Bet sizing

The basic principle is to give the other player the hardest decision possible. This is aggressive play, and results in the maximum number of errors by the other player, thus the maximum profit to you. With a bad player, you may instead try to give them what should be an easy decision that you expect them to get wrong. This is more profitable than giving them a hard decision, because a wrong hard decision generally them costs less than a wrong easy one. But good players always get the easy decisions right, so you have to give them hard decisions in order to win.

Note that I'm only talking about the pure bet size decision here. You've already decided on your basic strategy. For example, it's sixth street and you show three hearts, while the other player paired her first up card. You think she has three of a kind, and nine out of the thirty-six cards you haven't seen will give her a full house.

You think this through and decide you'll go all-in on the river, whether or not you have the flush or get one. You think she'll call if she gets the full house, and fold if she doesn't. Since she will get more information from the next card than you will, you want more money in the pot now. But since you have a 75% chance of winning, you'd like her to call your bet.

If she figures the situation the same as you do, she has a 25% chance to win the pot plus your stack and a 75% chance to lose whatever bet she has to call now. Say the pot is $2,000 and your stack is $10,000 and hers is bigger. A 25% chance of winning $12,000 is worth $3,000, which is the same as the 75% chance to lose $4,000. So if you bet $4,000, she has a hard decision. If you check or bet a small amount, she has an easy decision; also if you go all-in now.

Of course, in real poker it's always more complicated than this. Maybe she already has the full house, or maybe she only has the one pair. Maybe she doesn't believe you have a concealed heart. Maybe she's on tilt, or too timid to take a chance. All sorts of other considerations can apply, so you seldom do a mathematical computation like the example above.

The idea is to first put yourself in her shoes, bet sizing has little to do with your hand or what you think of her hand; it has everything to do with what she thinks of your hand. Second you think about how she expects you to play the hand, and based on that, what bet gives her the hardest decision now.

For each bet size, there have to be at least two possible meanings, otherwise your bet gives away your hand. So you can't only think of this hand, you have to think of what else you might have for which you would make the same bet, but want her to make a different decision.

For this purpose you can divide things up into half-pot-sized bets, pot-sized bets, bets of two or three times the pot, and all-in bets. Suppose the other player to folds about the fraction of the time that the bet is a fraction of the pot plus the bet, that is one-third of the time to a half-pot sized bet, half the time to a pot-sized bet and so on. That means you're getting full value of your bet from fold equity, you would never have to win at showdown. That would mean you're too tight, you should add more weak hands to this bet size. If the fold fraction drops to less than half the value above, you can probably improve your profit by adding more strong hands.

(Twoplustwo)