Friday, February 29, 2008

Theory of Poker and mistakes

Somebody asked about the two mistakes in Theory of Poker.

First is the Fundemental Theorem of Poker. It's not fundemental, it's not a theorem, and it's not about poker.

It basically says that if I have KK and you raise for all the chips and I know you have AA, KK, QQ, JJ and each of those possibilities is equally likely then I've made a mistake if I call and it turns out you have AA.

It's results oriented, it says it's a mistake to act on what you actually know, it has nothing to do with expected value. It's wrong.

The other error is David's idea about playing hours, not results. He claims that if you have an overall expected value of $1 per hour and you play 10 hours then you've earned $10 no matter what the actual outcome.

That's wrong on so many levels it takes more than a single blog post to discuss it. It's just an absurd idea.

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Blogger Dr Zen said...

Hmmmm. The FTOP is only a way of describing what we're trying to do. We tend to think in terms of whether we're inducing "mistakes" from a range of hands, so that against an opponent who can have that range, our bet is good. You can think of it as 3/4 your mistake to call and 1/4 mine to bet, if you wanted. Hey, I should write a book, because that was pretty good.

I know you differ from him on the playing hours thing, but how do you reconcile long-run expectation with what happens right now? Say I'm playing limit, I'm on the turn and I face a bet and close the action. The pot is 4.5BB and I have the nut flush draw on an AcQc5s9h board. I'm pretty sure my opponent has top pair. I think he will check and fold the river if it flushes (just to make it simple). Now, I call because this is a good bet for me *in the long run*. On this occasion, I'm more likely to lose than win. But over the long run, I will hit my flush a bit less than once in five times. The river comes a heart, so I lose my bet, but I still feel good about taking it, no? I can see both sides of it: I lost one big bet by calling, but I made whatever in the long run, so long as I call every time I have the best of it. I'd love for you to write a longer, more detailed post about why you so strongly don't like the notion that you make your expectation per hour, even though you lose.

1:15 AM  
Blogger phlash74 said...

The FTOP says that if your action would change if your opponent turned his hand faceup, you lose by taking that action. Yet you lose much more by tailoring your action to a specific holding than to the situation (position, your opponent's play, your opponent's image of you, etc.)

As far as the hourly expectation goes, the major mistake in my opinion is thinking that results follow expectation. Expectation is generated by results, not the other way around. You can "expect" to win every time you sit down, but if you lose every session, your expectation is clearly inaccurate.

Also, the other problem with expectation is that it is based on results generated by game conditions that might not be present now. It might be the same limit at the same casino, but you aren't ready to play your best for whatever reason. Just because you beat that game for $x an hour before doesn't necessarily mean you will earn $x an hour for the session you're about to play. Relying on expectation can lead to self-delusion about bad results, thinking they are just the result of running badly.


1:19 PM  
Blogger DMW said...

phlash74 I concur.

The results based thinking over at 4 is getting to be some kind of ideology.

Example, I got back from AC today and talked to one of the internet pros, who has been a graet winner online. I grumbled "the 1/2 nl games at AC were so tight, I have no idea how you beat them." He told me that I would need to play at least 10,000 hands to figure out if I was winning or not.

6:43 PM  

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