How many chess games are possible?

Summary

How Many Chess Games are Possible? By John Mount on January 27, 2026 • How Many Chess Games are Possible? Here is a fun question: how many different games of chess are possible? Counting the number of possible chess games is quite hard, as the numbers are large and chess board positions can be quite complicated. In this note we will try to estimate the number of possible short games of chess. Long games with many possibilities This allows Labelle to bound the number of possible long chess games to the range 1029241 to 1034082. We will restrict ourselves to typical and short chess games. Warmup: the number of typical games by the Fermi problem method The Fermi problem method is to propose an approximate break-down of what we want to know into arithmetic over a few other things we can in turn try to estimate. The trick is to pick a arithmetic form that is both simple enough to calculate over and plausible enough to be a good estimate. For the chess problem we propose the estimate number_of_typical_games ~ typical_number_of_options_per_movetypical_number_of_moves_per_game. This equation is subjective, in that it isn’t yet justified beyond our opinion that it might be a good estimate. It is then a matter of finding usable values for typical_number_of_moves_per_game and typical_number_of_options_per_move. We also need to know how many different possible moves a player is typically considering. We get an estimate by examining a puzzle from Lichess.org: We can work out that black has 46 legal moves by counting. We write this as 10log10(46) ~ 101.66 for easier calculation. Then our Fermi estimate is that there are easily on order of (101.66)100 = 10166 typical games of chess. This has some of the grace I tried to describe in “The Joy of Calculation”. This sort of argument was famously used by Claude Shannon to argue a lower bound of 10120 possible chess games (ref). These estimates, while useful, are subjective, far apart, and sensitive to the subjective ad-hoc inputs. We w...