Poker: Probability of single opponent having a flush with 3 suited cards on board

[morrowcosom]

I run into the dilemma of having a great hand and then a possible flush hits, so I tried to calculate the probability of a single opponent having a flush when the board has 3 suited cards by the river.

I used the old 1-(unhelpful cards/unseen cards) trick, but my answer seems too high, and I hope it is!

3 suited cards on board:

1- [(36/46)*(36/45)]
=38%

Three of the flush cards are already taken, so 10 are left to be helpful, 46 unseen cards remain, they must have one of these as well as another helpful card, so 9 helpful cards remain out of the 45 unseen.

Thanks for the help, I hate this situation.

 

[dacruick]

so there are 7 cards that you can see. You have 2 cards, and there are the 5 community cards. Let's say that 3 of these 7 are hearts. that means there are 45 cards left, and 10 of them are hearts. So what are the chances that your opponent has 2 of the 10.

I think it would be 10/45 * 9/44. And I get the answer 4.5%. This seems like a reasonable number. But this type of math is pretty useless in terms of poker simply because him having 2 hearts would be a reason to be in the hand to begin with.

EDIT: This could be flawed though. I did it backwards in the terms that I "drew" your opponents cards after the river. Maybe you would find the right answer if you found out the chances of having a suited pair, and then multiplied that by the chance that the suited pair suit comes up 3 times in 5 cards. In any case though, I'm sure 4% is close.

 

[Fredrik]

No matter what the correct probability is (I haven't thought about it), the result tells you nothing about how you should play in these situations. If we're talking about no limit hold'em, if he calls your bet on a Qxx flop with two diamonds, the turn is a third diamond, and he bets both the turn and the river (or raises your turn bet and shoves the river), the probability is close to 1.

 

[morrowcosom]

In the course of the game, the probability does matter. It is a great time to bluff or be bluffed. I have been bluffed and bluffed with it. Ex. Raise like hell on the third diamond when I have a two pair, and the price is right.

For me, their is always comfort in knowing statistics.

 

[Fredrik]

In the course of the game, the probability does matter.

It really doesn't.

It is a great time to bluff or be bluffed. I have been bluffed and bluffed with it. Ex. Raise like hell on the third diamond when I have a two pair, and the price is right.

You're bluffing with two pairs on a three-flush board? Why? To fold out sets? Or did you mean that you're betting/raising for value to get called by one-pair hands? It's a bad idea to try to fold out sets and small flushes because you usually don't know if he's capable of folding them. (Also, if the pot is small because you both checked one street, they're a small part of his range). It's also a bad idea to raise for value, because very few people make hero calls with one-pair hands there. You have to be sure that the opponent is a complete maniac to even consider it.

 

[dacruick]

It really doesn't.


You're bluffing with two pairs on a three-flush board? Why? To fold out sets? Or did you mean that you're betting/raising for value to get called by one-pair hands? It's a bad idea to try to fold out sets and small flushes because you usually don't know if he's capable of folding them. (Also, if the pot is small because you both checked one street, they're a small part of his range). It's also a bad idea to raise for value, because very few people make hero calls with one-pair hands there. You have to be sure that the opponent is a complete maniac to even consider it.

This is all too speculative for me to even weigh in on. Any poker player that doesn't consider probabilities to augment his/her game is probably not helping their cause. You have to use intuition, psychology, probability, and pot odds to be the best player you can be.

Unfortunately, I find in this particular flush scenario, probabilities are out the window. This is one of those where he either has it or he doesn't. In terms of a heads up all in call though, probabilities are a great tool