I'm re-reading ToP for the umpteenth time, and had a situation last night that got me to thinking. I'll post the hand when I get home from work.

Here's my hypothetical scenario:

NL holdem and you've got AA on the button with one opponent. Flop was Ac8c9d. Opponent bets 1/3 pot, and lets say he's been known to bet his draws, so you're pretty sure he's on a flush or open ended straight draw(maybe both). Say there was 9XBB, and he bets 3XBB.

First question: How big do you raise?

With a this draw, I'm wanting to either drive him out, or make him pay big for his flush. I'd usually go with somewhere between 1/2 pot and pot size raise, depending on what I think he'll call. That would be a 6 to 12 X BB raise. I now think this is wrong according to Sklansky's Fundamental Theorem.

Basically, I want my opponents to make mistakes, ie act differently than they should if they could see my hand. If my opponent has at best 15 outs, he has about a 31% chance of hitting, or close to 2:1 odds (1/3 of the time he hits, 2/3 of the time he doesn't) of hitting on the next card. A half pot raise faces him with call 6XBB to win 18XBB, or right at 3:1. He's gotta make that call, and he's correct in doing so. The person making the mistake is me, because if I knew he had 15 outs, I should raise enough to make it wrong for him to call. In this case thats somewhere bigger than the pot.

Note this gets worse if he figures to stay for two cards, but lets not go there yet.

Second question: What is the correct action if his remaining stack is less than the pot? You basically can't make him make the mistake. If he calls, he's doing the right thing according to Sklansky, I think. So what is the correct action on your part? All "play the player" considerations aside (some people just wouldn't call, regardless of the math, if it was going to bust them), shouldn't you just call?

You can't fold, your odds of winning are 1:2(69%), and you're calling 3XBB to win 12XBB. This doesn't even consider the fact that the board could pair, making you unbeatable. Plus, that just sounds stupid.

If you raise, you're putting more money into a pot when it is correct for your opponent to call. So you're only choice is to call, right?*.

Third question: Now assume its you who can't cover the pot bet. Say your stack is only 6XBB, for a piddly raise of 3XBB. I don't think that changes very much, but it points out the importance of keeping as much money on the table as you can. Without enough money to make it incorrect for your opponent to call, you are allowing him to stay in the pot without making a mistake.


*Note, this I really think this is the wrong answer. You're basically making the bet that you will win the pot. Anymore money you put in the pot is a good bet. You're betting one for one with a 69% chance of winning at that point. You should take that bet everytime.