Thursday, June 28, 2007

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.

7 comments:

Temposchlucker said...

I do like the approach of HDK, since it helps him (and us) to formulate new things about the game. I have the same objections as you against his statements. Only you have formulated it better.
I like to add something.
Since there is no perfect play, there are no absolute errors. If both players aren't able to see each others errors, then the errors are non existent. Which adds an element of psychology into the competition.
I see you use Ockhams aftershave, can I have some?

svensp said...

Hi,

Just two remarks:

"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."

I think, there is perfect play. If we agree that in any situation for any two moves, given infinite time we can find out which one is better or if they are equal then (for there is a finite number of possible moves) there is a best move in any given situation. Of course we never have infinite time, so it is unobtainable in general. But that imho doesn't make its existence/non-existence irrelevant/ignorable for practical purposes: If one strives to get as close to perfect play as possible (given constraints like time and abilities) it helps to know that it exists. If it wouldnt exist this would mean there would exist situations with no best move (not in the sense of two equally good, but that there is no final criterium for a decision) and so it would be pretty senseless to even search for it, because criteria would be useless, for no possibility of ordering would exist.

"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."

This is a great idea, sounds true.

kind regards,
svensp

hisbestfriend said...

Tempo,

I think I understand where you are going, but I don't think failure to see error is a conclusion of no perfect play. I think that error is what defines under a master. Like leaving a piece en-prise or missing the tactic.

I think that 2 players can miss each others errors due to lack of skill levels, and in that case I am sure that the pope does you know what in the woods! Or something :-)

But more seriously, you're right, and computers do try and emulate that with "contempt".

hisbestfriend said...

Svensp,

Than you for your comment! Seriously, it helps in my cloudy thinking to be challenged.

I am not sure but in the first bit of feedback, you have gone from disagreeing, to nearly making my point precisely. I don't agree that there is no reason for a search, but that perfect play is not what makes the measurement, but that individual skill is what makes one better at doing it.

Perfect play seems possible in chess because of opening books and tablebases, and the bounding of the game. Even if it is like the chessboard and the grains of rice story. It just seems like it is possible, doesn't it?

Let's try this with go, in which the move tree cannot be bounded by the atoms in a thousand universes, or a thousand thousand. (I actually think it is way more than that, but you get the point). You still try and think deeply as a player, and you do make decisions as a player. And the better decisions win. You just cannot know at a given ply if you have won or lost. And it is impossible to know. But I think it still makes the game playable.

The battlefield is not the truth. But that the result is the truth, and the battlefield is the process.

That skilled players *do* make better decisions, and that relative skill is what decides the game, more than anything else.

That ever improving skill is practically possible, because achieving perfect play isn't. And that since perfect play isn't, there are cases where it is impossible to say that you have one or lost at a given ply, that there isn't truth at the board, only a view. Until it is won or lost.

Or as Bobby Fisher would say: I believe in good moves.

svensp said...

hisbestfriend,

I agree, perfect play isn't possible and skill is the best measurement for the outcome of a game (if it's not a clear cut victory ("clear cut" relative to the abilities)). So from the perspective of someone looking outside wondering how a game will end, I agree that the question of existence of perfect play is irrelevant. Not so for someone playing in the game.

I'm afraid I don't know much about go, only heard it is pretty interesting and even more complex than chess. So I can't tell if it is so:

"You just cannot know at a given ply if you have won or lost. And it is impossible to know."

If that was so, wouldn't it make the game random? Obviously, you don't think so, I'll have to think about this again, interesting point of view as well as the ideas concerning battlefield/truth/result.

"That skilled players *do* make better decisions, and that relative skill is what decides the game, more than anything else."

I agree, my point was like: The reason there are better decisions and worse decisions is the (background) existence of perfect play (even though it's unreachable). Of course, in actual play which decisions are made is all important not the concept of "perfect play" or its current meaning.

"That ever improving skill is practically possible, because achieving perfect play isn't. And that since perfect play isn't, there are cases where it is impossible to say that you have one or lost at a given ply, that there isn't truth at the board, only a view. Until it is won or lost."

I think there is truth at the board, but it is simply not this truth which determines the outcome, but the best approximation to it by one of the players (how much the view fits the truth and how much the player profits from it (no use if one recognizes deeper than opponent that one is lost...)). The better the players and the less complicated the position the more this truth does de facto determine the outcome. But this might as well just be a play with words, I think our opinions aren't that different from each other.

Thanks for your entry and extensive answer, good stuff for thinking.

kind regards,
svensp

HardDaysKnight said...

Great post. I’d like to make a few comments:

HBF: "One of his presumptions is that chess is solely a game of errors."

Not soley, but in the sense that from any given position, a move either maintains the inherent quality of the position, or it degrades the position from the perspective of the player making the move.

However, a player must have the skill to identify the error, and make moves that exploit it. From such a position there may be any number of moves that sufficiently exploit the error.

HBF: "[Chess] is a challenge of skills. That nothing is more important than the difference in skill levels in determining game outcome, "

I totally agree.

HBF:"The question is, not which is reality, but which best describes reality and be best leveraged in reality."

From a tournament player’s perspective, I completely agree. My metaphysics is the attempt to correct my misapprehensions: 1) I want to stop pressurizing myself, to stop entering the bog, the abyss of unwarrented calculations, and unfounded speculations, in an attempt to create a blow-out move ex nihilo. The answer? Realize that you can only win if he errs, so look for his errors, and take advantage of them. 2) I want to stop fearing that my opponent can destroy my position ex nihilo. The answer? Realize that if the position was good before his move, it must be good after his move, and there must be resources to meet his move.

So, while I think that the metaphysics is essentially and objectively true, it is also my attempt to gain leverage.

Thanks again for your interesting blog.

Let the discussion continue!

Regards, HDK

hisbestfriend said...

svensp,

There is this sort of game progressions for tic-tac-toe, checkers, chess and go. They are all bounded simple games, but the move trees are dramatically bigger in each case. Where you have perfectly solvable on one end, to on the edge, to conceivably, to unconceivably. You don't need to know the game well, just the concept of the move tree and perfect play being unobtainable, for this discussion.

Which gives you a range of theories, and where theories break down, and where only theories can exist.

Not knowing (certainty) if a game is won or lost doesn't make it random I don't think. I think there is a concept of winning and losing. Proof of non-randomness is that the skilled players keep winning. (This is part of the argument in poker and bridge).

And ultimately the discussion of game theory, is there "truth" in the game, or is there only "truth" in the outcome. And from my bong holding friend on the front (the good images just COME to me!), is that if you can't achieve perfect play, then the only truth is in the outcome. And what happens on the battlefield, while it may be scientific in nature, tends towards art. Hey maybe they should make a movie!


And HDK I am not ignoring you, but you have again given me an everlasting gobstopper to chew on. I will reply, but I need to digest the concepts a bit first.