Poker strategy is a very complex and nuanced thing, as it must take into account elements of psychology alongside elements of mathematics and probability. But there is a fundamental theorem of poker, articulated by David Sklansky, that serves as the basis for a lot of important poker strategies. This theorem is stated as follows: “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.” The converse is also true, according to this theorem of poker strategy.
This theorem, while stated as something that seems somewhat obvious and factual, is actually an expression of a mathematical element in poker strategy. If you, as a poker player, could successfully see every single one of your opponents’ cards, then your poker strategies would be perfect. You would never fail to implement the correct strategy in any given situation. But, of course, in an actual game, you cannot see your opponents’ cards, and thus your poker strategies are more prone to failure, or mistakes, as the theorem describes them. All you can do is make the best possible decision based on the information available, but the key is to control the available information, such that your own poker strategy will lead to gains for you, and your opponent’s poker strategies will lead to losses for him or her.
The best way to explain how this theorem affects poker strategy is with the simple example of bluffing. By bluffing and pretending that you have better cards than you actually do, you are adjusting the information available to your opponent. If your opponent could see your cards, then he would know better than to change his poker strategy based on your bluffing, but as he cannot see your cards, he can only respond to your actions. Thus, you would have forced your opponent to act differently than he would have, had he been able to see your cards, and as a result, you gain, and your opponent loses.
In essence, this fundamental theorem of poker implies that players should adopt poker strategies that seek to force their opponents to fault, in a fashion similar to tennis. The objective is not necessarily to simply beat the opponent outright, but is instead to trick the opponent into making consistent enough mistakes that the opponent loses. Poker strategies should reflect this implicit idea, that perhaps the most important way to the play the game is not with a focus on your own play, but with a focus on the play of your opponents. Watching your opponents, focusing on what their own particular strategies and styles of play seem to be, and so on will serve you very well in determining what the correct course of action in any given situation is, both in terms of your reaction to them, and in terms of how best to mislead your opponent.