Chess is larger than the observable universe
The number of possible chess games is on the order of 10 to the 120. The number of atoms in the observable universe is on the order of 10 to the 80.
Established2 min read
Shannon estimated the game-tree complexity of chess at about 10¹²⁰, from an average of about 40 legal moves and a game length of about 80 plies, trimmed for sense. Atoms in the observable universe, at roughly one atom per cubic metre of average density times the volume out to the horizon, land near 10⁸⁰. The chess number is larger by forty orders.
This is combinatorics, not astronomy. No one plays 10¹²⁰ games. The rules, applied without repeating a position forever, still describe more histories than there are atoms to write them on. A small rulebook can be bigger than a cosmos.
Caveats
- Both numbers are estimates. The gap is so wide that the estimates would have to be grotesquely wrong to reverse the inequality.
- Legal positions are fewer than legal games. Even the position count, around 10⁴⁴ to 10⁴⁶, is still vast beside a human life.
Sources
- 1Shannon C. E.. Programming a Computer for Playing Chess. Philosophical Magazine 41, 1950.