Fundamental Theorem of Poker
The Fundamental Theorem of Poker was formulated by David Slansky. It encapsulates the essential nature of poker as a game of decision making under the conditions of incomplete information and volatility.
Statement of the Theorem
The Fundamental Theorem of Poker is usually stated in natural language but is actually based on strong mathematical foundations (Law of Iterated Expectation).
- Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain;
- and every time you play your hand the same way you would have played it if you could see all their cards, they lose.
Because poker is a Zero Sum game, the converse of the theorem immediately follows:
- Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain;
- and every time they play their hands the same way they would have played if they could see all your cards, you lose.
The Fundamental Theorem of Poker always applies to heads up poker, or when an otherwise poker game is reduced to a game of two people. It applies to multiway pots almost always, with a few exceptions.
These exceptions were first highlighted by Andy Morton in a newsgroup, after whom the principle was named Morton's Theorem.
It should be noted that Morton's Theorem is in direct contrast with the Fundamental Theorem of Poker.