Is There is an Ideal Opening Move in Chess?

Is there an ideal opening move in chess? Ideal meaning that it would enable the player to guarantee a tie or a win if played correctly throughout the game. 

This obviously sounds ridiculous but consider:

Theorem 1: Chess is a finite game.
Definition 1: Board State
Lemma 1: There are finitely many positions in chess.
Lemma 2: There are only finitely many possible turns in chess.
Definition 2: Game State
Conclusion: The game states exhaust the possibilities for chess. A game with the game state given is fully described. The number of game states is finite (equal to the product of the number of positions and the number of turns). Therefore, the game of chess is finite.
Theorem 2: If a position that ends the game is accessible from the position at the beginning of a player's turn, that player can guarantee that the game will end.
Lemma 3: There is no chance in chess.
Lemma 4: Chess is a game of perfect information.
Lemma 5: Every position has finitely many positions that are accessible from it.
Conclusion: If a position is a game ending position, a player can determine that it is because there is perfect information. There is finite set of positions accessible from a given position in chess, so the player can always determine if one of them is a game ending position by analyzing each one. The player can also guarantee that a move will lead to the desired position because there is no chance.  
Final Proof: There is an ideal opening move in chess.
Lemma 6: With each move, the number of accessible game states is reduced.
Lemma 7: An ending state is accessible from every game state that is not itself an ending state.
Lemma 8: A player can only move into an end state that results in a tie or a win.
Definition 3: Chess Tree

From every game state A, there is a finite set of game states reachable from it (the legal max is 218 and the minimum is of course 0 for end states). Call the members of this set B1 ... BN. From each of B1...BN, there is a new set of game states accessible for that position. This process is recursive until the set of game states accessible from a final game state is empty. These can be arranged in a topological structure called a chess tree, which will be used to visualize the game. Such a tree would look like this, but it would be of much greater complexity [http://i.investopedia.com/inv/dictionary/terms/TREE_D~1.gif]
Assumption: There is a path down the tree that will allow White to win or tie the game no matter what Black does.
Conclusion: There is an opening move that will guarantee a win if played correctly. 

If you want an ideal first move--one that guarantees no less than a draw with best moves for both sides you can try:

1. a3  or 1. b3  or 1. b4 or 1. c3  or 1.c4 or 1. d3 or 1. d4  or 1. e3  or 1.e4

or 1. f4  or 1. g3 or 1. h3 or 1. Nf3  or 1. Nc3  or 1. Na3 or ` 1. Nh3

Hoever there is no opening at all which will guarantee a win if played correctly.  This is because the game of chess is a draw if played perfectly by both sides.

I guess it would depend on what your opponent moved. I mean, they have 20 possible moves on move 1. That would have to be a really good move to be able to not be stopped by any of the 20 choices.

Right. Again, this is all hypothetical. I don't think we can truly solve chess because of the vast theories behind it. There are, after all, more positions in chess than atoms!

We cannot solve chess in the sense of giving all the possible games but most good players already know that if both sides played perfectly the game of chess is a draw.

There's almost certainly more than 1 perfect game, and IMO there is almost certainly more than 1 "best" first move.

Fatal flaw: No one plays correctly, not even computers - it's impossible at the moment, and for the foreseeable future. This mean - at least in one sense (the practical sense) - that there is chance in chess.

In any case, what wafflemaster says may well be true. Your "proof" would need to exclude that too.

(I suppose that's why this thread is in the Fun With Chess section.) 

"We cannot solve chess in the sense of giving all the possible games but most good players already know that if both sides played perfectly the game of chess is a draw. "

This be false!

Actually one can play a perfect game. I have as well as millions of others.

But a perfect game is not solved as a draw.

A perfect game is not solved as a draw in the sense that we do not have a zillion pages of computer analysis to "prove" a perfect game is a draw but the overwhelming circumstanial evidence is that it is a draw.

Shepi, you may say that most good players do not already know the game of chess is a draw--but simply put--you are wrong.

lemmas numbers 3 and 4 are ambigous and very possibly wrong.

lemmas 6 or 7 depend on the meaning of the word "accessible" what is your meaning?

your conclusions have flaws.

I'd go with smile, an nod, and shaking your opponent's hand.

I thought White has the advantage and therefore perfect play on either side will end with a win for white.

Because White's extra tempo advantage dissipates as moves are played, it may become an insignificant factor in a "perfect play" game - unless that game is relatively short. Pure speculation, of course.

The idea of the chess tree is not quite correct. Since two distinct parents can have the same children(means that a state can be reached by different move order) this should be a Chess Lattice, meaning that there can be more than one solutions to your question!

The best game of chess that I played is the one I lost!!!

Chess has not been 'solved' yet, so we don't know the outcome of the 'perfect' game - http://en.wikipedia.org/wiki/Solving_chess

Wouldn't be preferrable to devote the time you spent to write down this errr, thesis on chess, and which says nothing to anyone, to the study of a few classical games?

You probably don't know that much more since you suggest pawn promotion is an impurity.

http://www.chess.com/forum/view/general/pawn-promotion-an-absurd-chess-impurity