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#1
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HoldŽem 3 cards suited on flop...
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 donŽt hold any card of that suit. Also consider that all players see the flop with any 2 suited cards. Thx in advance. |
#2
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Re: HoldŽem 3 cards suited on flop...
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%. |
#3
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Re: HoldŽem 3 cards suited on flop...
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. |
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