Proof of Fundamental Theorem of Poker?

[rufus]

"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."

Assuming (1) rational knowledgable players, and (2) using full-knowledge value as a baseline, this should be obviously true for heads-up play - in multi-player pots, implicit collusion limits it.

Sklansky's theorem is based on complete game-state information, which means that it's applications to actual play decision making (where there isn't nearly so much knowledge) are very limited.

[The 13th 4postle]

AP superuser account is your proof

[Vetgirig]

Poker is a Zero sum game

http://en.wikipedia.org/wiki/Zero-sum

The wins of one player comes from the loss of another player. So to win one must get the opponent to make mistakes.