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View Full Version : Flaw in Fundamental Theorem of Poker?


1p0kerb0y
09-27-2004, 06:43 PM
Upon re-reading The Theory of Poker, I came across the fundamental theorem of poker and began thinking about it,

[ QUOTE ]
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

[/ QUOTE ]

So I got to thinking about this, and not only is it 100% true, it is virtually the basis for winning the game. I mean think about it: If you could see all of the exposed cards at once, you could play virtually perfect poker, assuming you were good at the mathematics and such. Poker would be a 0 sum game (minus the house cost). Or would it?

See, the thing is, I know players who would virtually STILL play incorrectly at times EVEN IF they knew what my cards were! Several examples of this would be drawing to a hand when they don't have the correct pot odds to do so; Failing to raise when they have a nice pot equity edge, even though the hand is not yet made, etc.

So is there a way to improve the Fundamental Theorem of Poker to make it EVEN MORE TRUE? You bet. (no pun intended there) Is it important that we do this? I don't know. How important is the Fundamental Theorem of Poker? When you consider that in The Theory of Poker it is described as being the equivalent of the Fundamental Theorem of Calculus to calculus, I would say it is very important to make it as true as possible as well as as accurate as possible.

So what if it were worded such as:

Every time you play a hand differently from the mathematically correct way if you could see all your opponents' cards, they gain; and every time you play your hand the same way as the mathematically correct way if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the mathematically correct way if they could see all your cards, you gain; and every time they play their hands the same way as the mathematically correct way they if they could see all your cards, you lose

I don't pretend to be a poker scholar or the such, rather I am a stundent interested in learning and understanding the game to the highest level possible, although I am fairly certain I will never come close to reaching the point that David Sklansky has. It is possible that I am being very meticulous here, but it is also possible that I have found a more correct wording of the theorem.

Either way, I expect to get totally FLAMED for this and hope that you all realize that I am just giving FOOD FOR THOUGHT.

maurile
09-27-2004, 07:02 PM
It's better the way it's already written.

Your addition doesn't add anything of substance; it just makes it wordier. The implied assumption that you and your opponent are both doing the math right, and aren't on tilt, is understood without having to be explicitly stated.

There are exceptions to the FTOP in multiway pots. Search the RGP archives for "Morton's theorem".

submariner
09-27-2004, 07:04 PM
I'm not sure how you think your version is different (other than wording) than the original. I think it is implied in the original that the person who knows what the other has, plays correctly.

Obviously, if you know what the other player has, and still (deliberately or through ingnorance) play incorrectly, then you won't make money, and the theory no longer applies to your action.

BTW, you can't make something that is true "even more true".
Something either is true or it isn't. There aren't degrees of "true".

Scotch78
09-28-2004, 12:21 AM
[ QUOTE ]
BTW, you can't make something that is true "even more true".
Something either is true or it isn't. There aren't degrees of "true".

[/ QUOTE ]

My name is Scott.
My name is Scott Zimmerman.
My name is Scott Louis Zimmerman.

Any definition of "truth" that assigns all three statements the value of "true" will necessarily produce degrees of truth as a side effect. Any definition that prohibits variable degrees of truth will necessarily assign a value of "false" to at least two of the statements.

Scott

submariner
09-28-2004, 12:48 AM
Assuming it is true that your name is Scott Louis Zimmerman,
(and I'm not questioning it, but it could just be an example), then each of the three statements is true, and each is exactly as true as the other. Each successive one provides additional information, but it no more (or less) true than the any other one.

jdl22
09-28-2004, 01:37 AM
A better change than the one you did is to say should instead of would.

Scotch78
09-28-2004, 02:22 AM
My full name is in fact Scott Louis Zimmerman. But since you don't want to take my word that each is true to varying degrees, I've decided not to take your word that each is true at all :-). Please prove to me why each one is true. That is, give me a definition for "truth". For any definition you give me I will show you why one of the following three results must entail: at least two of the statements are false; all three statements are true, but to varying degrees; or the definition is inconsistent.

Scott

kiddo
09-28-2004, 03:08 AM
Well, I guess there is more about you then your name? Color of your eyes? Education, parents.... whole world.

You misstakenly thinks that telling it all is absolute truth and only tell a bit is a lesser degree of truth. A truth is a statement that coresponds to reality. What this means is a tricky question, but saying: "My name is Pete" when it actually is Pete, and thinking this statement is less true then "My name is Pete and I got blue eyes" when you (also) got blue eyes, is plain wrong.

If "Theorem of Poker" is like saying 2+2=4, there is nothing strange about saying: 2+2(+2)=6. This doesnt change the truth of the first statement. It tells more but got nothing to do with the truth.

jrobb83
09-28-2004, 03:30 AM
[ QUOTE ]
A better change than the one you did is to say should instead of would.

[/ QUOTE ]

And if appeared like this in the original text, we wouldn't have people coming here every so often making "groundbreaking" posts about how the FTOP is flawed.

To bad S&M assumed that any one who uses the FTOP would play the way they should. /images/graemlins/wink.gif

Scotch78
09-28-2004, 04:08 AM
[ QUOTE ]
You misstakenly thinks that telling it all is absolute truth and only tell a bit is a lesser degree of truth

[/ QUOTE ]

According to your claim that, "A truth is a statement that cor[r]esponds to reality," I'm going to assign the previous statement a truth value of false. The corresponding true proposition would be, "You mistakenly believe that I think anything less than the absolute truth has a lesser degree of truth."

[ QUOTE ]
A truth is a statement that coresponds to reality. What this means is a tricky question

[/ QUOTE ]

That's why I keep pressing for a definition of "truth" so that I can explain why there are variable degrees of it. If would you clarify what you mean by "correspond", it should be enough to start the discussion though.

[ QUOTE ]
saying: "My name is Pete" when it actually is Pete, and thinking this statement is less true then "My name is Pete and I got blue eyes" when you (also) got blue eyes, is plain wrong.

[/ QUOTE ]

Agreed, that's why I made no such claim. "My name is Pete" picks out one property of your existence: your name. "My name is Pete and I have blue eyes" designates two independent properties: your name and your eye color. I claimed that using three different signifiers for one signified will result in the problems under discussion.

Matt Ruff
09-28-2004, 09:44 AM
[ QUOTE ]
I mean think about it: If you could see all of the exposed cards at once, you could play virtually perfect poker, assuming you were good at the mathematics and such. Poker would be a 0 sum game (minus the house cost).

[/ QUOTE ]

Poker is a zero-sum game, whether you are playing perfectly or not.

-- M. Ruff