What is the chance the board has a flush. And two players have no flush card.
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1 Answer
I was curious so I ran the numbers
Board has a flush is
4 x combin(13;5) / combin(52;5) = 0.0019807923 = 1 / 504.85
No player has a flush card
combin(39;4) / combin(47;4) = 0.4611386763
Net = 0.0009134199 = 1 / 1095
In real life it will be lower as if the flop is a 3 flush hands with a big flush card will hang around.
answered Mar 25, 2018 at 12:38
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The conditional probability is higher: if no players have hearts, for example, the chance of the board having five is higher because the remaining cards are rich in hearts. You see this in stud as well: if one player has a flush, it is more likely for another to have one in a different suit. Mar 26, 2018 at 18:43
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@LeeDanielCrocker I dealt the board first as I think it is easier to follow. Mar 26, 2018 at 18:51