How many possible games of chess are there?

Question

Estimate the number of different possible games of chess. Work from a typical number of legal moves in a position and a typical game length, and compare your answer with the number of atoms in the observable universe, about 10 to the 80. Then say why the number of distinct positions is much smaller.

Accepted Answer

About 10 to the 120 games, vastly more than the 10 to the 80 atoms in the observable universe. The number of legal positions is only about 10 to the 44. Games. A typical position offers about 30 legal moves. A move pair (one by White, one by Black) therefore gives about 30 × 30, about 1,000, continuations. A typical game lasts about 40 move pairs. So the number of possible games is about 1,000 to the 40 = 10 to the 120. This is the Shannon number, estimated by Claude Shannon in 1950 as a lower bound on the size of the game tree; more careful modern estimates, allowing for the fact that games …

How many possible games of chess are there?

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