the problem is how very many possible combinations of piece positions that can be accomplished in a single game of chess, much less over every game in existence.  Not to mention when pieces get taken away, or when Queens are added to the board.

I have no idea how long it'd take, however I do know that brute forcing that would take an absolutely monumental amount of time and computing power, and that's with even the most efficient code.

Let's take an example, you have a fully set board.
First turn, you have 8 pawns that can move either 1 or 2 spaces, and 2 knights, that can each hit 2 positions, making the total number of outcomes 20.  So you now have 20 boards.  Now each of those 20 boards would have an additional 20 boards, from the same initial setup of Black, which makes the 2nd turn give you 20*20, or 400 unique combinations.  It only gets worse from there as you get to the pieces that can move multiple spaces, and you have to add one scenario for each and every space they could move.  A single queen alone could spawn 20 board configurations.

TL;DR - don't try to program this with Brute Force, I have no idea of any way to do it off the top of my head, and I'll probably be thinking about it for weeks now, but unless you don't want your computer to Crash due to running out of RAM, you'd better leave this one be.

Yeah I've been thinking about it and haven't been able to come up with much.  I have a bit of an idea but I can't put it into actual workable words/pseudocode yet.

That would be much more reasonable and easy, considering it'd only have to think ahead up to 5 or 6 moves, rather than entire games.

A quick Google leads to the Wolfram page with estimates: http://mathworld.wolfram.com/Chess.html .

4th Paragraph

I would suggest taking a course in Discrete Mathematics. Discrete deals heavily with combinatorial problems much like the original question. This question is interesting however because their can be infinite games in which a winner is never declared. I assume that's why Hardy found it necessary to limit the amount of moves to 40.

The link also raises another interesting question:

Google gives an estimate, Zombie wanted the exact answer.  Given that Chess has a limited number of Pieces, and places they can move, I'd think that there -would- be a definite answer (given that ties also counted as the end of a game) though it'd be a rather high number.

This is untrue and would only be true if pieces weren't limited by specific movement types and board size.  Each peace has, in fact, a finite number of states.


The question is how many unique -games- of chess could be played, not how many unique board configurations there are.  This means that the only thing that needs to change to make it a unique game is a single move.  Eliminating previously used boards isn't an option because of there being many options to change the game from that point.

possible outcomes: white wins, black wins, draw
3.

on a more serious note, if that's what he was thinking, it'd likely be a lot smaller, though still a large number, I took it to mean how many possible unique games overall.

the question would define a move in a game of chess as a move that pushes the game forward, to remove that possibility.

I wonder why no one has looked at the rules for when a draw occurs.
If you had you would have realized that a chess of games is guaranteed to be finite due to the 3-fold repetition rule and the 50-moves rules.
Refer to World Chess Federation's article 5 on the completion of the game. Look also at article 9 which elaborates on draws.

On a unrelated note I did not know about the Anti Doping Regulations in chess XD

I dunno how many possible unique games there are. It seems like a very hard combinatorial problem to solve.
There obviously are many more unique games than there are unique board configurations. In fact I believe there are many many more, like millions or billions times more.
You can store the possible board configurations with transitions between them marking possible moves. Yes, I am talking about a directed graph structure where states are board configurations and transitions are possible moves. You can perfectly fine code all possible moves in such a structure which definitely will be much smaller than a game tree describing all the possible moves. It will not be entirely trivial to roll out paths since you have to take care that the rules are fulfilled. You can for example only take a cycle x amount of times.

You can say that you use less space at the price of speed.


More on the practical side I can tell you that no top Chess AI use pattern recognition.
I dunno why the minimax game tree based approaches worked better.
That said Alpha-Beta pruning is a search algorithm which improves on minimax so I bet that's what's used in practice.
I have also heard about using the null-move heuristic is often used though I don't know what it entails.

I hope I have given you some more to think about with my limited knowledge on computer chess ^^
*hugs*

yeah I was actually going to mention that about draws.


that removes the possibility for an infinite number of chess games.
Sure it's still a large amount, but we're anticipating that to begin with.