[pzhon]

I like this approach. It applies to other situations, such as analysis of the stop&go technique associated with Greg Raymer, calling from the blinds with about 1 PSB left with the intention of pushing any flop.

I think the main conclusion of this article is incorrect: "if your opponent is acting optimally, it is never better to make a small raise preflop, planning to push any flop and to call any preflop reraise, than it is just to push all of your chips into the center before the flop." For example, I think it is likely for it to be right to do this with AA (and other hands) in some circumstances, even without assuming suboptimal play by your opponent. Here are some problems I have with the analysis:

[img]/images/graemlins/diamond.gif[/img] You are free to make a small raise with other hands without the intention of calling a reraise, or of calling a stop&go on any flop, or of pushing any flop if your opponent checks to you. That I might make a small raise with AA, then call all-in or push any flop, provides cover for the times I might make a small raise with a weaker hand. My opponent does not know that I plan to push the flop with this hand when I make a small raise.

Compare the situation with a multi-round bluffing game. We know I either have the nuts or a bluff. If I push on the first round, I can bluff less frequently than I have the nuts. If I make smaller bets on 2 rounds, then with deep stacks I can bluff almost 3 times as frequently as I have the nuts. When I have the nuts, I will bet and bet again. Some of the time, I bluff once and give up. It is not wrong to bet less than all-in with the plan of betting again on the next round.

In that example, there wasn't a flop that gives your opponent more information, and it was right by a lot to bet on both rounds. The betting amounts may change, but the fact that I should use my option to bet on both rounds is not changed by a modification of the bluffing game that gives you a small amount of information after the first betting round. Maybe you believe there is enough information on the flop in Hold'em to give up the option to bet on multiple rounds, but that would take a separate argument, and I don't agree.

[img]/images/graemlins/diamond.gif[/img] You don't know that the pot will be heads-up against that particular opponent, and neither does a caller who is not last to act. You might get called in multiple places. You might get a call, and then someone might raise, or there may be a reraise and a call. This might add more dead money, or it might give you the information you need to fold. Even if you end up heads up, a small raise might be called by a different player.

[img]/images/graemlins/diamond.gif[/img] "Since she is increasing her EV, your EV must decrease... While the situation above is not a two-person game, she increases her EV by gaining chips from you so this must cost you EV." No, both players may gain if they are risk averse. I believe that was the theoretical justification given by Raymer for the stop&go: It may give up some expected chips against a good player, but it decreases your chip variance. Much of the time, the decrease in variance is not worth much, but it is important in SNGs. See the past discussion of the stop&go in the STT forum.


I like the attempt, but I think the analysis was faulty and I disagree with the conclusion.