Is there a perfect algorithm for chess? [closed]

Answer 1

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 2

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 3

Mathematically, chess has been solved by the Minimax algorithm, which goes back to the 1920s (either found by Borel or von Neumann). Thus, a turing machine can indeed play perfect chess.

However, the computational complexity of chess makes it practically infeasible. Current engines use several improvements and heuristics. Top engines today have surpassed the best humans in terms of playing strength, but because of the heuristics that they are using, they might not play perfect when given infinite time (e.g., hash collisions could lead to incorrect results).

The closest that we currently have in terms of perfect play are endgame tablebases. The typical technique to generate them is called retrograde analysis. Currently, all position with up to six pieces have been solved.

Answer 4

Some games have, in fact, been solved. Tic-Tac-Toe is a very easy one for which to build an AI that will always win or tie. Recently, Connect 4 has been solved as well (and shown to be unfair to the second player, since a perfect play will cause him to lose).

Chess, however, has not been solved, and I don't think there's any proof that it is a fair game (i.e., whether the perfect play results in a draw). Speaking strictly from a theoretical perspective though, Chess has a finite number of possible piece configurations. Therefore, the search space is finite (albeit, incredibly large). Therefore, a deterministic Turing machine that could play perfectly does exist. Whether one could ever be built, however, is a different matter.

Answer 5

There are two mistakes in your thought experiment:

1. If your Turing machine is not "limited" (in memory, speed, ...) you do not need to use heuristics but you can calculate evaluate the final states (win, loss, draw). To find the perfect game you would then just need to use the Minimax algorithm (see http://en.wikipedia.org/wiki/Minimax) to compute the optimal moves for each player, which would lead to one or more optimal games.

2. There is also no limit on the complexity of the used heuristic. If you can calculate a perfect game, there is also a way to compute a perfect heuristic from it. If needed its just a function that maps chess positions in the way "If I'm in this situation S my best move is M".

As others pointed out already, this will end in 3 possible results: white can force a win, black can force a win, one of them can force a draw.

The result of a perfect checkers games has already been "computed". If humanity will not destroy itself before, there will be also a calculation for chess some day, when computers have evolved enough to have enough memory and speed. Or we have some quantum computers... Or till someone (researcher, chess experts, genius) finds some algorithms that significantly reduces the complexity of the game. To give an example: What is the sum of all numbers between 1 and 1000? You can either calculate 1+2+3+4+5...+999+1000, or you can simply calculate: N*(N+1)/2 with N = 1000; result = 500500. Now imagine don't know about that formula, you don't know about Mathematical induction, you don't even know how to multiply or add numbers, ... So, it may be possible that there is a currently unknown algorithm that just ultimately reduces the complexity of this game and it would just take 5 Minutes to calculate the best move with a current computer. Maybe it would be even possible to estimate it as a human with pen & paper, or even in your mind, given some more time.

So, the quick answer is: If humanity survives long enough, it's just a matter of time!

Answer 6

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.