Hold´em 3 cards suited on flop...

[rid.br]

Hello.

I really would like to know what is the probability of someone
flopping a flush on Holdem. Considering a 10 handed game and that i am one of this players and don´t hold any card of that suit. Also consider that all players see the flop with any 2 suited cards.

Thx in advance.

[jason1990]

The probability player 1 was dealt two suited cards that match the suit on the board is

p_1 = (10*9)/(47*46).

The probability that player 1 AND player 2 were dealt two suited cards that match the suit on the board is

p_2 = (10*9*8*7)/(47*46*45*44).

We can continue until p_5, but p_6 and beyond are all 0 since at most five players can flop a flush. So, by inclusion-exclusion, the probability that at least one player flopped a flush is given by the following formula, in which xCy denotes x!/(y!*(x-y)!):

sum_{n=1}^5 { (-1)^{n+1}(9Cn)p_n }.

Using this, I get that the probability someone flopped a flush is about 33.3%.

[rid.br]

Thank you very much for your help.

I saw some chart that matches with this result of about 33% too. So i think thats it.