Sunday, September 2, 2007

Gap theory

David Sklansky first described the theory in his seminal tome on tournament poker.

"It requires a much better hand to call a bet or raise with than to make a raise with."

In tournament poker, the two governing facts are that when you run out of chips, you lose, and that when you're opponents run out of chips, they lose.

Here's an example of the gap theory at work:

Full Tilt Poker Game #_: $10 + $1 Sit & Go (_), Table 1 - 100/200 - No Limit Hold'em - 11:54:17 ET - 2007/09/02
Seat 1: villain AO (1,765)
Seat 4: hero (4,890)
Seat 6: (2,980)
Seat 9: (3,865)
villain posts the small blind of 100
hero posts the big blind of 200
The button is in seat #9
*** HOLE CARDS ***
Dealt to hero [Jc Tc]
Seat 6 folds
Seat 9 folds
villain raises to 400
hero calls 200

Suited connector in position. Let's see a flop.

*** FLOP *** [9s Qc 3s]

Nice. There's the straight draw.

villain bets 600

That's a continuation bet. He could have any two cards. It would have been more convincing if he had done a stop-n-go (that is, bet all-in on any flop). That would have been a very hard call with just an outside straight draw and backdoor flush draw. I probably would have had to lay it down. Instead...

hero raises to 1,365

There's the gap at work. I have an outside straight draw. By straight pot odds, that's not a correct play. But tournament dynamics are different. I am betting his life (not mine) at 2:1 odds. Though he looks pot committed, the kicker here is that if he loses, he is out on the bubble (if he wins, everybody at the table will have about the same sized stack, so really all I am risking here is my chip lead). That gives him extra real money fold equity. And yet...

villain calls 765, and is all in
hero shows [Jc Tc]
villain shows [Jh As]

Yes, his ace-high is the best hand at this point, but unless he was totally convinced that his ace was good (I'd been playing the back half of this tournament fairly aggressively, so it's not entirely out of the question that he might have thought it), it was an amazingly foolish call. I did call a pre-flop raise. There's no way I had, oh say, AQ? maybe QK? Heck, even AK has him beat (though AK in that spot would probably have folded to the post-flop bet).

*** TURN *** [9s Qc 3s] [6h]
*** RIVER *** [9s Qc 3s 6h] [8d]
hero shows a straight, Queen high
villain shows Ace Queen high
hero wins the pot (3,530) with a straight, Queen high
villain stands up
*** SUMMARY ***
Total pot 3,530 | Rake 0
Board: [9s Qc 3s 6h 8d]
Seat 1: villain (small blind) showed [Jh As] and lost with Ace Queen high
Seat 4: hero (big blind) showed [Jc Tc] and won (3,530) with a straight, Queen high
Seat 6: didn't bet (folded)
Seat 9: (button) didn't bet (folded)

Now at this point, our villain starts berating me in the chat window. That, more than anything, is what earned him a blog post. But still, it's worth bringing it up.

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