Set over Set

[LetYouDown]

For this problem, you're looking for the total number of boards that contain your criteria divided by the total number of possible boards. Order is irrelevant for a flop.

[C(2,1) * C(2,1) * C(46,1)]/C(48,3) = 1.06% = 93 to 1

The C(2,1) is the # of ways to choose one of the remaining cards of the pocket pair you hold. There's 2 cards left, so obviously two of them can appear and meet that criteria. The second C(2,1) is the same thing for the other pair. You now know 6 cards (4 in player's hands, 2 on board)...so there's C(46,1) cards left in the deck. So there's C(2,1) * C(2,1) * C(46,1) ways the board can come for two players with pairs to flop a set and/or quads. There are C(48,3) total ways the board can come.

HTH

[bluewilde]

I'm not sure if your guys' calculations answer this, but what is the chance for set over set for "n" random hands. That is, in an n-handed game, what are the chances two different players with random hand flop a set from a PP. I'm trying to take into account the chance that they're both dealt pocket pairs and they both hit sets, I was under the impression that the 93-1 was for two guys with PPs both hitting sets, that it doesn't take into account the chance these guys will both be dealt PPs in the first place.

I only ask because I saw this 3 times in a home game the other week, and I was pretty sure that the chances of this were very very remote. It was in a set of about 250 hands, so I wonder if I should suspect cheating (I would never play in a game with people I didn't trust, but if the numbers are convincing I'd have to reconsider my group). Like the time one of these guys insisted he'd gone 9 hands without a card over 7, and I estimated the chances of that at (24/52*23/51)^9. Is that right? Either way, I doubted the occurence.

[PauliF]

thanks let you down

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Another time I flopped quads, another turned quads, and a third guy rivered a royal.

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How does the betting go when there are two quads on the turn such that the third guy has even the slightest reason to stay in the hand for the river?

[Jimmy The Fish]

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Another time I flopped quads, another turned quads, and a third guy rivered a royal.

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How does the betting go when there are two quads on the turn such that the third guy has even the slightest reason to stay in the hand for the river?

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All-in, either preflop or on the flop. If he held KsQs, and JsTsTd flopped, and he was short-stacked...

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