Can sum1 who doesn't suck at math tell me if I'm doin it rite?

RobMcB · #1 09-17-2007, 05:46 PM

OK, I am figuring out the probability that my opponent who holds a random hand has a pair of kings or queens on this board:

Preflop: Hero is CO with T[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/spade.gif[/img].
5 folds, Hero raises to t150, Button calls t150, 2 folds.

Flop: (t375) 6[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img] (2 players)
Hero bets t150, Button calls t150.

Turn: (t675) Q[img]/images/graemlins/club.gif[/img] (2 players)

What I do is I take the 3 remaining queens and kings (6 cards) and then multiply them by all the remaining unseen cards (52 - 7 = 45) to find out how many combinations there are that would make one pair of queens or kings.
6*45 = 270 combos of at least 1pair of Q's or K's. For the sake of this example let's not complicate the math by worrying about the probability our opponent has a set or small 2pair.
Ok so after the turn is dealt we have seen 6 out of 52 cards. Our opponent has a random hand, so he is holding any one of 1,035 combos (46*45/2).
The probability of our opponent having at least 1 Q or K is roughly %26.
AMIRITE?

ncray · #2 09-17-2007, 06:16 PM

6 known cards, so 46 to choose from
6C1*40C1/46C2 contain a single K or Q = 23.18%
6C2/46C2 contain KK, QQ, or KQ = 1.44%

Paul2432 · #3 09-18-2007, 12:55 AM

[ QUOTE ]
OK, I am figuring out the probability that my opponent who holds a random hand has a pair of kings or queens on this board:

Preflop: Hero is CO with T[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/spade.gif[/img].
5 folds, Hero raises to t150, Button calls t150, 2 folds.

Flop: (t375) 6[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img] (2 players)
Hero bets t150, Button calls t150.

Turn: (t675) Q[img]/images/graemlins/club.gif[/img] (2 players)

What I do is I take the 3 remaining queens and kings (6 cards) and then multiply them by all the remaining unseen cards (52 - 7 = 45) to find out how many combinations there are that would make one pair of queens or kings.
6*45 = 270 combos of at least 1pair of Q's or K's. For the sake of this example let's not complicate the math by worrying about the probability our opponent has a set or small 2pair.
Ok so after the turn is dealt we have seen 6 out of 52 cards. Our opponent has a random hand, so he is holding any one of 1,035 combos (46*45/2).
The probability of our opponent having at least 1 Q or K is roughly %26.
AMIRITE?

[/ QUOTE ]

Your opponent does not have a random hand. He called a bet before the flop and on the flop, which weights his holdings towards a K. If you base decisions on the odds based on his holding a random hand, you will be makinga lot of mistakes.

Paul

httassadar · #4 09-18-2007, 04:30 AM

This sort of problem continues haunting me.

Should the K or Q on board change the probability of your opponents hole cards? I think to figure out the probability of his holding K or Q, all 8 cards are counted. His cards are dealt before the flop/turn.

Same as the well-known car-sheep problem? Behind three doors, one car and two sheep. You pick up one door and then shown one other door which is a sheep. Should you change to the third door to get a better chance of car or it makes no difference?

Back to poker, if the flop are 3 spades, and you want to calculate the prob that he made flush. The Bayesian prior should be 13C2 / 52C2, not 10C2 / 52C2 right?

To make things worse, I think your hole cards should count. Ie, hero's pair of ten would increase the probability that his opponent gets Q or K.

oddsock · #5 09-18-2007, 03:28 PM

[ QUOTE ]
This sort of problem continues haunting me.

Should the K or Q on board change the probability of your opponents hole cards? I think to figure out the probability of his holding K or Q, all 8 cards are counted. His cards are dealt before the flop/turn.

Same as the well-known car-sheep problem? Behind three doors, one car and two sheep. You pick up one door and then shown one other door which is a sheep. Should you change to the third door to get a better chance of car or it makes no difference?

Back to poker, if the flop are 3 spades, and you want to calculate the prob that he made flush. The Bayesian prior should be 13C2 / 52C2, not 10C2 / 52C2 right?

To make things worse, I think your hole cards should count. Ie, hero's pair of ten would increase the probability that his opponent gets Q or K.

[/ QUOTE ]

Problem is that the car/sheep situation is purely random - there are no other factors in place that can help you. (Solution by the way is to ALWAYS change the original choice!).

If you have no read on your opponent whatsoever then a K or Q appearing on the turn will reduce the chances of the opponent having a K or Q in his hand from a purely mathematical point of view in the same way that a one-suit flop would mathematically reduce the chances of an opponent having the same suit hole cards. That does not mean they won't have the cards that are mathematically less probable, so as a poker player you need to use the other tools at your disposal to make as accurate read as possible.

ncray · #6 09-19-2007, 12:47 AM

[ QUOTE ]

Should the K or Q on board change the probability of your opponents hole cards?

[/ QUOTE ]

Yes. What happens if there are 4Ks on board? The probability of your opponent holding a K is 0. To see in general why this is the case, think about how the cards are distributed in the deck. ABCDEF... If there are for simplicity 2 opponents, then player 1 gets A and C, 2 gets B and D in the shuffle. E is burned, and the flop is FGH. We're fixing FGH, and looking at all the combinations of AC or BD (for a given flop, what is the probability that a given player holds a certain hand).

httassadar · #7 09-19-2007, 03:46 AM

Thanks ncray, for a good explanation. The card game is different than the car/sheep game.

In the c/s game, the door opened to you depends on your choice of the first door, so knowing it is sheep won't affect your chance of hitting a car.

But in the card game, the community cards won't change should you have AA or 27, so knowing the board changes the distribution of hole cards.