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What is the chance the board has a flush. And two players have no flush card.

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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.

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  • Can confirm, numbers are correct. – Raymond Timmermans Mar 25 '18 at 20:38
  • 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. – Lee Daniel Crocker Mar 26 '18 at 18:43
  • @LeeDanielCrocker I dealt the board first as I think it is easier to follow. – paparazzo Mar 26 '18 at 18:51

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