Friday, 16 September 2011

Number of possible chess games

"How many different games of chess are there?" was a question I was asked at the Amaroo School Chess Club the other day. Clearly the question was about the number of possible games played using standard rules, as opposed to the number of variants. In fact I do not know the answer to either question, but I'm certain that the number of variants is substantially less than the number of possible games.
One possible answer is the Shannon Number, named after Claude Shannon. He estimated a minimum of 10^43 possible positions (not games), although this included illegal positions. If we treat different sequences of moves that lead to the same position as distinct game, the number of games increases to 10^123, which is more than the number of atoms in the universe.
So while I don't have an exact answer for my class next week, I can at least tell them it is a very big number!

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