Zermelo's theorem and opening theory

According to Wikipedia, Zermelo's theorem states that in any board game, the first-player can force a win, or the second-player can force a win, or both players can force a draw. In other words, with perfect play the game will always end in the same result. However, it must satisfy the following conditions:

1. The game board is finite
2. There are only two players
3. The game is of perfect information (nothing is hidden, unlike poker)
4. The players alternate turns
5. There is no chance element

Since chess satisfies all five of these conditions, we can therefore conclude that, with perfect play, chess is either a draw or a forced win for one of the players, and although it has not been proven with mathematical certainty, the consensus among chess experts is that chess is a draw. Even Kasparov himself once said after a last-round draw that "Chess is a draw" to waiting reporters.

If chess is a draw, this raises some interesting questions for opening theory. For example, while it is often said that white starts the game with a first move advantage, this advantage can only be really manifested as having more winning chances in a practical scenario, as opposed to starting the game with a true theoretical edge. Furthermore, while openings such as the Ruy Lopez are favoured more by Grandmasters because it is regarded as theoretically best, other openings such as the Italian Game are equal in value in that both of the openings should lead to a draw with best play - it's just that if someone defended accurately against the Italian they can equalise much more easily than in the Spanish. This is one reason why the Italian is a better opening for beginners, as if it is not defended well against then this can often be much decisive than in the Spanish, even if in theory the two openings are of equal value because they lead to draws.

If two Gods played chess, I think most people would agree that they would shake hands before they even started, as they would both know it to be a pointless pursuit. So really, chess opening theory is all about gaining a practical edge, as I believe that most if not all of the well known openings lead to theoretical draws, it's just that some perform better in practice than others. 

Does anyone else think chess is a draw, or do some of you think it is forced win for white (or even black)?

Edit: I meant to say that according to the theorem one of the players can force a win or that both players can force a draw.

Unless I misunderstand, I don't see the value of this theorem. We don't play perfectly and are unlikely to do so.

In the last generation a lot of games went through the process of being solved.  

The process of chess getting close to solved has already altered opening theory.  But really I don't think the existence of perfect knowledge will matter too much.  Right now there is readily available perfect knowledge up to 7-8 piece endgames.  Do you play 7 piece endgames perfectly?  

"Does anyone else think chess is a draw, or do some of you think it is forced win for white (or even black)?"

Since we will never play perfectly, it doesnt matter.

White has an edge but it's not enugh to force a win so It would be always draw or stealmate

....tracking !

This is why I will be starting calvinball.com in a couple weeks time.  Come check it out!

Wow, talk about willfully misrepresenting a position!

Zermelo's theorem states:

in any finite two-person game of perfect information in which the players move alternatingly and in which chance does not affect the decision making process, if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. force a win). It can alternately be stated as saying that in such a game, either the first-player can force a win, or the second-player can force a win, or both players can force a draw.^{[1] (Source: wikipedia)}

The initial post intentionally deleted the key phrase: if the game cannot end in a draw

To give a sense of just how wrong the initial post is, think of the game of tic-tac-toe. It fits Zermelo's Theorem perfectly. 

Just about every chess expert on the planet knows that chess is a draw. There are many people here who don't, but...

i'm not going to go reread it but...I thought that is exactly what he did say?  meanwhile, study up on calvinball.

Zermelo's theorem tells next to nothing about chess since we don't have this kind of perfect knowledge (about the whole graph which is huge I mean) and maybe we'll never have it.

Actually Zermelo's theorem is trivial. Here is a sketch of the proof of this result.By position we mean the state of the board but also every information relevant to it (in chess for instance, it include rights to castle, number of times every previous board state has been repeated and the conditions for 50 moves rule) For every position we call the depth of the position the maximum number of moves of any game starting from it (and which is played with legal moves of course); if the game can go on forever we'll say the depth of the position is infinite (rules of chess including the 50 move rule prevent this possibility completely so the depth of every position is finite). Stalemate and checkmate positions have depth zero.

We 'll say a position admits perfect play if from this position, one of the players can force a win or both players can force at least a draw.

Then every position admits perfect play. Otherwise let us call N the smallest integer which is the depth of a position without perfect play. Consider such a position. Then every position reachable form the curent position has always a depth strictly inferior to N by assumption and thus admits perfect play, because of this the player to play has three possibilities:
1°) He wins in at least one position reachable by playing one move from the current position
2°) He can force a draw in at least one position reachable by playing one move from the current position
3°) Whatever he does, the next position is a forced win for his opponent.

So we can conclude that this contradict our assumption because in case 1, ith is a forced win for the player to play, a forced draw in case 2 and a forced loss in case 3. So such a position cannot occur.

In particular, the starting position of the game admits forced play.
Please notice that the reasoning above somewhat mimics the thinking process of a player.

A lot of people are hung up on the idea of perfect information. In gaming theory, it simply means that both sides can see everything the other side has and can do. In that sense, chess is a perfect knowledge game. 

The OP left out the bit that Zermelo's theorem states about draws. 

I do agree tho, that this is basically a trivial theorem. In a nutshell, it says either the game is a forced draw, or one side or another can force a win. 

Gee.

I do not understand something here. What is so special about Zermelo's theorem? I mean we can either win, or loose, or draw, right? I don't get it.