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Server Time: 12/1/2008 10:45:55 AM PACIFIC |
 flush odds for pair vs. same pair, cellardoor_sf, 13. Oct 2003 19:45 | ||
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| My query: If you are heads up against someone holding the same pocket pair (in my case it was JJ vs JJ), what are the odds that 4 (or 5) to a flush will hit? | ||
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| Re: flush odds for pair vs. same pair, geecee, 13. Oct 2003 22:14 | ||
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| Let me take a crack at this one (while I'm no expert I've been fooling around with probability and odds for the heck of it). Since you know 4 cards, there are C(48,5) = 1,712,304 possible boards. One card of each suit is known to be in the 2 hands. There are C(12,5) * 4 suits = 3,168 ways to make a 5 flush board. There are C(12,4) * 4 suits = 1,980 ways to put 4 flush cards on the board. Multiply 1,980 * 36 unknown cards of the non flush suits = 71,280 four flush boards. Add 3,168 and 71,280 = 72,072. Divide by 1,712,304 = 4.21% which is equivalent to odds against of 22.76:1. | ||
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| Re: flush odds for pair vs. same pair, Stl10202, 14. Oct 2003 13:32 | ||
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| Well did either pair of jacks win with a flush? One time I saw KK up against AA and the KK caught its flush on the river, oh the greatness of poker. | ||
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| Re: flush odds for pair vs. same pair, cellardoor_sf, 14. Oct 2003 16:57 | ||
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| Yes the other pair of jacks caught 4 clubs for the flush, knocking me out of a tourney. Kind of a tough beat but that's life. | ||
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| Re: flush odds for pair vs. same pair, TrippH, 14. Oct 2003 17:48 | ||
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| the first card on the board will obviously be of one of the 4 suits already held, so the chance that a flush will come in that suit is: (11/47)(10/46)(9/45)(4) = 44/1081 a flush could also be made in another suit if the last 4 cards are all of that suit (runner-runner-runner-runner if you will), the chance of which happening is: (12/47)(11/46)(10/45)(9/44) = 3/1081 so the chance of any flush occurring in this situation is 47/1081 = .04348 = 1 in 23 ... of course the chance that you will make a flush is half that or 1 in 46 | ||
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