment of three consecutive hands.

The point is that  ¹/₇₇₃₅ is the number to start with. This comes from my web site Mathematics and Poker.

Brian