Morton's Theorem

Could someone please clarify this for me? As I understand it, this is basically dealing with implict collusion (?). If there are many draws out against one made hand, at a certain point the made hand is losing money by continuing to bet; he is only making money for the draws, who collectively are favorites to beat him.

This may be a wrong interpretation by me. If it is correct, I have heard that the best way to deal with it is to not push your made hand until you see at least the turn. This would be similar to the concept of making "seemingly irrational checks" on the flop with top pair, from the When the Pot Gets Big section of HPFAP (loose games disucssion). If someone has a more correct interpretation I'd like to hear it. I have heard this theorem alluded to a number of times but never fully laid out.

Thanks.


Tim

http://www.loukrieger.com/articles/morton.htm

Say the pot is three way and you bet your top pair on the flop. You believe you are against a good (flush or straight) draw and a bad pair so both your opponents are trying to suck out on ya and the one with the bad pair is drawing very slim.


The opponent with the flush draw calls your bet and now it's on the guy with the fishy pair. He has 5 outs at most and the pot is just small enough that he is NOT getting the right odds for a call. Do you want him to call, as he'll be making a mistake?


Morton's Theorem says that (for certain pot sizes) you want this guy to fold. By incorectly calling with no pot odds he is hurting himself AND you. The best draw is the sole beneficiary of his mistake. Not only that, his mistake took some money away from the player with the best hand.


Of course, this means that in multiway pots you can shove Sklansky's Fundamental Theorem of Poker where the sun don't shine.


This does NOT mean the best hand shouldn't bet in the above example. The best hand is still making money on the bet, but would be better off if the sucker folded his ugly draw.


Angelina Fekali

Studying People Inc.

Ljubljana, Slovenia

http://www.fekali.com/angelina

Thanks to Mike for providing the link to LK's article. Great stuff. And to Angelina who explained it better in laymans term.


IMO the main thing to remember is this. We can try very hard to manipulate our opponents to do one thing or another (fold or call). Sometimes we are successful and sometimes not. But the truth is that our opponents are still going to make the final decision. Our job is still to make correct decisions more they they do. If that means checking the flop with top pair top kicker then so be it.


Then, the next thing to think about is would it be that wrong to give a free card? They are going to call anyway. We'll see what the turn brings. I can save a bet if a scare card comes on the turn. I do not advocate giving free cards with vulnerable hands like top pair, top kicker. Besides if the scare card isn't what your opponent is looking for, it becomes just as scary to them.


KC50

Thanks to all, I really appreciate your responses. It makes much more sense now. Gary Carson really got excited about this theorem in his book and I didn't fully get what he was talking about.


Tim

a greater +EV,checking the flop or betting--assuming one has top pair,top kicker and his

other two opponents have a good draw and bottom pair respectively? Also assume a small pot on the flop.

Thanks

Sitting Bull

Giving free cards is baaaaaad in hold'em and this one is no exception. You should bet, this way the fish with the bad draw at least has a chance to throw his hand away (or maybe the big draw will raise and knock the fish out). If he doesn't you still make money on the bet although you are better of with the fish out of the picture. Morton's Theorem will not change the way you play much, it will only help you understand what's going on in some situations.


I'll try to clarify some more with three pot size examples:


1. If the pot is very, very small, say something like three or four small bets, you want to bet. The bad draw is getting ridiculous pot odds and has no business to continue with the hand. He makes a big mistake by calling and as the pot is not in the Morton Zone, you want the bad draw to call!


2. If the pot is a bit bigger, but just not there yet to give the bad draw correct odds for a call, you again want to bet, but this time the pot is in the Morton Zone and you'd prefer the bad draw to fold. His incorrect call eats into your EV and hands over some of your money to the third guy with the beauty draw. Still, you are earning money on your bet, free card is a nyet-nyet.


3. The pot is huge, both your opponents are getting a good price on a call. Again, you should BET for value (not expecting any folds) and again make some EV there. Of course, you wish they both folded but it ain't gonna happen, keep dreaming. Shrug it off and BET!!!


Bottom line: Bet-bet-bet!!!


There are situations in hold'em where the best hand cannot bet for value and maybe this is where all these passive checking ideas are coming from. Consider the following situation:


You have TsTc on a flop of 8h7h2s and you are against AhKh, Qh8s and 6s5s. In this case TT is the best hand, but cannot bet or raise for value on the flop as it is an underdog to the field (meaning it will win less than 25% of pots, less than the 4-way fair share). It's a situation that can only happen on the flop and not on the turn (the best hand is very rarely an underdog on turn) because there are *two* cards to come. The draws need to hit only once, but TT needs *two* blanks to hit by the river.


It's obvious that you should check your TT, but you are not giving a free card here, you are *getting* one. This has nothing to do with Morton's Theorem, of course.


Angelina Fekali

Studying People Inc.

Ljubljana, Slovenia

http://www.fekali.com/angelina

It seem to have been alwready well explained, but ill still add my 2cent.


Let us imagine you bet, get called by a good draw (GD) and the last player to act has a very slim draw (SD). The pot size is such that SD exactly gets the pot odds to call: his EV does not change whether he folds or calls. Do you want him to fold or to call? If SD calls he has say 3 out. Do these outs become your outs if he folds or the GD outs? In the first case you want him to fold, in the other you want him to call. Now in the first case, if the pot was a litle bit smaller, you would still want him to fold (and make the corect choice). If you where in the second case and the pot would be a litle bit bigger, you would want him to call (and again, play well).


BTW, the second case i discuse, rooting for a player to *correctly* call, seems to me much less discused. Maby it never happens ?


Gatlif

Great post.


Can you give a link or something where the maths behind Mortons Theorem are explained? Or is it based on simulation? I really would like to get into the maths behind it. Thanks!


Regards

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