The Metaphysics of Chess

This is in response to an interesting article by Hard Days Knight.

I had planned to write a comment on his blog about this, but it became bigger than just a comment, a topic was required.

Beware that I am not a trained Game Theorist. Though I play one on the Internet. All conclusions and basis and actual game theory is purely a coincidence. Though I would appreciate any thoughts you might have. I am using HDK's page as a jumping off point. This isn't personal, but is instead my take on things.

He has some fundamental presuppositions, that he then utilizes to jump to some conclusions. The problem is that it sort of seems like chess, but different enough that it made me search for what I think might be wrong. This is my take.

One of his presumptions is that chess is solely a game of errors. I am going to represent this as a balance. Each side has a bowl of errors. One person adds errors from their bowl, and then the next. The game becomes eventually one sided and a loss if they have in balance have put in too many errors. Skill can be represented I suppose, by the granularity of errors at hand, and the granularity of the tools available to put the errors in. A novice makes big errors, a grandmaster makes little one.

Another way to think of this, is as Jenga, when each side pulls out a piece, until eventually there is catastrophic failure (tactics).

There is a presumption that the game is a draw from the beginning. There is no proof of this, only belief. It could be believed that white is winning, or that it is a zugzwang and black is winning. From a game theory standpoint, it is possible to construct games where there is no such thing as a draw, or that there is no such thing as a winner.

I personally think this view is an inappropriate algebraic reduction of the game, and it gives a highly distorted view of the game. And that this distorted view, leads to distorted conclusions. I don't see the game as solely a collection of errors, but rather a starting state, and that then information is added to the game. There is a range of information from error or nonsense (by a novice or a blunder), to sensical information (from master to super grandmaster).

Here is my stunning addition to the game theory. If perfect play is unobtainable, than perfect play's existence cannot be distinguished from its non-existence and therefor can be totally ignored for practical play purposes. This actually a pretty heavy paragraph, and it may have been stated somewhere else first, but if not (TM). Unobtainable Perfect Play. Or UPPity(TM).

The conclusions that I make, if there is no practical thing as perfect play, is that the single most important consideration for determining the outcome of a game, is not it's initial state, nor the material, but the relative skill of the players. Chess and Go are two examples of no practical existence of perfect play or UPPity games. Tic-Tac-Toe is a game that does have obtainable perfect play. And you can create games where white always win and black always wins. And in these cases relative skill is not important. It can be independently determined what the best move is always.

If there is no such thing as perfect play, it can often be impossible to measure the certainty of the game at a given ply level, and that the game is not necessarily determined at the ply. Which means that there does exist a state of "winning" and "losing", even if you are not certain to win or lose. I am guessing that there may be a correlation to the fuzziness of the measure with how unobtainable the perfect play. (Go V. Chess) But I could be wrong.

Perfect play determines the maximum skill level for a player. But if it is impossible to obtain perfect play, then skill is practically and undistinguishable as unbounded. It is possible to be more skillful than anyone/thing at the time, and still be able to have skill improvement beyond that level.

I personally think that at any given ply, there is not an absolute that can be known about the position, and that there is a single best move (though there occasionally is). I think it is wrong to think of the game as moving towards entropy from move 1. I think at it's highest levels it is a game where information is added, and the ability to deal with and leverage that information (skill), is where it is played. Not error. I think that it is possible to create games that are based on error. I also think that there is a level where error is the most important thing in games such as chess. But I do not think it is a game that is defined by error.

So chess is a just like it appears to be. It is a challenge of skills. That nothing is more important than the difference in skill levels in determining game outcome, not who moves first, and not material consideration. And that skill is best represented by information added to the game, not by just minimizing error. And that making a machine that plays, does not necessarily represent "the" truth, but "a" view about the game.

This entire argument seems similar to Einstein vs. The Quantum Physicists. A causal and knowable reality, or one that can be only supposed. The question is, not which is reality, but which best describes reality and be best leveraged in reality.