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The Fundamental Theorem of Poker July 4, 2005

The Four universal principles in poker as expounded by Sklansky are outlined in the table below:

I will give two classical examples of these principles:

Case One: You have J7 in the big blind in heads up play aginst an AK.

J7 in BB vs AK in SB in a 20-40 HE game AK raised preflop and bet the flop. On the turn he gets raised by the J7
Board on the turn is:
Actual winning percentage for the AK: 22.7% Winning percentage if AK were up against a straight or two pair: 9.1% Money in the pot if AK calls the raise: $280 Pot percentage of the $40 call: 14.3% Is it correct for the AK to call here if he knew what you had? Yes! Therefore, you want him to incorrectly fold. Is it correct for the AK to call if he were up against a straight or two pair? No! Therefore, you want him to incorrectly call if you had a J9 for two pair or KQ for the straight. Analysis: Since the actual winning percentage is greater than the pot percentage of the $40 call, the $40 call is correct IF your opponent knew what you had. However, you want your opponent to misread you for two pair or a straight and therefore fold. If he does so, you gain equity!

Case 2: You have 33 in the big blind in heads up play against an AA.

33 in BB vs AA in SB in a 20-40 HE game AA raised preflop and action was capped on the flop. On the turn he gets raised again by the 33
Board on the turn is:
Actual winning percentage for the AA: 4.5% Winning percentage if AA were up against two pair: 18.2% Money in the pot if AK calls the raise: $400 Pot percentage of the $40 call: 10% Is it correct for the AK to call here if he knew what you had? No! He will only win 4.5% of the time. Therefore, you want him to call your raise, even though the pot is so big already. Is it correct for the AK to call if he were up against two pair? Yes! Therefore, you want him to incorrectly fold if you had a JT for two pair. Analysis: Since the actual winning percentage for the AA is so small: he needs to hit a two-outer out of forty four cards, you make more money in the long run if he calls you, and you therefore want him to misread you for two pair and call to try to counterfeit you on the river.

Now I need to explain this a bit further: In both cases that we mentioned, your opponent is an underdog to win and there is nothing he can do to change that. Whether he's up against a set with pocket aces or he's up against just a pair of jacks with AK, he is putting in his money as an underdog and you should expect to win the pot most of the time. But that still does not mean that you want him to call. If the pot is big enough already, then you will sometimes lose more money in the long run by having him call you than by having him fold. He, in turn, will lose less money by calling than by folding and that's what makes his call correct and is costing you money in the long run.

It's like being dealt two eight's in Blackjack against a dealer's face card. This hand will cost you money in the long run regardless of what you do with it but you will lose less money by splitting them than by hitting or standing and that's what makes splitting correct. The "house" wants you not to split them, not because they are afraid that you'll win; they are counting your money anyway, but they can expect to count even more of your money in the long run if you hit or stand.

And so, when we say "you want your opponent to call" or "you want your opponent to fold" we are talking about situations where you can expect to win the pot most of the time anyway. However, you want him to make the move which will cause you to win even more money! If the pot offers your opponent favorable odds to try to draw out on you, then you want him to fold thus increasing your long term profit. Otherwise, you want him to call.

Summary: Even in situations where you are a favorite to win, you will sometimes make even more money by having your opponent fold and sometimes by having him play. That's where the FTOP (fundamental theorem of poker) comes in. You want him to misread you or just play bad and make the wrong move so that you make the most money.

On the other hand, when you are the underdog, it will sometimes be correct for you to play so that you lose less in the long run. At other times, you will be such a big underdog that it is incorrect for you to stay in. Always make the move that is most profitable or least costly to you in the long run.