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Server Time: 1/8/2009 10:24:48 AM PACIFIC |
 Mathematical odds of 2 quads, Scott Bickley, 18. Dec 2003 11:09 | ||
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| Let's suppose I hold 2 sevens and am going head up against an opponent with 2 sixes. What are the odds of both of us hitting our quads by the river? Can someone demonstrate for me? Thanks, | ||
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| Re: Mathematical odds of 2 quads, Mikewad, 18. Dec 2003 16:24 | ||
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| They are long, damn long. Good Luck 1 | ||
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| Re: Mathematical odds of 2 quads, jajo, 18. Dec 2003 17:34 | ||
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| There are a total of C(48,5) = 1,712,304 possible boards. There are only 44 combinations that will contain quads for two players holding a pocket pair. Four specific cards must be there and then the last card can be any of the 44 remaining cards. 1x44=44. 44 / 1,712,304 = .0000256. That makes it a .00256 percentage chance that this will occur. Since 1,712,304 / 44 = 38,916 this means that in every 38,916 times the cards are dealt, quads will occur only once. | ||
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| Re: Mathematical odds of 2 quads, stdioh, 26. Dec 2003 20:52 | ||
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| To put that into perspective, a pro who plays 2000 hours a year will see about 60,000 hands go by. That means he'll have about 3500 pocket pairs dealt to him in a year. Lets say that he plays 2500 of these hands at least long enough to make his set and be married to the hand (and that includes the small ones he throws away in early position, etc - 2500 may be a lot of pairs to play, but that all depends on style so let us leave that alone) ... of the 2500 times he has a pair, most of the time somebody else at the table will have a pair, better or worse. Lets invent a number (that I think is reasonable) and say that 2000 times somebody else has a pair long enough to see a set and get married to the hand, etc. So for each of these 2000 times that our pro butts heads with an opponent both of them holding some pocket pair (neato - that's about once an hour) he takes a shot at being on one end or the other of the quads over quads scenario. Thus, he's got about a 1/40,000 shot each of 2000 times, so roughly once every 20 years our pro should actually hit a quads over quads showdown. That's not much at all. It seems that everybody in a cardroom has a story about losing in quads over quads, but few have stories of winning in that situation. A lot of them are lying and maybe some were cheated in shady places. A few really happened. But this is a once or twice in a lifetime thing. | ||
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| Re: Mathematical odds of 2 quads, stdioh, 26. Dec 2003 20:53 | ||
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| Now, all that said, quads over quads should happen at a table where you are sitting more than it should happen when you are involved in it, so you might "see" it quite a bit, but there's a difference between being in the hand and just being there. | ||
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