There is an Ideal Opening Move in Chess

Introduction:This debate has become somewhat disorganized, so I'll pick out the key points so I can respond concisely. I will try to do so as charitably as possible. Con still seems to have numerous misunderstandings. His case rests on trying to differentiate chess from other solvable games based on irrelevant differences.Theorem 1:Con his agreed to this. I ask that it not be contested next round since I will not be able to reply.The Resolution:Con's argument here rests on his overlooking of the word "enable." You can always voluntarily throw a game of chess (unless you are in an odd configuration where a loss is literally impossible). A guaranteed win is enabled if the player cannot fail to win if he makes the right moves. The fact that players do in fact make the wrong moves is irrelevant.Con's interpretation of an ideal move is silly. As I said in Round 3, this means that no game can have a perfect strategy, even "Who can name the highest number?" because a player can fail to employ that strategy. Surely whether or not something is often done correctly has no bearing on whether or not there is indeed a correct way.Chance in Chess:Con is still confusing the difference between uncertainty in the game and human error. It is perfectly consistent to say that a person will fail to take information into account that is available to him. The rules of the game allow Player A to see that a rook threatens his bishop. If he doesn't notice and makes the wrong move as a result, that is a result of his error, not uncertainty within the game about whether the rook was threatening this bishop. Against, contrast with Risk and Stratego, games of genuine uncertainty.Con does agree that players will always move successfully. But maybe some people are so stupid they can't even do that, or play chess at all? Why does Con arbitrarily choose the average human as his standard? It is surely plausible that chess grandmasters (or even skilled amateurs) never fail to perceive events on the board. What his argument really hinges on is our inability to comprehend every possible sequence of events. But this has nothing to do with chess either; it's a coincidence of biology (or really physics). A computer program has been designed that is unbeatable at checkers, and the only reason that chess has not been similarly solved is that it is more complex and requires more computing power. He is taking a purely human-centric approach to a game that exists in the abstract.If it is easier, pretend that there is a race of supermen who are smarter than the smartest computer and never make mistakes. If they play chess, it will still be the same game, but none of these factors will apply. It is silly to define solubility in terms of human brain or computational power. Otherwise abstract mathematical problems (what is the 9347109374th prime?) could switch from solvable to unsolvable based on human technology. But solubility is itself an abstract mathematical concept and should not change when a computer is invented.Game States & Chess Trees:Con seems to agree to my prior claims. However, there is a discrepancy:Con: "I mistook this argument as the Pro claiming that there exists a path from the beginning of the game to the end that always guarantees a win or a tie."I did say that! You examine the tree for White and see if there is a path that leads to a win or tie no matter what Black does. If there is, White has a perfect strategy. If not, then no matter what White does, Black can counter. But that means Black has a perfect strategy, because Black can always counter White! It's a really elegant proof when you understand it.Finiteness of Chess:The real debate seems to lie under this heading, though it is a misnomer because Con agrees that chess is finite and thinks there are complicating factors.Con seems to agree that Tic-Tac-Toe is solvable (though he seems to contradict himself on this), and argues that chess is meaningfully different. I interpret his argument like this:"Tic-Tac-Toe is different from chess because in Tac-Tac-Toe, nothing is ever undone. In chess, pieces can be removed, moved, and switched, but in Tic-Tac-Toe they can only be added."But my argument is indifferent to this entirely. It only concerns game states. What the differences between those game states are determined by is irrelevant to the solution to the game. An equivalent game to chess (which would be much harder to understand) would consist of nothing more than a series of numbers representing game states and functions represented moves. The board, the pieces, and the legal moves are all irrelevant to the fact that the game states can be arranged in a topological structure according to which the correct combinations are legally accessible from one another. I emphasize the word topological because the final design of this tree is the only important thing. Con has nothing more than an unproven intuition that more complex rules meaningfully alter the inherent nature of the game. The only reason I need to appeal to the rules at all is to justify Theorem 1, which is very obviously correct.Con says: "Just because one wins a game of chess it doesnt imply that a perfect strategy exists because that particular route to victory that person just took could have been countered in numerous ways, along with any other path to victory that other people have taken."This is to miss the point entirely. I am sure that the huge majority of paths can be countered. The question is, can all of them? As we see above, either answer implies an ideal move! If there is a sure path to victory, then each move that leads down it is an ideal move. If there is no path, then the opponent has a series of ideal moves to victory: counter every time!Con also says, " If a move were truly ideal then it would still be able to guarantee victory despite human error..."I think this is a preposterous standard because a player can always throw a game.Con must agree that there a situations in which a player can force checkmate later in the game. This is the premise on which chess puzzles rest. I defy Con to tell us that there is no ideal move for Black in this position: http://0.tqn.com... Yet surely he can fail to make it. Con must give up this argument to stay in the bounds of a reasonable discussion.Conclusion:My initial proof and subsequent explanation meet the "weak MIT standard" of proof: while not fully deductive from axioms, it is laid out in common language rigorously enough so as to be immune to attack from a well caffeinated mathematician.The Con position is based on mistaken intuitions about the game. He brings in a series of folk game theoretic notions like luck, mistakes, and odds. Luck and odds are rigorously defined in terms of probability and they do not exist in chess. Someone who claims to have lost chess because of luck or who says the game is broken because of a mistake is surely a sore loser. In my opinion, a great deal of appreciation for the mathematical beauty of the world is lost by restricting oneself to simplistic conceptual schemes such as this. Accordingly, Con has offered no proof whatsoever that his objections are actually relevant. I have thoroughly examined each of them an explained why that are not.Voting Points:These are my suggestions on who you should vote for. I'll explain why I think this is good to do in the comments if anyone cares. I urge Con to include this also.Conduct: TieI think that conduct was good on both sides.Spelling and Grammar: ProCon makes numerous spelling and grammatical errors, and his case is badly organized. I have occasional typos, but I am generally far more articulate.Arguments: ProSee my conclusion :DSources: TieSources were not important to this debate, so I urge a tie vote.