odds of community quads on texas holdem
December 4th, 2011 at 1:44:35 AM
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I was wondering if anyone knows the odds of community quads on Texas holdem when 2 are flopped then runner runner community quads?
ex. flop 10 4 10
turn 10 4 10 10
river 10 4 10 10 10
ex. flop 10 4 10
turn 10 4 10 10
river 10 4 10 10 10
December 4th, 2011 at 2:37:35 AM
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For the final community board of 5 cards out of a 52 card deck;
1. There are 2,598,560 combinations of the 5-card flop.
2. 624 of them will have a four of a kind.
3. This is once in every 4164 hands (0.00024) - not often at ALL!
This is a good question to google, and to look up on more math-oriented sites.
1. There are 2,598,560 combinations of the 5-card flop.
2. 624 of them will have a four of a kind.
3. This is once in every 4164 hands (0.00024) - not often at ALL!
This is a good question to google, and to look up on more math-oriented sites.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
December 4th, 2011 at 3:12:29 AM
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Thanks for the reply
December 5th, 2011 at 11:24:04 AM
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I think Paigowdan read the problem wrong - he calculated the probabbilty of a quad appearing in the five community cards, including where there is a three of a kind in the flop.
There are (52 x 51 x 50) / 6 = 22,100 different combinations for the flop, of which (13 values for the pair x 6 combinations of the two suits in the pair x 48 cards that have a different value than the pair) = 3744 have a pair but not three of a kind. From there, there are 49 cards available for the turn, two of which match the pair, and for each of those, there are 48 cards available for the river, one of which matches the pair. The total probability = 3744/22100 x 2/49 x 1/48 = about 1 in 6942.
If you want to know the chance that, once you already see a pair in the flop, the turn and river will make it a four of a kind, that's 2/49 x 1/48 = 1 in 1176.
There are (52 x 51 x 50) / 6 = 22,100 different combinations for the flop, of which (13 values for the pair x 6 combinations of the two suits in the pair x 48 cards that have a different value than the pair) = 3744 have a pair but not three of a kind. From there, there are 49 cards available for the turn, two of which match the pair, and for each of those, there are 48 cards available for the river, one of which matches the pair. The total probability = 3744/22100 x 2/49 x 1/48 = about 1 in 6942.
If you want to know the chance that, once you already see a pair in the flop, the turn and river will make it a four of a kind, that's 2/49 x 1/48 = 1 in 1176.
