Sklansky’s Fundamental Theorem of Poker

[BB] Benny the Book continued the vitally important education of Joey the Juvenile, “On pages 17-18 of his book, The Theory of Poker, the poker philosopher David Sklansky states his 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.'”

[JJ] “Well, get me a deck of marked cards that only I can read, and I’ll do my best”, Joey the Juvenile joked.

[BB] His dad ignored him and resumed, “Your goal isn’t to win more hands. Your goal isn’t to stack your opponents, as enjoyable as that is. Your goal is to make fewer mistakes and induce your opponents to make more mistakes. The beauty and the pain of poker is that you can play perfectly according to the Fundamental Theorem and still lose. You can play horribly and still win. But in the long run, good play is rewarded, and bad play is punished.”

[BB] “So what is perfect play? It’s maximizing your Expected Value every time you act. Suppose you have pocket Aces and raise under the gun to five times the big blind. Everybody folds and you win the blinds. Is that perfect play?”

[JJ] “Probably not, but it might save you from a bad beat.”

[BB] “You’ve virtually assured yourself of a small profit but at the expense of possibly much larger gains. (Yes, some crazies will call your big bet anyway; in that scenario, your bet may not be incorrect as you are intentionally deviating from theoretically perfect play to exploit your opponents’ less-than-optimal tendencies.)”

[BB] “Playing against weak opponents, you simply bet your good hands for value and bluff your bad hands when you think you can steal the pot. If your opponents are bad enough, you’d actually want to build the pot on the early streets before taking it down on the river, maximizing your gains.”

[BB] “If everyone folds to you on the button with 7♠2♦, what should you do?”

[JJ] “I’ll bet to steal the blinds.”

[BB] “And that might be right. But it was a trick question because I didn’t tell you who your opponents are.”

[BB] “If the blinds are both tight and willing to let you steal, then you definitely should bet. If the blinds are loose preflop but very weak postflop players, you might limp, hoping to get lucky or steal the pot later. And if the blinds are both better players than you, you should fold without regret.”

[BB] “Another example: if you have top pair and think your opponent is just on a flush draw with one card to come, should you overbet the pot so you don’t get sucked out on?”

[JJ] “I know a few people here do that, but I’m guessing that you’re going to say it’s wrong.”

[BB] “The EV1 of that overbet is the pot size, P. But your opponent has only a 20% chance of improving to a winning hand, so a half-pot bet can be a much better bet. If they fold, there’s no difference. But if they call, they’ve just made a -EV decision: 0.2 * 1.5P – 0.8 * 0.5P = -0.1P. If they’re a calling station who loves to chase draws, a three-quarter pot bet might be even better (EV = 0.2 * 1.75P – 0.8 * 0.75P = -0.25P). Maybe even a full pot-size bet (EV = 0.2 * 2.0P – 0.8P = -0.4P). Of course, you need to avoid putting any more chips into the pot if the flush card hits or the implied odds will turn the tables.”

[JJ] “But how do I know my opponent is on a flush draw in the first place? I see people paying off ‘just to see’ all the time. It’s like we’re living in Missouri.”

[BB] “If I knew the answer to that, I’d turn pro, or at least move up to a bigger game. I’d recommend you watch Elias the Eagle play. And once you’re comfortable with the basics, maybe he can help you take the next step.”

[BB] “For now, just try to stay disciplined (your favorite word, I know). If a player is representing a flush by betting, he or she probably has it. Curiosity killed the cat — old English proverb.”

[JJ] “But knowledge is power — Sir Francis Bacon.”

[BB] “Give a man a fish, and he eats for a day. Teach a man how to fish, and he eats for a lifetime — ancient Chinese proverb.”

[BB] “Teach a man how not to be a fish, and he eats well for a lifetime.”

[JJ] “Who said that?”

[BB] “I just did. Your mom and I really do hope you’ll move out of the house after college.”

Footnotes:

  1. Yesterday’s post was all about EV (Expected Value).
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