TOP #3 - The Fundamental Theorem of Poker

[wallenborn]

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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.

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The beautiful thing about the Fundmental Theorem is how little it assumes. It doesn't assume that a universally correct strategy exists, nor that anyone at the table knows it. Instead, it only assumes that the players at the table play rationally enough that their decisions never get worse with more knowledge.


Typical plays that create mistakes according to the Fundamental Theorem are:

[img]/images/graemlins/spade.gif[/img] Bluff bets and raises, from the blind steal to the river bluff
[img]/images/graemlins/spade.gif[/img] Slow-playing a made hand early to induce action later on
[img]/images/graemlins/spade.gif[/img] Blocking bets to keep your opponent from making the next street too expensive for you


"Mistakes" According to The Fundamental Theorem of Poker

Making a mistake according to the Fundamental Theorem does not necessarily mean playing badly. If you raise because your hand beats your opponent's range, and he happens to have a hand near the top of his range, you have not necessarily played badly, but you have made a mistake according to the Fundamental Theorem.

You play winning poker by playing as closely as possible to the way you would play if you could see your opponent's cards; and you try to make your opponents play as far away from this Utopian level as possible. The first goal is accomplished mainly by reading hands and players accurately. The second goal is accomplished by playing deceptively.


Multi-Way Pots

In heads-up situations, the Fundamental Theorem is universally true. In multiway pots, however, sometimes you should want our opponents to make the correct play.




Older threads:

TOP #1 - Beyond Beginning Poker
TOP #2 - Mathematical Expectation and Hourly Rate

[wallenborn]

We touched the FTOP before in the discussion on NLHTP #1.

[Jurrr]

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In heads-up situations, the Fundamental Theorem is universally true. In multiway pots, however, sometimes you should want our opponents to make the correct play.

[/ QUOTE ]Can someone explain this (I don't have the book with me right now)?

[raistlinx]

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In heads-up situations, the Fundamental Theorem is universally true. In multiway pots, however, sometimes you should want our opponents to make the correct play.

[/ QUOTE ]Can someone explain this (I don't have the book with me right now)?

[/ QUOTE ]
It is more applicable to fixed limit games in practice since you can't guarentee how much people will bet in a NL game. One example is situations where you bet/raise draws for value and would like people to correctly raise with the best hand so you can trap more money in the pot from the other players.

Another example is when the pf raiser is immediately on your left and you feel he will raise if you bet. If you are holding a vulnerable hand you would bet into him and hope he (correctly) raises. Many draws which would have called 1 bet (correctly) will now fold for 2 (correctly) and you have increased your equity.

[wallenborn]

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Can someone explain this (I don't have the book with me right now)?

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I'm prepared for that question:


Multi-Way Pots

In particular Morton's Theorem (there actually is a Wikipedia entry about it) shows that there is a rather sizeable class of situations where you'd like at least one of your opponents to play correctly: if you have top pair, top kicker in early position on the turn, a middle position player has a flush draw, and a player in late position has second pair, then if you bet out, the flush draw calls, and the late position player calls incorrectly, he is costing himself equity that flows exclusively to the flush draw. In addition, he might cause equity to flow from your top pair to the flush draw. That's right: he makes a mistake according to the Fundamental Theorem, and you get punished, too!

Andy Morton wrote: "[The Fundamental Theorem] in general does not apply to multiway situations."

In limit hold'em the class of situations where Morton's theorem holds is rather broad since the required pot size is common. In No Limit, you can bet enough that you want the second pair to call incorrectly, but even there the equity flows mostly to the biggest draw at the table. So in multiway pots while you think you are pricing out a draw, you might actually end up doing the value betting for one.

[wallenborn]

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One example is situations where you bet/raise draws for value and would like people to correctly raise with the best hand so you can trap more money in the pot from the other players.

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Exactly. This is a big reason to play a flush draw or an open-ender fast in a multiway pot.

[Jay.Yang]

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One example is situations where you bet/raise draws for value and would like people to correctly raise with the best hand so you can trap more money in the pot from the other players.

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Exactly. This is a big reason to play a flush draw or an open-ender fast in a multiway pot.

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But if you knew that a person on your left would raise if you bet and his raise would push out the rest of the player so that the pot would become heads-up, then you'd probably would want to just c/c with your flush draw, instead of betting out?

[Albert Moulton]

In NLHETAP, there is a section on trading small mistakes (by you) on inexpensive, early streets for big mistakes (by villain) on expensive, later streets.

In other words, sometimes the implied odds in NLHE with deep stacks justify knowingly making a "mistake" in the hope that if you hit your hand or set up a bluff later that villain will make a bigger "mistake" later on.

I think the notion of knowing when and how to trade mistakes is critical to NL.

[raistlinx]

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[ QUOTE ]
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One example is situations where you bet/raise draws for value and would like people to correctly raise with the best hand so you can trap more money in the pot from the other players.

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Exactly. This is a big reason to play a flush draw or an open-ender fast in a multiway pot.

[/ QUOTE ]

But if you knew that a person on your left would raise if you bet and his raise would push out the rest of the player so that the pot would become heads-up, then you'd probably would want to just c/c with your flush draw, instead of betting out?

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Yes. You would bet here with a vulnerable hand and hope he raises, knocking people out and protecting your hand. Note that you might do this even if you feel the person on your left had you beat.

[wallenborn]

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But if you knew that a person on your left would raise if you bet and his raise would push out the rest of the player so that the pot would become heads-up, then you'd probably would want to just c/c with your flush draw, instead of betting out?

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Right. This is only an issue of getting money in the pot while keeping everybody in, so it doesn't matter who is the aggressor. If you know someone will do the betting for your, fine, let them.