Races - sometimes it's not a coinflip

I've been thinking about this scenario a bit:

Full table, 3 limpers. Someone pushes and you look down at AK. Call or fold?

A lot of the time the guy pushing will have a PP lower than kings. So it'd be a race. What I think changes the odds in favor of folding is the limpers, because some of them are likely to have aces or kings in some form and that will limit your chances of improving.

Let's say that one of the limpers has a small PP. One has a weak ace and one has a decent king. They'll all fold their hands no matter what. But you're down to 4 outs to improve now and that means you're a 2-1 dog in the hand if you call.

So... dunno if I'm seeing ghosts. Just something to think about. The math behind the coinflip of races assumes that the overcards have 6 outs. Sometimes they don't and to me limpers would signal that it's likely that I don't have 6 outs.

The limpers could have small PPs, they could have suited connectors.

Actually, I suspect that the most significant thing that you can say about the dead cards in this situation is probably that the people who didn't limp are pretty unlikely to have an A, so your odds are probably slightly better than they normally are.

The important thing to note here is that it's very rare to find a situation in which dead cards should be considered in preflop decisions because you can't define your opponents folded hands that well.

You didn't give stack/blind sizes or position in the tournament, so nobody can tell you if you should call here, but assuming nothing very out of the ordinary, folding AK here's pretty bad, and folding AK here because you're your outs are dead is horrible.

[jcm4ccc]

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I've been thinking about this scenario a bit:

Full table, 3 limpers. Someone pushes and you look down at AK. Call or fold?

A lot of the time the guy pushing will have a PP lower than kings. So it'd be a race. What I think changes the odds in favor of folding is the limpers, because some of them are likely to have aces or kings in some form and that will limit your chances of improving.

Let's say that one of the limpers has a small PP. One has a weak ace and one has a decent king. They'll all fold their hands no matter what. But you're down to 4 outs to improve now and that means you're a 2-1 dog in the hand if you call.

So... dunno if I'm seeing ghosts. Just something to think about. The math behind the coinflip of races assumes that the overcards have 6 outs. Sometimes they don't and to me limpers would signal that it's likely that I don't have 6 outs.

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Well, let's say that it's true that two or three limpers means that you lose two of your outs with AK.

In a full table of ten, there are 18 unseen cards (9 opponents). So if you know that there is only one A and one K among your opponents, then your odds improve to hit one of your outs:

1-((28/32)*(27/31)*(26/30)*(25/29)*(24/28)) = 51.2% chance of hitting an Ace or King by the river.

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Well, let's say that it's true that two or three limpers means that you lose two of your outs with AK.

In a full table of ten, there are 18 unseen cards (9 opponents). So if you know that there is only one A and one K among your opponents, then your odds improve to hit one of your outs:

1-((28/32)*(27/31)*(26/30)*(25/29)*(24/28)) = 51.2% chance of hitting an Ace or King by the river.

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Nice.

If you assume that your opponent (the guy that pushed all-in) has a lower PP, then - on average - the other guys will have 2 aces or kings (6/48*16).

So if the other players have 2 aces/kings, the odds of hitting an ace or king are the 'usual' 48%.

But yeah - the only situation where the odds change is when you can put the rest of the players on more or less than 2 aces/kings. And that sounds impossible. So I'll stop worrying about it and just call... [img]/images/graemlins/smile.gif[/img]

What sparked these thoughts is a 3 way all-in where I and another guy both had AK and the third had QQ. That looked pretty bleak for us until we made a straight to split the pot...

[ansky451]

You are not seeing ghosts, you are simply ignoring all the variables. If you are going to count all the limpers and assume some of them folded an ace, then you have to count what cards the players who folded are folding.

[Sam T.]

If I'm at ~15BB and there are three limpers to me on the button I'm shoving AQ, AJ, even ATs. Please, God, let the SB fold his AK.

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If I'm at ~15BB and there are three limpers to me on the button I'm shoving AQ, AJ, even ATs. Please, God, let the SB fold his AK.

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[img]/images/graemlins/smile.gif[/img].

I haven't been watching the WSOP, but wasn't there a hand where someone (Matusow? Hellmuth?) folded AK in this spot because he thought another player in the hand held one of his A's, making him a dog in a race. I remember thinking when I first heard this that it seemed wrong for the reasons mentioned above- was there more to that hand, or did the pro in question just use some bad reasoning?

I think you can safely say that you're in better shape with AK if the people in early position have all folded rather than limped in this scenario. But to say that the rest of the people at the table hold more or less than 2 aces/kings sounds foolish since most people will fold weak aces and kings 100% of the time from EP.

Maybe I'll try doing some empirical work. Count the numbers of folders/limpers before someone opens. And then see if A/K hits the board. Could be interesting to see if there's some sort of correlation.

Anyone know of something that can capture hand histories automatically on Pokerroom?