Saturday, October 10, 2009

Analyzing NLHE:TAP Concept 15

After this post, I'll be one quarter of the way through the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by Sklansky and Miller.

Concept No. 15: Bet more than usual when your opponent likely has a hand that he thinks might be good.

Taken literally, it seems to me that Concept 15 is useless. A recurring problem I'm having with these analyses is that the concepts are worded so vaguely or figuratively as to lose any clear meaning. In these cases, in order to do my analysis, I feel obliged to parse the concepts into something that both makes some sense and could plausibly be what Sklansky and Miller were trying to say.

Let's look closely at concept 15 to see if we can glean something from it. It starts out "Bet more than usual when..." Okay, so this suggests that in "usual" cases, Sklansky and Miller assume that we will bet within a certain range of amounts, but that in some unusual cases (to be revealed at the end of the concept's sentence) we should be betting more. So far, so good. Let's look at the end of the sentence to find out what these unusual cases are: "... when your opponent likely has a hand that he thinks might be good." Hmm. This doesn't seem like an unusual circumstance. In fact, since we almost never know what our opponent is holding or thinking, it seems to me that it's almost always the case that it's at least somewhat likely that he thinks his hand might be good. Sklansky and Miller's unusual circumstance is actually the norm.

As worded, I don't think the concept makes enough sense to be analyzed. Let's try to salvage it by giving it some plausible interpretation that can be analyzed. Using clues from S+M's analysis of this concept, I think they are trying to say something like: "If you hold the nuts and you somehow know your opponent has a made hand (as opposed to a drawing hand), bet more than you would if you knew he was on a draw." I think this must be what S+M are trying to say; I'm looking back at the book at the chapter on "bet sizing" (p54), and this is essentially the advice given.

The standard here is still too vague because not all draws are alike. If I know my opponent has 21 outs going to the river, he has a 21/44 chance of winning. Then, ignoring implied odds, the correct play is to bet over 10.5 times the size of the pot and hope he makes a bad call (if you don't have this much, just go all-in). On the other end of the spectrum, my opponent might have only 1 out. Here (again ignoring implied odds), you need only bet over 1/43 of the pot. Suppose the pot is $430. In the first case you should be betting over $4515. In the second case you should be betting over $10. So there isn't really a "usual" amount to bet if you somehow knew your opponent was on a draw unless you knew how many outs he had.

Let's refine the advice a little further and say, "If you hold the nuts and you somehow know your opponent has a made hand (as opposed to a drawing hand), make a big bet of around the size of the pot." In the book, one example of a "normal" bet against a draw is 1/3 of the pot, so a pot-sized bet seems like it should qualify as big.

I still don't think this advice is good in general. First of all, you almost never actually know what sort of hand your opponent is holding, so it makes the whole argument moot. Supposing you could know that your opponent didn't have a drawing hand hand, the correct bet size would still depend on your opponent's hand range and your opponent himself. Some players get very suspicious of very big bets because they suspect they are bluffs. Against such players, it really is a good idea to be big with the nuts, but not all players are like this. You also need to consider your opponent's hand range. The stronger his range, the more you should bet. In particular, if your opponent's range is very weak, you should usually be betting almost nothing. This invalidates the advice that you should generally be making a big bet. Sometimes yes, sometimes no.

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