Three different numbers people mix up
“How many possibilities are there in chess?” can mean three different things, and they differ by many orders of magnitude.
| Question | Answer | How sure |
|---|---|---|
| Possible games (move sequences) | ≈ 10120 for typical-length games; far more if every legal game counts | Rough estimate |
| Legal positions (board states) | ≈ 4.8 × 1044 | Statistical estimate, about 2 significant digits |
| Legal moves in one position | 20 at the start; usually 30–40 in a middlegame; 218 at most known | Exact for any given position |
Games outnumber positions because many different move orders arrive at the same position. After just three single moves (1.e4 e5 2.Nf3, say), there are 8,902 possible games but only 5,362 different positions.
Exact counts, move by move
Programmers call this count perft: every legal sequence of moves from the starting position, to a given depth. A “ply” is one move by one player, so 2 plies is one move each.
| Depth | Possible games | …ending in checkmate | Different positions | Source |
|---|---|---|---|---|
| 1 ply (White just moved; move 1) | 20 | 0 | 20 | Computed here |
| 2 plies (Black just moved; move 1) | 400 | 0 | 400 | Computed here |
| 3 plies (White just moved; move 2) | 8,902 | 0 | 5,362 | Computed here |
| 4 plies (Black just moved; move 2) | 197,281 | 8 | 72,078 | Computed here |
| 5 plies (White just moved; move 3) | 4,865,609 | 347 | — | Computed here |
| 6 plies (Black just moved; move 3) | 119,060,324 | 10,828 | — | Published |
| 7 plies (White just moved; move 4) | 3,195,901,860 | 435,767 | — | Published |
| 8 plies (Black just moved; move 4) | 84,998,978,956 | 9,852,036 | — | Published |
| 9 plies (White just moved; move 5) | 2,439,530,234,167 | 400,191,963 | — | Published |
| 10 plies (Black just moved; move 5) | 69,352,859,712,417 | 8,790,619,155 | — | Published |
| 11 plies (White just moved; move 6) | 2,097,651,003,696,806 | 362,290,010,907 | — | Published |
| 12 plies (Black just moved; move 6) | 62,854,969,236,701,747 | 8,361,091,858,959 | — | Published |
“Computed here” rows were generated with chess.js 1.4.0 when this page was built and match the published values. Deeper rows come from the published perft tables on the wismuth.com chess statistics page and the Chess Programming Wiki. The checkmate column is “games of exactly that length that end in mate”.
Fool’s mate, 1.f3 e5 2.g4 Qh4#, is one of just 8 games that end in checkmate after exactly two moves each (out of 197,281). Open in the analysis board
Growth is the point
Every extra ply multiplies the total by roughly 20 to 30. After ten plies (five moves each) there are already 69,352,859,712,417 games, around 69 trillion. Keep multiplying for a 40-move game and you reach the territory of the Shannon number.
The Shannon number: where 10120 comes from
In his 1950 paper “Programming a Computer for Playing Chess” (Philosophical Magazine 41, no. 314), Claude Shannon wanted to show why a computer could never play chess by brute force. He assumed a typical game lasts about 40 moves and that each pair of moves (one for White, one for Black) offers about 1,000 possibilities, roughly 30 choices each. That gives about 1,00040 = 10120 games.
It is an order-of-magnitude argument, not a count. It ignores short games and counts only “typical” lengths. If you include every legal game, including absurd ones where knights shuffle for dozens of moves between each pawn move, the true number is vastly larger. It is still finite, because the repetition and 75-move rules (see draws in chess) force every game to end.
Try it: the game-count estimate calculator
Change Shannon’s two assumptions and see how the estimate moves. The formula is simply (choices per move)2 × moves per game.
≈ 10118.2
The calculator uses logarithms, so it works with numbers far too big to write out. It is only as good as its assumptions: real games vary in length and the number of choices changes every move.
How many chess positions are there?
Shannon guessed about 1043. The best modern figure comes from John Tromp, who built a way to number every candidate position, sampled millions at random and checked each one for legality. His published estimate is about 4.8 × 1044 legal positions, accurate to roughly two significant digits (ChessPositionRanking).
Even that is far too many to store or search. And most of those positions are bizarre ones, full of promoted pieces, that never occur in real games.
How many moves are possible in one position?
The most legal moves known in a single legal position: 218, in a composed position by Nenad Petrović. chess.js counts all 218. Open in the analysis board
At the start each side has 20 moves. In typical middlegames it is usually somewhere around 30 to 40, which is where Shannon’s “about 30” came from. A lone king can have as few as one move, or none at all, which is stalemate.
The record for a legal position is 218 moves. You can count them yourself by loading the position into the analysis board.
Is chess solved?
No. Nobody knows whether perfect play from the starting position wins for White, wins for Black or draws.
- Endgames with up to 7 pieces are solved. Endgame tablebases give the perfect result and best move for every such position, kings included.
- 8 pieces is in progress. In February 2026 Lichess released a partial 8-piece tablebase covering positions with at least one pair of opposing pawns (Lichess announcement).
- The full game is out of reach. With around 1044 positions there is no realistic way to check them all, so even the strongest engines, such as Stockfish, play extremely well without having “solved” anything. See how strong Stockfish is.
Smaller games have been solved: checkers was proved a draw in 2007.
FAQ
How many possible chess games are there?
Nobody knows the exact number. Claude Shannon’s famous 1950 estimate of about 10120 describes the game tree of typical 40-move games; counting every legal game, however long and silly, gives a vastly bigger number.
How many chess positions are there?
About 4.8 × 1044 legal positions, according to John Tromp’s statistical estimate (2021–2022). That is far fewer than the number of games, because many different games reach the same positions.
How many possible moves are there in chess?
White has 20 legal first moves. In a typical middlegame there are roughly 30–40 legal moves; the most known in any legal position is 218.
How many chess games are possible after 2 moves?
After one move each there are 400 possible games. After two moves each there are 197,281, and after three moves each 119,060,324.
Is chess a solved game?
No. Nobody knows whether perfect play leads to a White win, a Black win or a draw. Only endgames with up to seven pieces are solved completely.
Are there more chess games than atoms in the universe?
Yes, by Shannon’s estimate: 10120 is far larger than the roughly 1080 atoms commonly estimated for the observable universe.
What is the Shannon number?
Shannon’s rough estimate of 10120 possible chess games, from about 1,000 possibilities per pair of moves over a 40-move game. It is an order-of-magnitude illustration, not a count.
Is the number of chess games infinite?
No. Repetition and move-count draw rules force every game to end eventually, so the number is finite, just astronomically large.
Sources and method
The counts for depths 1–5, the distinct-position counts for depths 1–4, the 8 four-ply checkmates and the 218-move position were all computed with chess.js 1.4.0 while this page was built; the build stops if any disagrees with the published figures. Deeper counts are quoted, not recomputed. Estimates (the Shannon number, Tromp’s position count) are labelled as estimates.
- Claude E. Shannon, “Programming a Computer for Playing Chess”, Philosophical Magazine 41 (314), March 1950 (scan on archive.org).
- John Tromp, ChessPositionRanking (estimate of legal positions, about 4.8 × 1044).
- Statistics on chess games, wismuth.com: perft and checkmate counts by ply.
- Lichess: partial 8-piece tablebase, February 2026.
- Facts checked 11 November 2026. Tablebase progress changes; this page will be updated when 8-piece tables are completed.