Poker Lesson 04: The Fundamental Theorem of Poker

More years ago then I care to think about, a citizen of ancient Greece named Pythagoras, sat down and worked out a theorem of mathematics and how it works in the world. Not only was this a breakthrough in the field of mathematics, but it was the first recorded instance of somebody having way to much time on their hands. There are other, less known theorems. For example, chaos theory talks about butterflies flittering about and changing weather on completely separate continents. Due to the general insanity behind this idea, the message behind this theorem seems to be “Don’t smoke crack”. Less known then these two theorems, but more relevant to our general interest on this site is the “Fundamental Theorem of Poker”.

David Sklansky expresses this theorem beautifully in his book, “The Theory of Poker”. He writes that the ”Fundamental Theorem of Poker states that the best way for players to play is the way they would play if they knew their opponent’s cards”. In other words, “duh”. Obviously though, this is more complex then just the words stated in the theorem. Unless you have superpowers, or somebody behind your opponents with binoculars, there is no way you can actually know what they have in their hands.

Let's say you're holding jh and 10h. While your opponent is holding ks and qd. The flop comes: qh 8c 7h. You check, your opponent bets, and in response, you call. Then the turn comes: ad. You bet, trying to represent aces. If your opponent knew what you had, his correct play would be to raise you so much it would cost too much to draw to a flush or a straight on the last card, and you would have to fold. Therefore if your opponent only calls, you have gained. You have gained not just because you are getting a relatively cheap final card, but because your opponent did not make the correct play. Obviously if your opponent folds, you have gained tremendously since he has thrown away the best hand.

How could the opponent have known what was in your hand? How would they have known raising was the correct call? You are dealing with odds and probability. The odds of you completing your flush or straight were not good. If you pulled another Jack, the opponent could still beat you with a pair of Kings or Queens. The odds that you would pull three Jacks were equal to the odds the opponent would a triplet of Kings and Queens. You can see where this is going.

Staying on the happy side of the odds will result in more wins then losses. Occasionally that 10% chance that a player is going to beat you with an unlikely straight, is going to happen, and you will watch your money go into their stack.

Remember the words from the book, “The Theory of Poker”: “Every time you play a hand differently from the way you would have played it if you could see all your opponent’s 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. 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.

My thanks to David Sklansky and his book “The Theory of Poker” for the contributions they made to this article.