K,K under the gun

[Pat C]

$6/12 B & M. 9 handed very loose not too aggressive. I'm UTG with K,K and raise. Fold, fold, call, call, call..sb and bb call, 6 to the flop. Played for about 1 1/2 hours with everyone at table and I know those who called could be holding any two cards with the exception of CO whom likely holds a big hand. Flop is rainbow Q,9,7. check, check..I bet .. fold, call, call, call, call. 5 to the turn with this board? I believe I'd of already heard from someone holding two pair; maybe one or two players holding top pair with the rest drawing. Turn is a 3. check, check, I bet...fold, fold, fold, fold, b.b. check-raises. What's my play from here? B.B. is a weak player and has yet to check raise in last 2 hours I've played with him.

[Homer]

Here is what would be going through my head:

I'm getting 11:1.

I'm almost definitely behind.

This dude hasn't check-raised in two hours.

Would he check-raise me with two-pair or only a set?

If he has two-pair, I have 8 outs and am around 4:1 or 5:1 against.

If he has a set, I'm drawing dead.

Therefore, if he has a set more than ~55-60% of the time I should fold.

This is pretty close. I think I'll call and fold to a river bet if I don't improve because folding isn't fun, plus I don't want people to see me folding to a turn check-raise and start running me over.

-- Homer

[BottlesOf]

Hi Homer-

Can you explain where you get 55-60% from?

[Pat C]

he did have two pair...Q,3 if you can believe that behind a raise...but i guess you really have to like that type of a call. curious how you figured the outs...i had me at 5 outs if he had two pair...2 kings and 3 from the other card card on the board he didn't hold...and of course only 2 if he held a set. maybe i counted them incorrect. but at best i figured i had a 1:9 shot of hitting while getting around 11:1 on my money to call...so after thinking about it for a spell, i called the turn. i called the river too, but that was out of curiosity.

[Homer]

curious how you figured the outs...i had me at 5 outs if he had two pair...2 kings and 3 from the other card card on the board he didn't hold...

The board is Q973, you have KK and he has Q3. You win with a rivered K (2 outs), 9 (3 outs) or 7 (3 outs), for 8 total outs.

and of course only 2 if he held a set.

Oops, yes you have 2 if he holds a set. I wrote 0 for some reason.

but at best i figured i had a 1:9 shot of hitting while getting around 11:1 on my money to call

Where did you get 1:9? If he has two-pair, you have 8 outs out of 44 cards. So, you are (44-8):8 -> 36:8 -> 4.5:1 against. Getting 11:1 is plenty overlay if you know he has two pair.

i called the river too, but that was out of curiosity.

If you plan to be a long-term winning player, you shouldn't do this. Only call the river if you think you are better than 13:1 to win the hand (~7% chance).

-- Homer

[Homer]

If his opponent has two-pair he's 4.5:1 (18.2% chance) against and if he has a set he's drawing dead (actually I made a mistake, he has two outs in this case, but for now I'll just pretend he had 0 outs to show you what I was thinking). He's getting 11:1 (8.3%), so his opponent needs to have two-pair at least 8.3/18.2 =~ 8/18 = 44.4% of the time, which means he needs to have a set no more than 55.5% of the time to justify calling the turn. This isn't exactly right because it doesn't take into account times when he'll make two-pair on the river and still lose to his opponents set, but it's close to correct. Also, since he actually has two outs when his opponent does have a set, the percentage is a little low (his opponent can actually have a set a little more often).

It's best to take out pencil and paper and work out all the possible combinations of what can happen [(1) makes two-pair on river, loses to set; (2) makes set on river, beats set; (3) makes set on river, beats two-pair; (4) makes two-pair on river, beats two-pair], then work backwards to get an exact answer of what odds are required on the turn based on how likely it is that your opponent has a set versus two-pair. Then, when you're playing and someone check-raises your overpair on the turn, you won't have to do much thinking other than: (1) How likely is it that he has a set? AND (2) What odds do I need to call given that he has a set.

To be honest, I've never worked out these calculations, but I'm sure there are people out there who have, and they have an extra advantage over us (albeit a small one, though if you go through these calculations for all kinds of situations it adds up) because of it.

-- Homer