Is there a perfect algorithm for chess?

Question

I was recently in a discussion with a non-coder person on the possibilities of chess computers. I'm not well versed in theory, but think I know enough.

I argued that there could not exist a deterministic Turing machine that always won or stalemated at chess. I think that, even if you search the entire space of all combinations of player1/2 moves, the single move that the computer decides upon at each step is based on a heuristic. Being based on a heuristic, it does not necessarily beat ALL of the moves that the opponent could do.

My friend thought, to the contrary, that a computer would always win or tie if it never made a "mistake" move (however do you define that?). However, being a programmer who has taken CS, I know that even your good choices - given a wise opponent - can force you to make "mistake" moves in the end. Even if you know everything, your next move is greedy in matching a heuristic.

Most chess computers try to match a possible end game to the game in progress, which is essentially a dynamic programming traceback. Again, the endgame in question is avoidable though.

Edit: Hmm... looks like I ruffled some feathers here. That's good.

Thinking about it again, it seems like there is no theoretical problem with solving a finite game like chess. I would argue that chess is a bit more complicated than checkers in that a win is not necessarily by numerical exhaustion of pieces, but by a mate. My original assertion is probably wrong, but then again I think I've pointed out something that is not yet satisfactorily proven (formally).

I guess my thought experiment was that whenever a branch in the tree is taken, then the algorithm (or memorized paths) must find a path to a mate (without getting mated) for any possible branch on the opponent moves. After the discussion, I will buy that given more memory than we can possibly dream of, all these paths could be found.

Answer 1

Chess is an example of a matrix game, which by definition has an optimal outcome (think Nash equilibrium). If player 1 and 2 each take optimal moves, a certain outcome will ALWAYS be reached (whether it be a win-tie-loss is still unknown).

Answer 2

For the record, there are computers that can win or tie at checkers. I'm not sure if the same could be done for chess. The number of moves is a lot higher. Also, things change because pieces can move in any direction, not just forwards and backwards. I think although I'm not sure, that chess is deterministic, but that there are just way too many possible moves for a computer to currently determine all the moves in a reasonable amount of time.

Answer 3

It's perfectly solvable.

There are 10^50 odd positions. Each position, by my reckoning, requires a minimum of 64 round bytes to store (each square has: 2 affiliation bits, 3 piece bits). Once they are collated, the positions that are checkmates can be identified and positions can be compared to form a relationship, showing which positions lead to other positions in a large outcome tree.

Then, the program needs only to find the lowest only one side checkmate roots, if such a thing exists. In any case, Chess was fairly simply solved at the end of the first paragraph.

Answer 4

I know this is a bit of a bump, but I have to put my 5 cents worth in here. It is possible for a computer, or a person for that matter, to end every single chess game that he/she/it participates in, in either a win or a stalemate.

To achieve this, however, you must know precisely every possible move and reaction and so forth, all the way through to each and every single possible game outcome, and to visualize this, or to make an easy way of analyising this information, think of it as a mind map that branches out constantly.

The center node would be the start of the game. Each branch out of each node would symbolize a move, each one different to its bretheren moves. Presenting it in this manor would take much resources, especially if you were doing this on paper. On a computer, this would take possibly hundreds of Terrabytes of data, as you would have very many repedative moves, unless you made the branches come back.

To memorize such data, however, would be implausable, if not impossible. To make a computer recognize the most optimal move to take out of the (at most) 8 instantly possible moves, would be possible, but not plausable... as that computer would need to be able to process all the branches past that move, all the way to a conclusion, count all conclusions that result in a win or a stalemate, then act on that number of wining conclusions against losing conclusions, and that would require RAM capable of processing data in the Terrabytes, or more! And with todays technology, a computer like that would require more than the bank balance of the 5 richest men and/or women in the world!

So after all that consideration, it could be done, however, no one person could do it. Such a task would require 30 of the brightest minds alive today, not only in chess, but in science and computer technology, and such a task could only be completed on a (lets put it entirely into basic perspective)... extremely ultimately hyper super-duper computer... which couldnt possibly exist for at least a century. It will be done! Just not in this lifetime.

Answer 5

From game theory, which is what this question is about, the answer is yes Chess can be played perfectly. The game space is known/predictable and yes if you had you grandchild's quantum computers you could probably eliminate all heuristics.

You could write a perfect tic-tac-toe machine now-a-days in any scripting language and it'd play perfectly in real-time.

Othello is another game that current computers can easily play perfectly, but the machine's memory and CPU will need a bit of help

Chess is theoretically possible but not practically possible (in 2008)

i-Go is tricky, it's space of possibilities falls beyond the amount of atoms in the universe, so it might take us some time to make a perfect i-Go machine.

Answer 6

if you search the entire space of all combinations of player1/2 moves, the single move that the computer decides upon at each step is based on a heuristic.

There are two competing ideas there. One is that you search every possible move, and the other is that you decide based on a heuristic. A heuristic is a system for making a good guess. If you're searching through every possible move, then you're no longer guessing.