Sunday, December 27, 2009

Analyzing NLHE: TAP Concept 58

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 58: Any strategy relatively close to a game theoretical strategy is at least almost as good as the optimal strategy, and sometimes it's better.

Sklansky and Miller are a little messy with their terminology here, but I think they get their point across. The way I interpret this concept, I agree with the authors. Here's my interpretation: even if you don't know precisely what the optimal play is (and you probably don't), it's still worth trying to approximate it. Playing a strategy that is close to "optimal" (that is, unexploitable) is almost always better than playing a strategy that is not close to optimal. Furthermore, if you have identified exploitable weaknesses in your opponents, it can, in fact, be better (in terms of EV) to deviate from the optimal strategy. One problem I have with this idea is that there probably is no mathematically "optimal" strategy in games with more than two players... but I think the main idea still holds up.

I disagree with the last two sentences of the books discussion. It says: "If you plan to make a play that will give away your hand, choose a different play occasionally and make the same play sometimes with a different holding. If you do this consistently as you play, you'll usually do even better than the game theoretical strategy."

First, I don't agree that you should necessarily change anything just because you plan to make a play that will give your hand away. Hopefully, you've chosen this particular play because it maximizes your EV, so changing it can only reduce your EV. S+M suggest either choosing a different play occasionally (but assuming that you've chosen the play that maximizes EV, changing will lose you money), or making the play sometimes with a different holding (I suggest you only do this if you can do so without losing any EV with this other holding). I've discussed before why I don't like the idea of making certain plays "occasionally."

Second, S+M suggest that as long as you think about what your range and your opponent's range is, and you mix up your play, you can do better than the game theoretically optimal strategy. I doubt that this is true unless your opponents are tremendously weak. The problem is that it's impossible to avoid making mistakes, so very few people would ever be able to do better than if they could consistently play an "optimal" strategy. However, if your competetion is weak enough, you can probably find enough opportunities to exploit them to make up for all of your mistakes.

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