How Many Possible Chess Games Are There?
Claude Shannon, the father of information theory, estimated in 1950 that the number of possible chess games is approximately 10120. This number is so large that it exceeds the number of atoms in the observable universe (approximately 1080).
The Shannon number
In 1950, Claude Shannon calculated that the game-tree complexity of chess is approximately 10120. This means there are roughly 10120 possible game sequences (not positions, but complete games from start to finish). To put this in perspective:
- Atoms in the universe: ~1080
- Seconds since the Big Bang: ~1017
- Possible chess games: ~10120
Possible positions
The number of legal positions (board states that can actually be reached in a game) is much smaller: approximately 1044 to 1047. This is still an astronomically large number, far beyond what any computer could enumerate.
Why chess is "unsolvable"
Despite computers beating the strongest humans since 1997, chess remains unsolved. We do not know whether the optimal result with perfect play from both sides is a win for White, a win for Black, or a draw. The game-tree is simply too large to compute entirely. Current estimates suggest that perfect chess would result in a draw, but this has not been proven.