Morton’s theorem is one of the basic poker theories that is commonly used to study poker strategy, tactics, and gaming techniques. Morton theorem is named after its discoverer, Andy Morton, a poker player based in Los Angeles. The theorem was posted in the newsgroup.
This theorem is accepted as one of the basic principles of poker by the world poker community. It says that in multiway pots, a player’s expected value can be increased whenever their opponent makes a right decision.
Morton’s theorem can be used in situations when one of the players has a premium hand. However, there are two or more opponents on draws. This type of situation might often happen during a poker tournament. In this case, the player with the strong hand has an opportunity to make more money when their opponents fold to a bet.
The theory contrasts with Sklansky's Fundamental Theory of poker, which says that a player is expecting their opponents to make such decisions which decreases their own expected value. The difference between the two theorems appears due to the presence of more than one opponent, whereas the fundamental theorem of poker does not apply in a multi-handed situation, but in heads-up situations, i.e. when there is one opponent.
The scope of Morton’s theorem in a multi-handed situation is a subject of controversy. For instance, he shares the belief that the fundamental theory of poker hardly applies in multi-way situations.
Morton’s Theorem Example
Assume that John holds the Kings of club and Ace of diamonds, a top pair with the best kicker. The first three community cards (flop) are King of spades, 3 of Hearts and 9 of Hearts. Once the betting on the flop is over, John is with two other opponents in the game- Paul and Sam. John is sure that Paul is on a flush draw, and Sam is holding a second pair with a random kicker. The pot size is a value expressed in a big pot.
The turn brings a blank card. When John bets on the turn, Paul, holding a flush draw, is certain to call and will get a good pot odds, allowing him to call. Once Paul calls, Sam must choose whether he wants to call or fold.
To assess Sam’s probability of taking a specific action, it is essential that each of his actions must be evaluated. If Sam decides to fold, he won't win nor lose anything. If he calls, he either loses a huge bet or takes the pot. Continuing the game at this stage is fair if the pot is above 7.5, if below- it is best to fold.
The expectations of John are determined on the size of the pot in each case. John can earn income from Sam’s call, provided that the pot value is at least 5.35. If this index is higher, then Sam can earn more benefit from folding, than John from calling.
a) Sam should fold
b) John gets more money when Sam folds (correctly) than when he makes a wrong move, having called.
This theorem does not assert that all the mistakes made by the opponents will contribute to the reduction of the player’s expectations. This explains only some of the circumstances where the errors made by the opponents might cause the player to lose the prize amount.