Practical Application of Morton's Theorum?

[12AX7]

OK, I see a lt of discussion on Morton's Theorem going on...but what should I do to how I play as a result? I was thinking it meant I should push hard if I think have the best draw in a multiway pot...but perhaps not push hard if I had the large pair. Now I'm not so sure. After all, the EV of AA goes up as the number of callers increase, even though the winning percentage goes down. I.e, the additional caller's money more than compensates for the additional risk. Perhaps there is some made hand below which this is not true? Of course there seems to be another strategy problem here. If AA has higher EV against many callers, why would I ever raise with it and drive oponents out?

[Ed Miller]

After all, the EV of AA goes up as the number of callers increase, even though the winning percentage goes down. I.e, the additional caller's money more than compensates for the additional risk.

I'm not going to address your whole question (mostly for lack of time), but I did want to address this one. This is true BEFORE the flop, but not necessarily AFTER it.

The reason it changes between the first two cards and the flop is that you will sometimes flop a set with AA. A set is a STRONG made hand and benefits tremendously from a multiway pot.

People often think of the big pocket pairs as only made hands... assuming that they will still have only one pair after the flop. These hands are as strong as they are because SOMETIMES YOU FLOP A SET, and those times you don't, you still have a good pair.

[Monty Cantsin]

Morton's Theorem (please note: no u) says that there is a specific range of pot sizes and number of opponents where you actually want your opponents to fold, even though that fold is correct. It's a curious and beautiful little fact, but it doesn't really have much of a direct impact on how you play your hand.

Ed really covers this very thoroughly here.

If you are currently playing perfectly, and are interested in squeezing out that extra .01 of EV from your weak made hands in those situations where your x-ray vision and mind reading ability indicate you are in a Morton situation, then start adjusting. Otherwise, you probably have more to gain from mastering the more basic axioms of poker, such as bet when ahead. I know I do.

/mc

[Dov]

As David points out in TPFAP, sometimes the most positive EV move isn't the best one. This happens when your odds of winning are lower.

It is very situation specific, though. For example, if you are on a short bankroll, you would want to avoid close gambles, even if they are EV+. (Provided that losing the bet will put you out of action)

[12AX7]

Hi Ed, good point. Not sure if this changes the thinking any...but when I wrote the quoted statement it was based on monte carlo sims done to the river, a long time ago. I think I recall that AA against 1 caller won about 80%. Against 10 callers about 30%. I concluded that (.30 * 10) > (.80 * 1) or 3 > .80 thus I'd never want to chase callers out of the pot. On the other hand, I never did figure a way to actually dtermine if knocking some callers out would help or hurt the EV. At the time I had the Workware HE emulator but had not coded up any opponent strategies to test the value of raising opponents out. Someday, when I get another PC, guess 'll continue that research. Don't know where I'll get that particular simulator again, but thenperhaps the Turbo series would work as well. No experience with it though.

[pdubz]

Not sure if this the same thing that Ed Miller was saying, but the reason you need to raise preflop to force hands out is to get money in when you know you are ahead and force drawing hands out, or at least make them pay to play. The problem in your logic is that it assumes all-ins down to the river; however hands like 9Ts are only calling the flop if they have draws, and pocket pairs only if they've hit sets. If you don't raise preflop, 25o from the blind could hit say a 25K flop. Though you were ahead preflop, you are behind on the flop and yet you don't know it -- and may end up paying them off a lot of money. Now if you could get everyone all in preflop with AA everytime, that would be awesome [img]/images/graemlins/wink.gif[/img] but the fact is you need to know where you stand on the flop, the turn and the river. Raising preflop hopefully gives you that required information.