Saturday, February 27, 2010

Sixty percent of the time, it works every time

In the last post, I described a hand I witnessed where a player gave up a known 3-1 edge, for fear of getting sucked out on. But 3-1 is merely the smallest edge he could have given up.

Mr. Meek hasn't fully grasped the concept of fold equity. If a player is going to fold some percentage of the time, then you are going to win all of those hands.

When Brian Fantana said "60% of the time, it works every time" in the movie Anchorman - he wasn't talking about Sex Panther cologne - he was talking about fold equity. If I make a big bet, and I think my opponent will fold 60% of the time, then I win every one of those pots - 60 out of 100.

So let's review. My opponent has accidentally revealed his cards - he holds King Queen. I hold Ace-Jack. The board is eight-nine-ten rainbow, and I'm a 74% favorite to win the hand if it gets to showdown. What if I shove all-in though? Will my opponent call with a gutshot straight draw and two overcards?

We don't know that answer. He might. He might be feeling embarrassed about revealing his cards, and now he just wants to get out of there. Or maybe he's willing to call all in trying to hit the jack for the nut straight. We're not sure. But we do know that most reasonable players would have to fold this hand, because that's the correct poker play. So let's say this player might call 20% of the time for whatever reason.

If he calls 20%, that means he folds the other 80%. When he folds, we win 80% of the time, every time, just like Brian Fanatana said. The 20% of the time he does call, we will win 74% of those hands. Do the math and it adds up like this:

0.80 + (0.20 * 0.74242) = 95%.

Read that again - I will win the pot 95% of the time if I push all in here, assuming he calls off his stack 20% of the time with a straight draw and 2 overcards.

You might argue that 20% is too low - maybe the situation and his embarrassment makes him call more often. Well, here are the percentages we will win based on the percentages he will call, in 10% increments: (click to embiggen)

So even if our confused villain calls off his stack half the time in this situation (an almost ridiculous assumption) - we will win the pot a total of 87% of the time. 87% is more of an edge than pocket aces have over a random hand. And if you make the villain's call percentage something more realistic, like maybe 20-30%, the percentage of us winning only gets bigger - north of 90%

To conclude, when you add any reasonable amount of fold equity, failing to push all your chips in the middle with AJ, on an 89T rainbow board, when you know your opponent holds king-queen offsuit, is a bigger mistake than folding aces preflop.

Or, as I called it before, the worst poker play I have ever seen.

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