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#1
10-22-2006, 01:42 PM
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Odds of Higher Flush
I have two cards that are [img]/images/graemlins/diamond.gif[/img]s , the highest being a Q, and there are 3 lesser [img]/images/graemlins/diamond.gif[/img]s on the board to make my flush. I am positive that one other player also has a flush. How do I calculate the probability that he is holding the A or K of [img]/images/graemlins/diamond.gif[/img]s.
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#3
10-23-2006, 03:30 AM
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Re: Odds of Higher Flush
[ QUOTE ]
Would this be correct? (6/8)(5/7)=54% of the time he will not have an A or K. [/ QUOTE ] Yes. You can also get there by calculating that villian could have any of C(8,2) = 28 possible hands, of which 13 beat you (6 ways to make Ax, 6 ways to make Kx, plus AK). 1 - (13/28) = 15/28 = 54%.
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#4
10-23-2006, 08:27 AM
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Re: Odds of Higher Flush
[ QUOTE ]
I have two cards that are [img]/images/graemlins/diamond.gif[/img]s , the highest being a Q, and there are 3 lesser [img]/images/graemlins/diamond.gif[/img]s on the board to make my flush. I am positive that one other player also has a flush. How do I calculate the probability that he is holding the A or K of [img]/images/graemlins/diamond.gif[/img]s. [/ QUOTE ] As noted in Dave's post, any time you have a flush with a suited hand plus 3 of your suit on the board, there are 28 other possible flush hands out there. With the nut flush, assuming no straight flush, you beat all 28 of course. When you have the second nut flush, you are beating 21 of them, and losing to 7. When you have the third nut flush, you are beating 15 of them, and losing to 13. When you have the 4th nut flush, you are beating 10 and losing to 18. 5th nut flush beats 6 and loses to 22. 6th nut flush beats 3 and loses to 25. 7th nut flush beats 1 and loses to 27 8th nut flush loses to the other 28 possible flushes.
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#5
10-23-2006, 10:30 PM
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Re: Odds of Higher Flush
While the math is correct, you have to be careful in poker. If you make a bet figuring you've got a 54% edge, you could be in trouble. If he has the Ace, he's raising for sure. With the King, probably. With a lower flush, he may just call, or even fold. So when you win, you win smaller than you lose when you lose.
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#6
10-24-2006, 01:26 AM
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Re: Odds of Higher Flush
What if you figured in the kind of suited hands he's likely to play. Like maybe, any suited Ace, K-9, and suited 2 gappers below? I guess it would depend on the board then too.
PairTheBoard
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