There Are More Chess Games Than Atoms in the Universe

Sit down at a chessboard. You have 20 possible moves on your first turn. Your opponent has 20 possible responses. By the time each side has made just three moves, there are already over nine million possible positions on the board. By the end of a typical game, the number of possible sequences of moves is so large that it exceeds the number of atoms in the observable universe.

In 1950, mathematician Claude Shannon set out to estimate the total number of possible chess games. His calculation — now known as the Shannon Number — arrived at approximately 10 to the power of 120. Written out, that is a 1 followed by 120 zeros. To put that into perspective, the estimated number of atoms in the observable universe is around 10 to the power of 80. The Shannon Number is not just bigger — it is incomprehensibly bigger, by a factor of 10 to the power of 40.

Numbers of this magnitude are almost impossible to grasp intuitively, so comparisons help. If every atom in the universe were itself a universe, the total number of atoms across all those universes combined would still be vastly smaller than the number of possible chess games. Even if every person on Earth had been playing chess since the Big Bang — making one move per second — the total number of games completed would barely scratch the surface.

This staggering complexity is why no computer has ever fully solved chess — meaning no machine has determined the perfect sequence of moves from start to finish. The game tree is simply too large to search exhaustively, even with the fastest hardware available. Unlike simpler games such as draughts, which was solved in 2007, chess remains an open problem in mathematics and computer science.

What computers can do is play chess at a superhuman level. Programs like Stockfish and AlphaZero evaluate millions of positions per second and consistently beat the world's best human players. But evaluating positions is fundamentally different from solving the game. The difference is the difference between being very good at navigating a maze and having a complete map of every possible path through it.

For centuries, chess was regarded as a reliable measure of human intelligence. Modern research has complicated this view. Chess skill is more strongly linked to deliberate practice and pattern recognition than to raw intelligence. Top players do not calculate every possible move — they recognise familiar patterns from experience and focus their calculation on the most promising lines.

What chess truly reflects is the extraordinary capacity of the human mind to make sense of near-infinite complexity — to find structure, meaning, and beauty in a space so vast that no machine has yet fully mapped it. The game has outlasted empires, fascinated scientists, and humbled computers. The board is small. The possibilities are not.