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The Fundamental Theorem of OFC and POFC

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  1. #1

    Default The Fundamental Theorem of OFC and POFC

    In his 1987 classic The Theory of Poker, David Sklansky presented what he called The 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."

    Others have taken exception to this over the years, but many see it as a useful starting point in talking about how to evaulate plays in a game of incomplete information. But OFC and its variant POFC (which I vastly prefer, but that's another discussion) are fundamentally different from most other forms of poker. The hands are played face-up. Players can't use bets or raises as bluffs to win hands when their cards aren't best; the best made hand always wins. So Sklanksy's FToP doesn't really apply. But is there some other idea that might serve as a Fundamental Theorem of OFC and POFC?

    I'd offer (keeping Sklansky's basic structure as an homage): "Every time you play a hand in the way that maximizes your equity on later draws, your opponents lose; every time you play a hand in a way that fails to maximize your equity on later draws, your opponents gain. Conversely, every time opponents play their hands in the way that maximizes their equity on later draws, you lose; every time your opponents play their hands in a way that fails to maximize their equity on later draws, you gain."

    Since you can't know what will actually come--and distressingly often unlikely and even very unlikely things happen--the most sensible yardstick isn't whether you played your hand to maximize the equity for the cards that actually came, but whether at the set and on each draw, you played in the way that has the greatest chance of showing the most profit, knowing what you knew at the time of each decision. I know that at our current mixed state of knowledge and ignorance, OFC and especially POFC haven't been "solved" yet, and that figuring out some of the unimaginably complex problems involved in deciding what the optimum line of play is in some early-hand situations is beyond our capabilites as of now.

    But imagine that we could transport ourselves 50 years into the future, when Moore's Law has produced computers incredibly faster and more powerful than the ones we use and the code for all the algorithms necessary to figure out the optimum play in every spot have been written. Then it would be possible to decide whether a play was a "winning" play or a "losing" play as defined above in the Fundamental Theorem of OFC and POFC.

    I'd argue that even though we don't have the hardware or the algorithms to solve every spot right now, it doesn't matter in terms of the validity (or lack thereof) of the Fundamental Theorem of OFC and POFC. Your expectation over time is a function of the quality of the decisions you make, of how closely you adhere to the optimum play (even if the optimum play can't always be proven as of now).
    Last edited by OneByPhi; 02-01-2014 at 06:43 PM.
  2. #2
    Eric's Avatar
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    I think the game will be solved at some point. Once that happens it will be like playing a much more complicated version of blackjack. Every time you go against the basic strategy chart then you decrease your chances of winning.

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