8/30/2006

08-30-06 [poker] - 1

It's generally true that in any situation in poker you want to be very aggressive with your best hands & your worst hands, and conservative with your medium hands. This has been proven precisely for some simple poker-like games, but it's very hard to prove with real poker, but we can see intuitively that it's true.

First, think of your hand range as a float value in the interval [0,1]. That is, the "nut low" is a 0 and the true nuts is a 1. Now you're going to fold any hand worse than some threshold F, so you're playing hands in [F,1]. Now imagine this range as divided into 3 regions [F,A] [A,B] [B,1] . The bottom range are you "marginal" hands, hand you want to play but that are just barely worth not folding. The middle range are you decent hands, which beat bluffs and might beat some of his okay hands, but can't stand pressure. The top range are your hands you want to play a big pot with.

My contention is you should take the same line with the "marginal" and the "big" hands (that is stuff in [F,A] and [B,1]) and take the conservative line with [A,B].

One problem with this is if your opponent is really good, anytime you take the conservative line they know you have a marginal hand which lets them "play perfectly" by knowing what you have. This is easily addressed by mixing up your lines a bit. That is, the "big" line might not always mean just leading out big, it might sometimes be a check-raise. Similarly the "ok" hands might sometimes check-call and other times put a blocking bet out.

Let's look at one example : preflop reraising. Say the player on the button opens and you're in the big blind. Stacks are deep so it's not just a shove. You're going to fold hands < F. With hands in the middle [A,B] range you should just call his raise. With your big pot hands (very good and marginal) you reraise. This means you just call with hands like 99 (middling), and you reraise with AA and 22. The reraise with 22 is a semibluff. Mainly you're representing AA, but you could also flop good and make a big hand. It's nice to have this extra value so any time you are doing this before the river it's good to use hands that can improve.

Another good example is playing against continuation bets. Say your opponent raised preflop and continuation bet the flop. Again, some hands you fold, your mediocre hands you just call, and your worst & best hands you raise. Mediocre hands here would be things like top pair without the top kicker, 99 on a T-high flop, etc. Those hands you just call. You raise with hands like two pair, a set, sometimes TPTK. You also raise with hands like 22 that missed its set. As usual you get more EV if you can raise with hands that can improve.

When considering what to do with a hand, you first ask if you should just fold it. For example, 22 on the flop in the continuation bet example may or may not be a hand you should just fold, depending on the board & your opponent. If you do play it, is it better to play as (a bluff), (a small pot for showdown), (a big pot) ? So you classify it in those ranges and play accordingly.

Now, it's my guess that if you look at your range of hands, it should roughly be true that (A-F) = (1-B) , that is the "big" and "marginal" region should be roughly the same size. I have no evidence to support this, it's just a guess. Similarly I guess that it should be true that (B-A) = 2 * (1-B) , that is, the "ok" region should be roughly the same size as the other two regions combined, that is about half the hands you play should be in the "okay" region. In practice, the regions should be adapted to your opponent. For example, if your opponent is a maniac bluffer, you might not use the "marginal" region at all, every hand either becomes a "big" hand or a fold against him since he only plays big pots. On the other hand, if your opponent is a weak-tight nit, he will only play with the nuts, otherwise he'll fold. In this case the "ok" region goes away and your "big" region becomes very small, basically you either have to out-nit him and make an even better hand, or you want to make him fold.

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old rants