Can Chess Be Solved? Mathematics and the Limits of AI

Can the game of chess be solved by a computer, as English draughts was in 2007? With its 10 to the power of 120 possible positions (the Shannon number), chess represents one of the greatest mathematical challenges in history. Here’s the current state of knowledge.

The Shannon number: the immensity of chess

In 1950, mathematician Claude Shannon estimated the number of possible chess games at around 10^120 (a 1 followed by 120 zeros). By comparison, the number of atoms in the observable universe is “only” 10^80. This combinatorial complexity makes chess mathematically unsolvable with current and foreseeable technology.

Machines and chess

🤖 Deep Blue (1997)

IBM’s supercomputer beats Garry Kasparov by calculating 200 million positions per second. But Deep Blue doesn’t “understand” chess, it calculates through brute force. It’s far from solving the game.

🧠 AlphaZero (2017)

Google’s AI learns chess from scratch in 4 hours and crushes Stockfish. AlphaZero develops a positional “intuition” that fascinates grandmasters. But even AlphaZero cannot solve chess.

☑ Draughts solved (2007)

English draughts (8×8, 12 pieces) was solved by Jonathan Schaeffer after 18 years of computation: the result is a draw with perfect play from both sides. Draughts is far simpler than chess (10^30 positions).

❌ Chess unsolved

Chess will probably never be solved by brute force. It would require a computer capable of evaluating 10^120 positions, which exceeds the physical limits of the universe. Only a fundamental mathematical breakthrough could change this.

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Did you know? Modern electronic chess boards use engines like Stockfish that calculate millions of positions per second. They are far stronger than any human, but that doesn’t mean they solve the game. To find out more about the history of chess and AI, see our pillar article.