# Winning or losing in chess - a question of combinatorics?

I have observed that every chess game can be assumed as a sequence of moves that lead either to win or to lose (in a few cases to a drawn game). It is very interesting to Count all the moves that are possible in any chess game. May be $N$ the number of chess moves done in a game (contains moves done by white AND by black). Depending on the previous chess moves one can Count the number of chess moves $n_i$ for the move number $i$ that are possible. But how many possibilities are there for winning or losing related to all possible chess games? Is there any literature dealing with this question?

• $N$ is the number of moves in a finished game, right? – Vladimir Vargas Feb 7 '15 at 20:57
• yes, it is the number of moves when the game is finished. – kryomaxim Feb 7 '15 at 20:58
• Drawn games are very common in serious chess. – John Bentin Feb 7 '15 at 21:00
• Suppose white wins in the game $a$. ¿Is there a way in which white wastes one tempo (makes a move with no significance in the outcome of the game) such that black wins a second game $b$ just by reversing the opening? i.e., black plays what white played in game $a$, and white plays what black played in game $a$ (except from one move that isn't relevant in the game). I can't think of a counterexample, that's my conjecture. – Vladimir Vargas Feb 7 '15 at 21:05

Counting the number of possible paths of play is related to the task of actually solving chess, upon which there has been a lot of research. The difficulty is that there are incredibly many ways that chess can actually play out, which you hint at. I have seen in quoted that there are more possible paths of play than there at atoms in the universe. WolframAlpha tells me there are about $10^{80}$ atoms in the universe, so presumably there are more chess moves than that. Anyway, this is such a fun topic there's a Wikipedia page on it: