Fundamental Theorem of Poker

The fundamental theorem of poker, unlike other poker theorems, is a big general theorem that can, and should, be applied to every single poker hand, regardless of the poker variant. It was invented by a professional poker player and writer David Sklansky in his famous book “The Theory of Poker”.

Fundamental theorem of poker

“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.

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 gains and loses described in this theorem do not always refer to actually winning or losing a hand. It is more about long term approach to poker. In the short run anything can happen.

For example, if you go all-in preflop with KK against villain’s AA and win the hand, you still lose according to the fundamental theorem of poker. This is because pocket kings have only 18% equity against pocket aces preflop.

Fundamental theorem of poker description

If you could always see your opponents’ hole cards, poker would be an easy game. You would always make the right decisions:

  If you had the best hand, you would bet or check/call to induce a bluff and trap weaker hands.
  If you had the worst hand, you would fold, call with good odds to draw, or bluff if you believed you could make you opponents fold better hands.

Unless you are a poker room server administrator, a superuser, or a god, you will never be able to play a mistake-free game according to the fundamental theorem of poker. This is because you cannot see your opponents’ cards.

However, you can improve your hand reading skills. The better you are at reading your opponents, the more often you will be successfully able to put them on a specific range, and sometimes even on a specific hand.

Fundamental theorem of poker example

No Limit Texas Holdem game. $1/$2 blinds. 6 players, each with a $200 stack.

Your hole cards: 55

Villain's hole cards: KQ

The villain raises to $7 from early position. Everyone folds to you on the button and you make the call. The blinds fold.

Flop: J53

Your opponent continuation bets $12 into a $17 pot. It is your time to act. Your options are:

  Fold
  Call
  Raise

What is the most profitable action in this situation? Obviously it is not folding. You can raise but do you really think your opponent will call with such a weak hand? It is very unlikely.

The best action here is just to call. This way you can induce further bets and gain more. There are a lot of cards that will probably make your opponent to fire a second barrel on the turn, such as any ace, king, queen, or ten, and any spade. If he is very aggressive, he can even bet any other turn card with his two overcards.

Now let’s assume that your opponent holds not KQ but AA. Now raising can be much more profitable than calling. With two diamonds on the flop, when you raise, the villain may put you on a flush draw and reraise you. If you just call and a third diamond is dealt on the turn, your opponent will be much more reluctant to put any more money in the pot.

More articles on poker theorems:

  Poker theorems overview
  Baluga theorem
  Clarkmeister theorem
  Zeebo theorem

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