Morton's Theorem (refuting part of Sklansky's Theorem)
Has anyone else heard of this theorem? It states that Sklansky's Theorem does not work for multiway pots all the time. Morton's Theorem states that in multiway pots, there are situations where an opponent folding correctly actually benefits you and instances where their chasing incorrectly reduces your expectations. It applies to both cash and MTT games equally - anytime you are facing loose opponents. Since many of the questions posed on this forum seem to relate to sub-optimal play and loose opponents, I think this is a particularly interesting concept.
I'd be interested to hear what other's think about this idea and most importantly, what they think the best counter-strategy would be to combat these effects. Here's a link to the Wikipedia entry for the theorem (too long to post directly). I'll try to get some other links as well.
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A few more links to articles related to this theorem
http://www.loukrieger.com/articles/morton.htm
http://enacademic.com/dic.nsf/enwiki/1009236
https://www.pokerstrategy.com/glossary/Mortons-Theorem/
http://www.casinosmack.com/fighting-the-school-of-poker-fish-andy-mortons-theorem/
http://www.pokerengineering.com/?p=299
Anyone? Anything? You'd think that people would be a bit more interested in proven exceptions to Sklansky's Fundamental Theory of Poker. After all, the site uses Sklansky' FTOP as the basis for calculating Poker IQ, right? We're all training here so this has value to us all I'd think.
Added: there is very little material I can find on Morton or his theorem. If anyone knows any sources that continued the discussion after Morton died, I'd appreciate the direction. If you are a theory-geek like me, this is really cool stuff and seemingly forgotten about since 1997.
yeah @1warlock it makes total sense to me as I see this every time i go to the tables. We have discussed a hand i played like this. I raise KK ep+1 4x. Villain calls with 43o, an incorrect call. Draws out to a 44333 boat and cracks my KK. Had he folded correctly. I win. Since he called incorrectly. I lost. So a fold is +ev for me but some portion of hero's EV is lost with a call over the long run. In the hand he retains his 16,6% equity with the call and finishes with 100%. But with folding he relinquishes his equity to me. That's heads up too. Would be true for multiway also. When the two middle players fold their equity is divided among the remaining players according to their specific holdings. Calling incorrectly reduces Hero's EV because although calling in correctly, Villain hits the gutter anyway sometimes. Referencing the wikipedia example.
But I would say I still want the villains to call incorrectly because most of the time the gutter will not come in. Net +EV.
This is from a friend of mine on the topic that should shed a bit more light on it. The issue is that there are certain spots multiway where it is +EV for you as the best hand to have 1 of the other players in the hand fold correctly. This is a good example of how/why that works. Sklansky said that you always profit when opponents make incorrect decisions and lose when they make correct decisions. Well, that does not appear to be always the case in multiway pots. Therefore it looks like Morton did in fact find situations where the FTOP does not hold.
"Not sure if this is directly related, but I was looking at Equilab to look at shifts in equity in multi-way drawing situations and here is a spot I found interesting.
Player A holds AdAh
Player B holds 9h8h
The flop comes Th7h2c. In this scenario player A has 47.4% equity and player B has 52.6%. Pretty standard flip. But if you add a player C who holds KsTs, this new player has 10.4% equity, Player A’s equity goes down to 35.7% and player B’s equity actually goes up to 53.9%.
This seems like a prime example of Morton’s theorem in which player A may want player C to fold correctly (at least in some spots depending on the bet size) because player C’s equity share disproportionally goes toward player B. This seems to be due to players who are drawing having clean outs (e.g., any heart, J, or 6) while players with made hands are unlikely to improve (e.g.,to a boat by the river), so their equity is divided among additional players as long as those players have live outs. It also shows the beauty of combo draws, especially in multi-way pots.
This example makes me think that Morton’s theorem is true (the equity share of player C is not divided equally among players A and B, altering the expected value of bets). Is it fair to say that Sklansky’s theorem only holds for heads up pots? But from a practical standpoint, player A still wants to bet when they are likely to have the best hand, and they are able to re-evaluate if a heart or other scary card hits the board."
I believe Sklansky's theorem holds, his theory is that if you played the game with the cards showing, you win when your opponents make mistakes. It is no limit hold em. So in my opinion, if player A with AdAh raised 3x pre-flop both player B and player C would be wrong in calling the bet. If they could see the cards and know that player A had AA, they would both fold. If they call then Player A wins. The flop starts the process over. If the flop comes as you stated Th7h2c and everyone can see all of the cards. Player A would bet pot or more, player A could bet the right amount to insure he has an edge 5, 10 or 100%, if player B or player C call they lose according to Sklansky. On the turn it starts all over again. If all the cards are face up Player A becomes the house/Casino. That is how all of the big buildings and beautiful pools have been built in Las Vegas. I am not sure but I believe it is about a 3 percent house advantage that built them all.
Morton showed that while each individual action may be wrong, the collective actions turn out to be correct. This is why he termed it implicit collusion. If the players could see the cards and were actually working together (to split the profits), then the incorrect call still helps the correct call by disproportionately redistributing the best hands equity. Sklansky said that all incorrect calls help the player with the best hand. Morton showed that in multiway pots, this is actually not always the case.