A commonly cited estimate is that the number of possible distinct chess games is on the order of 1012010^{120}10120, often called the Shannon number. This is not an exact count but a reasonable lower-bound-style estimate for how many different complete games of chess could be played under standard rules.

What “possible games” really means

When people ask “how many games of chess are possible,” they usually mean:

  • Every legal sequence of moves from the starting position, ending in any legal result (checkmate, stalemate, draw by rule, or even absurd blunders).
  • Different move orders count as different games, even if they pass through the same positions.

This is different from counting positions , which is itself huge but still much smaller than the number of full games, because many move orders can lead to the same position.

The famous Shannon estimate

Claude Shannon, a pioneer of information theory, estimated the game-tree complexity of chess (roughly, the number of possible different games) as about 1012010^{120}10120.

Key ideas behind that ballpark figure:

  1. On average, a player has around 30–40 legal moves in a typical position.
  1. A “typical” game might last on the order of 80–100 plies (half-moves).
  1. Multiplying a branching factor of about 101.510^{1.5}101.5 to 101.610^{1.6}101.6 across that many plies leads to roughly 1012010^{120}10120 different games.

Because this is an estimate, some authors say “around 1011810^{118}10118” or “around 1012310^{123}10123,” but they are all in the same astronomical range.

Early-move counts: why it explodes

Even if you look only a few moves deep, the number of possible games already gets huge:

  • After 1 move by White and 1 reply by Black, there are 400 different possible positions.
  • After 5 moves by each side (10 plies), there are already about 69,352,859,712,417 possible distinct games.
  • After 15 plies, there are roughly 2,015,099,950,053,364,471,9602,015,099,950,053,364,471,9602,015,099,950,053,364,471,960 possible game sequences.

This rapid growth is why people sometimes say “there are more possible chess games than atoms in the observable universe,” since estimates for atoms are around 108010^{80}1080, far below the 1012010^{120}10120-scale game count.

Is the number finite?

Yes, the total number of legal chess games is finite , even though it feels “infinite” in practice.

This finiteness comes from rules that prevent endless repetition:

  • The threefold repetition rule allows a draw claim when the same position with the same rights repeats three times.
  • The fifty-move rule (or its FIDE-precise variants) lets a player claim a draw if no pawn move or capture has occurred in fifty moves by each side.

These constraints mean there is an upper bound on how long a legal game can last, and with a finite branching factor at each move, the total number of games is finite.

Forum-style quick scoop

Quick Scoop:

  • Estimated total possible chess games: around 1012010^{120}10120 (Shannon number).
  • Possible games after just 10 plies: about 69 trillion plus.
  • Possible games after 15 plies: about 2.0×10212.0\times 10^{21}2.0×1021.
  • The total set of legal games is enormous but still finite, thanks to repetition and move-limit rules.

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Wondering how many games of chess are possible? Learn why estimates reach around 1012010^{120}10120 different games, how quickly possibilities explode in early moves, and why chess is huge but still finite.

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