Wednesday, August 19, 2009

Analyzing NLHE:TAP Concepts 1-2

This is the first in what I'm hoping will be a series of discussions of the "Concepts" section of No Limit Holdem by Sklansky and Miller. There are 60 concepts total. Today I'll look at the first two.

Concept No. 1: When in doubt, bet more.

Right off the bat, I have to say I'm not a big fan of this one. My main problem is that it's not really clear what this means, although the discussion in the book gives some clues.

Taken literally, this concept suggests that it is always best to just push all-in: since there is doubt inherent in every poker situation (even with the nuts, it's not clear how much is best to bet), we should always be betting more than any given amount X, unless X is all-in. I know this is not what they are trying to say, so I guess we should not be taking this concept so literally.

Taken more figuratively, I can see two reasonable interpretations. One is that players are generally inclined to bet less than they should, especially when they are in a lot of doubt as to how much to bet. I think this is good advice, actually. Beginners, especially, tend to bet far too little (compared to what would maximize EV), and one reason for this is probably that they doubt themselves. However, in my experience, lots of intermediate players tend to bet too much when they are in doubt, trying to end the hand immediately. In any case, I don't think this is the interpretation that Sklansky and Miller were thinking of, either.

Judging by the discussion in the text, I think the authors are saying that the EV lost when betting too little is worse than the EV lost when betting too much. "Try to err on the big side," they say. "In general, you're better off betting a bit too much than you are betting a bit too little." These comments suggest that there is a bet size that maximizes EV, and I whole-heartedly agree with this. I also agree that it can be difficult to determine this bet size (usually, it's impossible). However, I do not agree that a player should stray from the bet size that he thinks will yield the greatest EV. They say: "try to err on the big side." I say: "try not err." If trying to decide between betting $X or $X+1, the authors suggest you bet $X+1. I suggest you choose whichever seems better!

There actually are situations where there rules might not allow you to bet the amount you think is optimal. For example, you might want to bet $17.50 in a game where you are required to bet in increments of $5. So what is better? Betting $15 or $20? Honestly, I don't know, but this concept suggests you should bet $20. Let's come up a sample situation. I doubt this will be very fruitful, but sometimes this can help to get a better idea of what's going on.

Suppose I'm bluffing into a $30 pot, and would like to bet $17.50 because I think I would win the pot 50% of the time with this bet (EV = $30*.5 - $17.50*.5 = $6.25). However, the rules require $5 increments, so I'll bet either $15 or $20.

Suppose betting $20 will win the pot 52% of the time. Then EV = $30*.52 - $20*.48 = $6.
Suppose betting $15 will win the pot 48% of the time. Then EV = $30*.48 - $15*.52 = $6.60.

Oops! my example broke because betting less than my supposed "optimal" amount was actually better than "optimal." Of course, these numbers are entirely dependent on my approximations of folding rates, but it doesn't look too good for the "bet more" philosophy!

Now let's try those same numbers again, except now I have a hand that I think beats my opponent 90% of the time.

My supposed "optimal" amount is still $17.50.
50%: my opponent folds and I win the $30 pot.
40%: my opponent calls and I win $47.50.
10%: I lose $17.50.
EV = $30*.5 + $47.50*.4 - $17.50*.1 = $32.25.

Betting $20: EV= $30*.52 + $50*.38 - $20*.1 = $34.60.
Betting $15: EV = $30*.48 + $45*.42 - $15*.1 = $31.80.

Once again, my example broke, but this time betting more had a higher EV than my supposed "optimal" bet size of $17.50. I have to admit that if these numbers were correct, I would do better betting $20 than $15 in general, but I think the real issue here is that I should have made my opponent more responsive to changes in bet sizes so that my examples actually made sense (maybe I should have used 55% and 45% instead of 52% and 48%). In any case, I think it's still an open question whether it's better to "err on the big side," but I still say it's better not to err at all if you don't need to!

Concept No. 2: Don't give action to tight and trapping players. Know who not to play big pots against.

I think we can all agree with this very straightforward advice. Tight players tend to have better cards, so you must be careful! I'm not sure why this was worthy of it's own "concept" on the list, but I suppose it is a common mistake people make.

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