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Morton’s Theorem

Morton’s Theorem is one of the basic theorems that is actively used to study gaming techniques, strategies and tactics of poker. The theorem is named after its discoverer, Andy Morton (participant of a significant number of prestigious tournaments), and is recognized by the world poker community as one of the fundamental principles of the game.

Morton’s theorem review

This theorem can be applied in situations when one of the players has fairly strong hands, but his / her potential gain depends on what actions will be taken by his / her opponents.

Statement of the theorem

Mathematical expectation of a participant, playing against two or more opponents, increases in those cases when they take the right decisions. And vice versa, if the opponents take wrong actions, his / her mathematical expectation decreases.

Being at the table with more than two opponents, one should be very careful. If we consider this situation from a different point of view, a few opponents can work together, making technical mistakes on purpose. It can be treated as a mere coincidence, but it may also look like an implicit or explicit collusion.

Morton’s theorem example

Player A holds top pair with a good kicker: the king of clubs – ace of diamonds.

Flop: 9 of hearts, king of spades, 3 of hearts.

After betting on the flop, player A is in the game with two opponents – player B and player C. Player A is sure that player B is on a flush draw and player C holds 2nd pair with a random kicker. The pot is a value expressed in high stakes.

Turn brings a blank card. If the player A bets on the turn, the player B will get good odds, allowing to call. Player C, in his turn, must decide what his next step will be: call or fold.

To determine the likelihood of the player C taking a particular action, it is necessary to assess each of his decisions. If the player C chooses to fold, he will neither win anything, nor lose. If player C calls, he will either lose a considerable bet, or will take the pot. At this, it is reasonable to continue the game if the pot is above 7.5., if below – it is better to fold.

Player A’s expectations are determined depending on the value of the pot on a case-by-case. Player A can receive income from the player C’s call, provided that the value of the pot is at least 5.35. If this index is higher, player C can get more gains from folding, than player A from calling.

Conclusion:

1. Player C should play fold.

2. Player A earns more if player C folds, than if he makes a wrong move, having called.

This theorem does not claim that all the mistakes of the opponents will contribute to the reduction of the player’s expectations. It only describes some of the situations in which opponents’ mistakes can cause the player to lose any given prize amount.