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| David Sklansky at the World Series of Poker |
The Fundamental Theorem of Poker is a principle first articulated by David Sklansky that he believes expresses the essence of poker as a game of decision making under incomplete information.
"Every time you play a hand differently, you would play if you could see all your opponents' cards, they win, and every time you play your hand the same way you would play if you could see all of them cards, they lose. Conversely, every time opponents play their hands differently, they would have if they could see all your cards, you get, and every time they play their hands the same way as would have played if would see all your cards, you lose."
The Fundamental Theorem is said in common language, but its formulation is based on mathematical reasoning. Every decision made in poker can be analyzed in terms of the expected value of winning a decision. The right decision to make in this situation is a solution that has the highest expected value. If you could see all your opponents' cards, you can always calculate the correct solution with mathematical precision. (This, of course, true heads-up, but this is not always true in multi-way pots.) The less you deviate from these good decisions, the better the expected long-term results. This is a mathematical expression of the fundamental theorem.
Example
Suppose Alice plays Limit Texas Hold 'Em, and is dealt 9 ♣ 9 ♠ under the gun preflop. She calls, and all others fold to the big blind who checks. The flop came A ♣ K ♦ 10 ♦, and the big blind bets.
She now has to make a decision based on incomplete information. In this circumstance, the correct decision is almost certain to lose. There are too many turn and river cards, which can kill her hand. Even if the big blind does not have A or K, there are 3 cards of a straight and 2 cards of the same suit on the flop, and he can easily have a straight or flush draw. It is essentially approaching 2 outs (9 more), and even if she catches one of these outs, it may not hold up.
Let's assume, however, that she knew (with 100% certainty), the big blind held 8 ♦ 7 ♦. In this case, it would be wise to pick up. Even though the big blind will continue to receive the correct pot odds to call, the best solution is to increase. (Calling will give the big blind infinite odds, and this solution gives less money in the long run than the increase). Thus, since by folding (or even call), she played the hand differently than she would play if she could see her opponent's cards, and so according to the Fundamental Theorem of Poker, her opponent made a gain. She made a "mistake" in the sense that she has played differently, than she would have played if she knew that the big blind held 8 ♦ 7 ♦, although this "error" is almost certainly the best decision based on incomplete information available to it .
This example also shows that one of the most important goals in poker to encourage opponents to make mistakes. In this part, the big blind is practiced deception, using a semi-bluff - he bet his hand in the hope that she will fold, but he still has outs, even if she calls or raises. He persuaded her to make a mistake.
Multi-way pots and tacit collusion
Fundamental Theorem of Poker applies to all heads-up solutions, but this is not true for all multi-path solutions. This is because every enemy player can make wrong decisions, but also a "collective decision" all enemies working against the player.
This type of situation occurs mostly in games with multi-way pots, when a player has a strong hand, but several opponents with a draw or pursue other weak hands. In addition, a good example is a player with a deep stack to make the game, which stands for the short stack opponent, because it can take more than the expected value by deep stacked opponents. This situation is sometimes referred to as implicit collusion.
The Fundamental Theorem of Poker is simply expressed and seem axiomatic, but its proper application to the myriad of circumstances that a player can encounter requires a lot of knowledge, skills and experience.
Source: http://en.wikipedia.org/wiki/Fundamental_theorem_of_poker
