Sunday, December 14, 2008

No-limit strategy note: bet sizing

Most poker players have a pretty good understanding of pot odds and outs, and therefore are often able to make a correct decision when deciding whether to call with a drawing hand. My suspicion is that many players do not have as good an understanding of how to correctly size their bets when they are in front - or if they do follow a "pot" or "2/3 pot" rule of thumb, they do not understand *why* it is correct.

I want to discuss briefly how we can judge whether a bet size is correct or not. Let's take a very simple example:

You hold Ah Ks, and the board reads 5h Kh As 2d. There is $100 in the pot, and there is one player left who called your preflop and flop bets. Both players have $200 behind. Let's first ask the question of what your equity is in this pot. To simplify the situation, we will remove implied odds and fold equity from the equation and say that both hands are face up on the table. Your opponent is drawing to a flush (as you strongly suspected) with Th 9h.

You might think that calculating your equity is a simple matter of working out how many cards do not make a flush for your opponent (36 out of 44) abd taking that proportion of the pot (or about $82). That is not correct - your pot equity on the turn is $100, for the simple reason that your opponent should not see a river card. There is a betting round remaining, and you will bet a suitable amount to ensure that your opponent does not have the odds to call. If your opponent calls without proper odds, your equity in the pot will actually increase.

So how much should you bet? In this situation, a bet of more than 8/36 (the ratio of his outs to non-outs or $23 in this case) will ensure that he does not have odds to call. In practice, you would probably wish to bet a fair amount more than this for a few reasons:
  • He may have more outs than you think, such as a gutshot+FD
  • You want to gain a significant amount if he calls poorly - you should make the biggest bet that you think he will call with bad odds.
A more important reason is that in reality you cannot see his cards, and therefore it may be very difficult to fold if the flush card comes. If your hand is so strong that you are not able to fold a dangerous river card, you need to take implied odds into account. In this situation, your opponent stands to gain the pot ($100) plus your stack ($200) if he hits his flush. Therefore, you must ensure that the bet is large enough that the odds offered (8:36) do not give him correct implied odds to call. In this case, $67 is the magic number or $100 if he has a gutshot FD.

In reality, we don't have the time to make very precise calculations about odds and equity so we use "rules of thumb" when we think our opponent is drawing. What is so special about a pot-size bet? A pot size bet offers your opponent pot odds of 2:1 on a call. This in conveniently close to the outs calculation for a big draw with a single card to come like FD+OESD (15 outs), FD+overcards (15 outs if the overcards are clean), FD+small pair (usually 14 outs). Therefore when you bet the pot on the turn, you ensure that only the biggest draw has a marginal call.

Betting on the flop is a bit more complicated due to the fact that there are two cards to come. In general as long as you price out the small draws they will have difficulty in calling given that they face another big bet on the turn if they want to see the river. Betting on the flop, you should not worry too much about the big draws because it is almost impossible to propoerly price them out. For example, a FD+OESD has 15 outs and two chances to hit - which adds up to a 55% raw equity assuming they can see both remaining cards. In other words, a big draw will probably shove the flop irrespective of your bet size.

On the basis of these thoughts, I would regard a bet of 2/3 to 3/4 pot as appropriate if you are not pot committed and the draw is clear. If you feel pot committed due to your hand strength or stack size, then a pot size bet should be the minimum.

This is a fairly simplified analysis which does not consider fold equity or multiple opponents, but I hope it explains my thinking on bet sizes. I'd appreciate any thoughts.

1 comment:

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