Quick odds question.

I know when you hold pocket pair, your chances are about %13 flopping your set. Whats the given odds on someone holding a pocket pair pre-flop? I know someone holding aces pre-flop is something around 1 in 240. What about holding 6's, or 7's, small pairs? Just wanting to know what the chances are i'm dealing with a set. Also, once you flop your set, what are your odds of making a full house? I know if someone is 4 to the flush on the flop, they have roughly a %36 chance of making it. If i hold a set, and someone is chasing the flush, whats my odds of making the boat? My first post, and couldnt think of anything else to say at the moment.

Also, what helped you guys out the most on your poking playing? I've read Theory of Poker, and Hold'em Poker for Advanced players (both by Skylanski). They have helped quit a bit soo far on the mathmatical side of the game. Thanks.

-Jake-

well, if the odds of pocket aces are 1 in 240...then logically pocket anythings would be 1 in 240

In terms of probability, an A has the likelihood of showing up as much as a 2 or a J.

Odds of having a pocket pair: (52/52)(3/51) = 1/17
Odds of having a certain pocket pair: (4/52)(3/51) = 1/221

Probability of being dealt a pocket pair: 5.8824%
Probability of being dealt a specific pocket pair, such as AA: .45248%
Probability that at least one of your 9 opponents at a 10 person ring has a pocket pair: 42.05%

Probability that exactly one of your 9 opponents was dealt a pocket pair: 32.5954%
Probability that exactly two of your 9 opponents were dealt a pocket pair: 6.33794%
Probability that exactly three of your 9 opponents were dealt a pocket pair: .792237 %
Probability that exactly four of your 9 opponents were dealt a pocket pair: .0618929 %.

Probability that someone flops a set AND exactly one of your 9 opponents has a pocket pair: 4.07442%
Probability that someone flops a set AND exactly two of your 9 opponents have a pocket pair: 1.48545%.
Probability that someone flops a set AND exactly three of your 9 opponents have a pocket pair: .2615%.
Probability that someone flops a set AND exactly four of your 9 opponents have a pocket pair: .0256124%.

Approximate probability that one of your nine opponents flopped a set (given that all pocket pairs see the flop): 5.85%.

Probability that, given a flopped set, you will improve to a full house or better after the river: 33%.

Probability that, given a flopped set, you will improve to a full house or better after the river: 33%.

This is an very interesting statistic that I did not know. I guess it hasn't come up enough for me to wonder about. But that guy with the 4-flush has 9 outs. And you'll have 7 outs on the turn card, and 10 outs on the river to win EVEN IF they hit the flush.

Thinking a different way: Even if one card of your set matches the suit of their draw, they only have 8 outs instead of 9. At the turn this is reduced to 7.

It's like a really close sports match. You flop the set and a huge lead. They turn the flush and jump way out ahead. But you still have 10 outs(21%) to win the game on the river.

Ideally, the same card that completes their nut-flush makes you the full house. :P :P :P

Wow, thats some nice stats ya gave us. Thanks man. I didnt imagine you had a 1/3 chance of catching a full house once you flopped a set. It's also cool to know that every other hand, at least someone will hold a pocket pair. I sometimes get paranoid when i turn a flush, when 2 of the same card is out there. Theres nothing better than making a full house, and someone has the flush. I keep praying that the same suit falls on every street. I have gotten VERY rich on that.

-Jake-