Saturday, December 19, 2009

Analyzing NLHE:TAP Concept 53

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

Concept No. 53: In heads-up pots, whether you are first or second to act is more likely to affect your decision in no limit than it is in limit.

I think Sklansky and Miller are having another issue with semantics (or perhaps it's my fault for taking them too literally), but any way I look at it, I can't see the use of this concept. It's also quite awkward trying to judge whether it's true. I happen to think it is true as stated, but not for the reasons the authors were probably thinking of. This post is an almost purely academic analysis of this concept's claim, without much poker insight, so let me apologize. I personally think it's rather interesting, though. First, let's look at the example Sklansky and Miller give.

Their example is that if you have the nut flush draw in limit holdem, you will probably want to bet regardless of whether you are in position. In no-limit, though, you should be much more willing to bet if you are first to act. If you check, they say, you are likely to have to face a bet anyway, so by betting out, you can set the bet-size yourself. If you are second to act, you might want to check to give yourself a free card and a chance to win a big pot.

Well, that is only a specific example. Let's take a step back and try to answer the question: Should your position be more likely to affect your decision in limit or in no limit? Of course, your position is only one of many factors affecting the decision of whether to check or bet. Your hand range, your opponent's range, and your opponent's tendencies are usually the most relevant. Let's imagine holding all of these other factors constant, and distill your "position" down to the following. If you are "first to act" and you check, your opponent has the opportunity to bet. If you are "second to act" and you check, the betting round ends. In either case, if you bet, your opponent has the opportunity to raise. So, in this formulation, you should always (whether you are playing limit or no limit) be more inclined to check if you are second to act, because you gain the added benefit of denying your opponent the opportunity to bet. So, the question simply becomes: Is this added benefit more valuable in no limit or in limit? I think the answer must be "no limit." Giving your opponent the opportunity to bet tends to be much riskier in no limit than in limit, because a bet can be much larger in proportion to the pot. So, denying your opponent this opportunity has greater value in no limit. Thus, I would have to agree with this concept's claim that, in no limit, your position is somewhat more likely to affect your decision than in limit.

In practice, though, we are more likely to bet when we are second to act than when we are first to act. When we are second to act, this means our opponent has checked, which means his range is weaker. When our opponent's range is weaker, we should be more inclined to bet. In my analysis in the previous paragraph, however, we held these hand ranges constant, which led us to the awkward and counter-intuitive conclusion that you would rather check if you are second to act than if you are first to act. This conclusion led me to agree with this concept's claim. However, this is, of course, not the point the authors were trying to make with the concept. This is made abundantly clear from their example about how you would play a nut flush draw, which incorporates plenty of good ideas about poker, but nothing that really addresses the concept's claim. It attempts only to show one specific case where the concept holds, and it fails even that because it does not hold the opponent's ranges constant (the opponent's range weakens after he checks).

I won't address the ideas that Sklansky and Miller were trying to get across in this concept, which they revealed in their example, except to say that I essentially agree with them.

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