odds someone has flush draw

[alphatmw]

9 random hands see the flop. every time the flop has 2 of one suit, what are the odds someone has a flush draw? same with 6 people, 3, and 2.

[jay_shark]

Good question and I remember thinking about this when I first started out playing poker .


Lets say flop is xxy where x belongs to the same suit and y is from another suit and you're the dealer . To find the exact probability at least one of your opponents has a flush draw you need to compute all the terms from the principle of inclusion/exclusion . Luckily for you , there is a more practical and efficient way of solving this which gives a very accurate response without all the hassle . Also note that this question is very much related to the probability someone at your table holds a higher pocket pair when you have pocket pair x at a n handed table . The probability at least one person has a flush draw is approximately :

1- [(49c2-11c2)/49c2]^9 = 35% . This means that the probability player 1 doesn't hold this specific flush draw is (49c2-11c2)/49c2 =0.953 . The probability player 2 does not hold this particular flush draw doesn't really have much to do with player 1's cards so we can treat them as being independent . If you take 0.95 to the ninth power you get the approximate probability that no one flops this particular flush draw in which case you take the complement to arrive at your answer .

[jay_shark]

You should be able to guess what the formula should be .
Let n be the number of players who have seen the flop with exactly 2 suited cards and all hands random .

1-[(49c2-11c2)/49c2]^n

Even if the hands were not random which it never is , the probability any one player doesn't hold that particular flush will probably still be close to 95% . Of course this has to be conditioned on the players' hand range but I would guess that it wouldn't be far off .

[geo8o2]

what are my odds of flopping a flush draw when i hold 2 of a suit? because i've been lagging it up at 6max tables. maybe i should cut J4s from my starting hands. =]

[jay_shark]

yeah I think it's a good idea you avoid playing j-4 suited but not always . I mean if the tempo is right and you haven't played a lot of hands then I don't have a problem with it .

11c2*39/50c3 =10.9% you will flop a flush draw with any two suited cards .