So much for mathematics, if reality has no bearing on the truth of certain mathematical statements.

Well, statistics is a branch of mathematics, so...

Nevertheless, here is another way of formulating my worry. The statistics you provided show a correlation between a player choosing white and the player winning. As anyone knows, however, correlation is not necessarily causation, i.e. just because two factors are correlated does not mean one causes the other. In order for the correlation to be a reliable indicator of causation, you need at least to screen off other potential causes, be it potential causes of white winning or potential joint causes of a player choosing white and winning. For example, perhaps there is a bias in strong players to choose white, not because white has an advantage, but because they like shiny white pieces. Or perhaps there is an odd psychological quirk that gives advantages to chess players when they go first. How do we eliminate such possibilities?

One way is to run experiments to rule out such odd explanations. But how can we rule out every other explanation? Here, experiments will be of no help. Fortunately, in the case of chess, there is another route available: we prove from a mathematical description of the game that white has a winning strategy. This way, we can show that the statistics are not merely reflecting an accidental correlation, but are actually a symptom of an underlying structural fact about chess.

Well. I believe that there is some kind of hidden hand operating in the background for deterministic games, such as chess, which would narrow down the correlation and causation aspect of white winning on average, rather than black.

It would be indeed strange to psychologize the issue and say that playing white brings in a false positive in terms of bias or some such reason.

But positing a "hidden hand" is just another way of saying that you believe that there is a structural feature of chess which explains the correlation. And this is exactly what requires proof, so that you can screen off the other explanations. Note also that causality is not merely statistical correlation; if you're saying that something has a cause, you're effectively saying that there is an underlying mechanism that explains how this something is produced. So this mechanism should be explanatory; a "hidden hand" falls short of this explanation, unless it is merely a placeholder for a structural feature, in which case we're back to the need for a proof.

No one as of yet proved that the game of chess ends always in a draw by two perfect players.

For checkers it was proven so it lost its appeal to me.
When someone will prove that chess also always ends in a draw it will lose its appeal to me too.
How about NHL 2013, quite a hard game to master.
:-)

No one as of yet proved that the game of chess ends always in a draw by two perfect players. — MathematicalPhysicist

But, given that the game is deterministic, that's a plausible outcome for chess, if white doesn't have a natural advantage over black, yes?

But white does have a natural advantage over black - as in he is the first to start the game.

Like in the westerners, the first one to shoot usually wins... :-D
https://www.youtube.com/watch?v=CTt1vk9nM9c

What game theory proposition do you claim to be refuting? You can't refute game theory itself. That would make no sense.

If you refute any of the fundamental propositions of a theory, doesn't that effectively refute the theory?

In any sufficiently complex game, given enough iterations, it can be demonstrated that both players become hyper-rational, and thus a winning strategy cannot be entertained.

Analogously, think about chess for a moment. Given that chess is the oldest game in human history, and given that it is deterministic, then through enough iterations it can be demonstrated that both players, given a sufficiently long backlog of past historical games, are going to face situations where winning becomes... impossible.

What is left to entertain is simply a mistake committed by either player to ensure victory. Since both players, given enough iterations, become hyper-rational, then winning becomes impossible, and the game looses its "fun-factor".

I believe the analogy can be demonstrated for ANY deterministic game, and thus, game theory has been refuted for any deterministic game.

Thoughts? — Shawn

Chess to some measure is confined to a chess board. The universe and reality is a chess board with trillions of trillions of spaces on the board. Victory or defeat out here is much more of a spectrum. I understand chess is extremely complicated though.

I half way understand what you are saying. If you are saying the theory is atleast slightly flawed, i'm not sure any of us could argue with that.

When i was in college they gave us a very banal explanation of the theory using prisoners and testimonies. Lets not forget when one guy goes to prison he might find a real nice friend (unlikely) and enjoy his meals for whatever reason. lol

The point is its possible to not completely lose or completely win.

Have a good day, Sir!

now that i think about it i never read alot about game theory and college only offered the banal example. I don't understand your OP.

You are right. What I mean is that OP is treating game theory as a single idea by not specifying what game theory premise he claims to have disproven. That is why I said it doesn't make any sense.

The universe and reality is a chess board with trillions of trillions of spaces on the board. — christian2017

Not really. Every game is inherently deterministic. Reality seems to have an element of non-determinism in it.

The universe and reality is a chess board with trillions of trillions of spaces on the board.
— christian2017

Not really. Every game is inherently deterministic. Reality seems to have an element of non-determinism in it. — Shawn

thats fair.

What I mean is that OP is treating game theory as a single idea by not specifying what game theory premise he claims to have disproven. That is why I said it doesn't make any sense. — Intermittent

Read my last post.

Can someone possibly help out with a proof of this assertion in the OP?