Is Chess solvable?

[MusashiStyle]

remember that both sides may choose to maneuvre their pieces back and forth ad infinitum ( this is if you exclude the 50 move rule or the 3 fold repition rule)

So then you want to solve chess with the 50 move rule and the treefold repition rule.

It seems to me that chess would be solvable then, but only because of these rules. Basically, these rules state that one side must move a pawn forward or make a piece exchange at least once every 50 moves or else the game may be declared "drawn".

So this rule forces all the pawns to queen or be exchanged. This would leave a situation with just pieces. But then the other side of the 50 move rule kicks in which forces all these pieces to be exchanged or else the game will be declared drawn etc.
So my point is that once you have a computer that can calculate all the way to the end of these lines, the 50 move rule enforces the non-infinity of moves.

Hope that makes sense.

[FortunaMaximus]

[ QUOTE ]
So my point is that once you have a computer that can calculate all the way to the end of these lines, the 50 move rule enforces the non-infinity of moves.

[/ QUOTE ]

You'd be able to keep the set within a finite bracket, sure.

That hardly lessens the scope of the problem. It's still a pretty huge solution set.

The issue probably is that it wouldn't provide a complete set.

And to devise an algorithm that takes into account solvable games while avoiding irrelevant loops, which the 3-fold repetition rule can filter for does not remove the problem of the one-fold and two-fold repetition issues. If those two other issues are accounted for, sure, then the algorithm clarifies a bit.

The halting probability of such a program would be nonzero, however. Even if the parameters involved are finite. Simply because of the space the data would occupy.

In linear processing systems, it is solvable, but it'd take too long. Memory can be reused as you would be able to discard the trash data after checking it. You would have to be extremely careful with the trashing process though. So the carrying capacity never needs to be astronomical.

In systems that use the compressed amounts of time that q-computing would permit, you run into an immediate problem that comes from being able to temporarily store vast sums of data. But it's possible, but not probable.

It leaves me wondering if such a calculation has a nonzero halting probability. It would seem this is not so given the seemingly simple exponential scope of the problem. The bothersome aspect is such an incorrect algorithm can run for eons without being certain of this.

If number or solution sets can be said to have substance or a form in three-dimensional space, what one is able to intuitively visualize is the solution, or the pieces, are far too heavy for the chessboard.

(1. a3) o_O

[madnak]

[ QUOTE ]
remember that both sides may choose to maneuvre their pieces back and forth ad infinitum ( this is if you exclude the 50 move rule or the 3 fold repition rule)

So then you want to solve chess with the 50 move rule and the treefold repition rule.

[/ QUOTE ]

Nah, you would only need to record each position. The positions themselves are independent of the specific game tree (that is, there is no difference between repeating the moves 50 times and 5,000,000 times, in game terms, so the computer doesn't have to distinguish between the two cases).

[Daisydog]

I believe it was either Ernst Zermelo or Harold Kuhn who proved that every finite game of perfect information has a pure strategy Nash equilibrium.

[Hercules]

To everyone, who says that the perfect ending in a chessgame is a draw, you might wanna read this:

1) The fact that many games end in a draw does not proof this fact at any point. Most players play prejudiced like 1.h4 is bad and 1.e4 is good. We (chessplayers all know, that like 50 years ago everybody would laugh at you, if you`d have played the Sveshnikov defense in the sicilian. Or what about isolated pawns?
There have been so many shifts in paradigmata, that it is impossible for us today to say that the current top players are playing optimal. Modern chess is more about dynamic factors and its more about exceptions than rules.
So if the GM`s don`t play optimal,then the results of them do not show anything.

2) However i believe that chess is a solved game, but i don`t know anybody, who has the key. Although computer programs are amazingly strong, they are still only "perfect humans". All their "knowledge" is knowledge given by humans. The main difference between top players and computers are, that the computers simple compute better and don`t do devastating mistakes (see the match Fritz vs Kramnik)
So i think we are still far away from "solving" chess. Every month there are some creative new ideas in the opening out there, which no one has ever thought of before.
So i can`t see anybody drawing conclusions on what the "perfect score" must be.
3) I have a friend and he ran some simulations with a computer and his output was, that BLACK wins most games theoretically. This is however a contradiction to reality, because white has obv a decent advantage in today`s thinking and playing.
But his simulation didn`t use brain. It just ran every legal move order (randomly) and spit out the fact that black won most games. That doesn`t prove anything, but it is something to consider before saying "a perfect game ends draw" etc...

[ChrisV]

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2) However i believe that chess is a solved game, but i don`t know anybody, who has the key. Although computer programs are amazingly strong, they are still only "perfect humans". All their "knowledge" is knowledge given by humans.

[/ QUOTE ]

This is not true. Computers don't have any "knowledge" of how to play chess, really. Their main advantage is brute force evaluation of millions of moves, which is completely different to how humans play chess. In fact, against the lesser computers of yesteryear, and even to some extent today, the tactic used by humans against computers was to play "anti-computer" chess, manouevering the computer into a situation it would play suboptimally. If computers were simply "perfect humans" this would not be possible.

[ QUOTE ]
I have a friend and he ran some simulations with a computer and his output was, that BLACK wins most games theoretically. This is however a contradiction to reality, because white has obv a decent advantage in today`s thinking and playing.
But his simulation didn`t use brain. It just ran every legal move order (randomly) and spit out the fact that black won most games.

[/ QUOTE ]

I would be surprised if this were not a sample size issue. I wouldn't expect to see any bias to White in this situation, I'd expect it to be 50/50.

[MidGe]

Of course, it could simply be like Tic-Tac-Toe, where whoever starts (white in chess), and plays optimally, wins if the other player plays sub-optimally otherwise it results in a draw. But since we are such a long way away from calculating it (via computers), we might as well assume so. It seems so from the results and rankings.

[AndysDaddy]

> Welcome to Microsoft Chess Master 8000!
> White to mate in 137
> What is your move?
&gt; <font color="red">h4</font>
&gt; Thank you. My move is:b6
&gt; Black to mate in 112
&gt; What is your move?