Are there more possible chess games than atoms in the universe?

Yes. The observable universe is usually estimated to hold between 10^78 and 10^82 atoms, often rounded to 10^80. Estimates of the number of possible chess games run to about 10^120 or more, which is roughly 40 orders of magnitude larger. The claim is about distinct games, meaning full sequences of moves, and not about board positions, which are far fewer. [1] [2]

The figure is called the Shannon number, after Claude Shannon, whose 1950 paper "Programming a Computer for Playing Chess" introduced the field of computer chess. According to [Wikipedia](https://en.wikipedia.org/wiki/Shannon_number), he assumed about 10^3 possibilities for a pair of moves (one by White, one by Black) and a typical game of about 40 such pairs, giving a conservative lower bound of 10^120 for the game-tree complexity. He offered it to show that solving chess by brute force is impractical. [2]

Victor Allis later estimated at least 10^123, using an average branching factor of 35 and an average game length of 80 plies (half-moves). The rough arithmetic is deliberately crude, as [oddtruths.com](https://oddtruths.com/truth/are-there-more-chess-games-than-atoms-in-the-universe) notes, but the gap to 10^80 is so large that the conclusion does not depend on the details. [2] [3]

On Stack Exchange, Douglas S. Stones gave a constructive argument. After a fixed opening, he restricted each side to bishop, queen and knight moves that never obstruct each other, never capture and never give check, leaving 14 legal moves per ply. Over 74 further plies that yields 14^74 distinct 40-move games, which is above 10^84 and so exceeds 10^80. He also notes that this uses only a tiny fraction of the available moves. In fact, if neither player claims a draw by repetition or the 50-move rule, the number of possible games is infinite. [4]

The comparison is often misread. The number of legal positions is much smaller. Shannon's own rough position count was about 3.7×10^34, though it includes some illegal positions and leaves out some legal ones. Allis gave an upper bound of 5×10^52 and estimated the true figure near 10^50. Later work proved an upper bound of 8.7×10^45, and John Tromp and Peter Österlund estimated about 4.822×10^44 legal positions with 95% confidence. All of these are well below 10^80. [2]

This distinction featured in a public exchange between Elon Musk and Chess.com. The Spectator called the games-versus-atoms comparison relevant but misleading for the question of solving chess, since positions matter more than games there, much as counting words differs from counting sentences. Counting only "sensible" games, with about three reasonable moves per ply, gives roughly 10^40. [5] [2]

Sources differ on details. One museum page quotes 10^111 to 10^123 for chess positions and 10^40 once illegal ones are removed, which mixes up positions and games and conflicts with the much smaller position counts above. The atom count is itself an estimate in the range 10^78 to 10^82. None of this changes the comparison, because the game count exceeds it by dozens of orders of magnitude. [1] [2]