Proof of Sklansky's theorem?

[Ralle]

I've been reading Sklansky's book The Theory of Poker, and
found it to be a very good book indeed. Especially I find
the chapters on semi-bluffing and raising to be excellent.

But, there is one thing that is missing. On page 17-18 he
presents what he calls The Fundamental Theorem of Poker.
Intuitively this theorem appears to be correct, but since
it is called a theorem, a proof should be included, or at
least available. Does anyone know where a proof can be
found?

[SoBeDude]

Just because there is a theorem, doesn't mean a proof exists, or if it did, that would be easy to unnderstand. Have you even tried to decipher any but the most simplest proofs?

Look at the 4-color theorem thats what, a couple of centuries old? No true proof exists, but it was proven true by an exhaustive computer program within the last 5-10 years (can't remember the details).

So the 4-color theorem, which has been widely believed to be true for a very long time, was and still has never been proven by a traditional mathematics proof...although some of the world's best minds have tried.

So although he may (and I repeat MAY) be taking some literary license with the use of the word theorem, I believe the concept is very sound, and, just like the 4-color theorem, much computer simulation has proven the concept to be valid.

Just my thoughts!

-Scott

[BonJoviJones]

I think you could construct your own non-rigorous proof quite eaisly, just by attempting to define a "Mistake" in poker and then attempt to come up with situations where you would make said mistake if you knew the cards.

It may even be trivial to prove in a more serious way, but I've never seen a poker idea solved in such a way and seriously doubt it's value.

[Clarkmeister]

The FTOP holds true in headsup situations 100% of the time. However, and I think this is mentioned in the book, there are certain multiway situations where the FTOP breaks down.

[angelo alba]

Simple. Prove it empirically.

Play with your cards showing [img]/forums/images/icons/tongue.gif[/img]

The 2nd worst critique I've heard is that the theorem is too obvious and banal to be worth mentioning.

The worst is that it's not much of a solace to be told that you've somehow come out ahead when the opponent merely calls and you lose, because, had he known what you really held, he would have raised.

(Naturally had you thought his raise was a bluff and THEN called or worse, re-raised---ouch!).

If memory serves the FTOP holds true in all situations, but it's of paramount importance heads-up, for obvious (I hope!) reasons. However, like Clarkmeister, I can't quote chapter and verse. So I could be way off as to what TOP really says.

Nevertheless, heads up illustrates it most clearly, and subsequent skills, eg; inducing calls against strong hands, are all based upon the FTOP.

What do ya'll think?

[rigoletto]

Hmmm... not being able to disprove a theory is not a proof of it's validity. That said, I agree with SoBeDude. Judge FTOP on it's practical use and you'll find that it works well.

[Ralle]

> Just because there is a theorem, doesn't mean a proof exists

That is not correct. A theorem is something to which there is a proof.
Otherwise it is called conjecture, hypothesis or proposition.

> Have you even tried to decipher any but the most simplest proofs?

I have deciphered many proofs of different complexity.

[Ralle]

> It may even be trivial to prove in a more serious way, but I've never
> seen a poker idea solved in such a way and seriously doubt it's value.

The point is that if you are going to use the word theorem, then there
should be a proof. Whether or not a proof would be interesting or useful
for the application is beside the point. It's a matter of terminology.

If you have an idea but no proof, then it's easy to state the idea, and simply
avoid calling it a theorem.

[mostsmooth]

umm, im no genius so forgive me, but i thought theorems were yet to be proven, and things that are proven become laws?
somebody help me!?

[tdiddy]

Just because there is a theorem, doesn't mean a proof exists

Excuse me, but by definition a theorem is proposition that can be proved from accepted premises. So, actually if there is a theorem, there must also be a proof of a theorem. If there is no known proof of the proposition, then it is called a conjecture even if it is widely believed to be true. Of course, Fermat's Last Theorem was called a theorem before it was proven, but it was actually only a conjecture until it was recently proved true.