Do bluffs contradict Sklansky's Fundamental Theorem of Poker?

Question

Suppose I am at the button position with a hand 3h 5h. I decide to play this hand and the flop comes Ac 10s 8d. Suppose everyone before me checks.

Sklansky's Fundamental Theorem of Poker implies that if I see opponents hands, I should not bet in case my hand is not the best. Although I do not know my opponents cards, I can be almost certain that my hand is not the best here. Even if no one has a pair, someone will most certainly have a kicker higher than 5.

Thus, according to my understanding of Sklansky's Poker Theorem, I should not bet here.

However, if bluffs are part of your strategy, from time to time you can bluff here trying to represent an ace.

My questions:

• does Sklansky's Fundamental Theorem of Poker imply that you should never bluff in this situation?

• If bluffing from time to time is a correct strategy, does that mean that the Fundamental Theorem of Poker is simply wrong (or at least not true for certain cases)?

Answer 1

Slansky's theorem must be considered from both the perspective of the hero and of the villain.

The first part of the theorem:

“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.”

...and the second part of the theorem:

“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.”

...so, referring to the example given by the OP, if the hero can make the villain(s) fold by making a bet, the villain(s) have made a mistake as defined by the theorem; because if the villain(s) saw knew that the hero did not have an ace, said villain(s) would not fold a lesser hand.

More abstractly, the theorem applies to bluffs very directly, since bluffs cause opponents to fold better hands, i.e. bluffs cause opponents to take an action they wouldn't take if they saw the cards.

A more simple example is useful: suppose I go all in preflop with a pair of deuces and one potential caller, and suppose the villain has a pair of jacks. The villain wouldn't fold the jacks if my cards were face up, therefore if the villain folds, then as per the theorem the villain has lost.

One might (reasonably) think that betting into the villain, with a worse hand, as a bluff would contradict the theorem; since if the cards were face up the hero wouldn't make that bet. However, I think it is pretty clear that Slansky would say that the final outcome of the hand is key, not action on each street.

So, whether or the bluff is good for the hero or the villain depends on the outcome of the hand. If the hero bluffs and it works, the villain lost, and conversely if the villain calls the hero's bluff with a better hand, then the villain won.

Also, it has to be the equity of the hands played, not the actual outcome. For example, suppose the hero is semi-bluffing with a draw to a nut flush and the villain has bottom set. The hero still loses if the villain calls, even if the hero hits the flush, because the hero was behind in terms of equity (assuming, of course, that the hero wasn't getting proper odds for the bet, if hero were then it wouldn't be a bluff).

Answer 2

Sklansky's Fundamental Theorem of Poker implies that if I see opponents hands, I should not bet in case my hand is not the best.

I disagree. I think it doesn't say "you shouldn't bet". It says "you should bet consistent with the knowledge that you are behind in the hand".

Imagine a poker game where you really can see all the cards. If you only bet hands where you were winning, then every time you bet everyone else would fold. To change this, you would need to also bet on some hands where you are down. You will find yourself having to bluff.

The theorem says that if this is a perfectly valid decision to make if you know their cards, then it's a win for you to make the same decision in a real game.

When you play many hands, you must play some bluffs even if it is not optimal strategy for maximizing value on this one hand. The theorem does not force you to optimize every hand in isolation, so bluffing is fine.