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... /images/graemlins/smile.gif

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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/images/graemlins/smile.gif.

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?

You want 6 outs out of 48 cards (12.5%) ( you discount your cards and Vilain cards).

Thinking the way you do, you have 4 outs, but the other players have 2 * 7 cards so you have 4 outs out of 34 cards (.118%). If One of them has a PP, you have 5/34 = 14.7%.

I hope this is clear for you. You are seeing Ghosts!!!

[ansky451]

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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?

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You will need a substantial sample size for this to work.

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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?

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You will need a substantial sample size for this to work.

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Somewhere on the order of 100k hands, maybe "only" 50k in which this exact scenario happens'd work.

It's much easier to just write a computer program that simulates this scenario, fixing your hand and your opponent's hand and keeping the other players at the table random. Give them different limping/raising/folding standards (a raise should just make the program throw out that set of data, as it completely changes everything) and see how your odds change.

Someone actually did just that with a similar problem known as the bunching effect and managed to show that it was real but completely insignificant. I don't remember who it was, but it was a card player article, so you could look through card player's archives (cardplayer.com) to see.

Please let this thread die now.

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Somewhere on the order of 100k hands, maybe "only" 50k in which this exact scenario happens'd work.

It's much easier to just write a computer program that simulates this scenario, fixing your hand and your opponent's hand and keeping the other players at the table random. Give them different limping/raising/folding standards (a raise should just make the program throw out that set of data, as it completely changes everything) and see how your odds change.

Someone actually did just that with a similar problem known as the bunching effect and managed to show that it was real but completely insignificant. I don't remember who it was, but it was a card player article, so you could look through card player's archives (cardplayer.com) to see.

Please let this thread die now.

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100K hands is way to much for something like this. When I took a statistics class, I remember being surprised at how small sample sizes you needed before you could deduct stuff. And if you're interested in finding out if an A/K drops based on the ratio of folders/limpers before the pot is raised, there isn't much variance. So the numbers should converge pretty quickly.

I did the analysis on a tourney I had lying around. There seems to be a rather large correlation. When an A/K drops on the flop there was a lower limper/folder ratio. But you seem to think I'm a crackpot, so I'll go away now /images/graemlins/smile.gif

Matusow called in raise situation with a pp because he (correctly) thought both of his opponents held aces limiting their outs. Is this the hand you're thinking of.