The commonly quoted answer is 10^120 — a 1 followed by 120 zeros, known as the Shannon number. For comparison, there are an estimated 10^80 atoms in the entire observable universe. Chess, played on a 64-square board with 32 pieces, has more possible games than there are atoms in existence. That number needs some unpacking, because it's actually the answer to a slightly different question than most people think they're asking.
Games vs. positions — two different numbers
This is where most casual explanations get muddled. There are two separate things you could be counting:
- A position is a single board state — where every piece is, right now.
- A game is an entire sequence of moves from the start to some ending point.
Many different move sequences can arrive at the exact same position — so the number of possible games is vastly larger than the number of possible positions. Mixing these two up is the single most common mistake in "how many chess games" explainers online.
The exact numbers, move by move
Here's where it stops being an estimate and starts being exact — mathematicians have precisely counted the early game tree:
| Half-moves (plies) | Possible games | Possible positions | |---|---|---| | 1 | 20 | 20 | | 2 | 400 | 400 | | 3 | 8,902 | 5,362 | | 4 | 197,281 | 72,078 | | 5 | 4,865,609 | 822,518 | | 6 | 119,060,324 | 9,417,681 | | 10 | 69,352,859,712,417 | 85,375,278,064 |
Read that last row again: after just five full moves by each player, there are already more than 69 trillion possible games. Chess doesn't feel explosive at move 5 — it looks like an ordinary opening — but the combinatorics underneath are already staggering.
Where 10^120 actually comes from
Claude Shannon — the founder of information theory, writing a landmark 1950 paper on computer chess — needed a rough estimate of how big chess's "game tree" was, to argue that no computer could ever brute-force it by checking every possibility. His method: assume roughly 30 legal moves are available at a typical position, and a typical serious game runs about 80 half-moves. That gives 30^80, which works out to roughly 10^118 — Shannon rounded it up to 10^120 to account for games running longer than 80 moves.
It's important to be honest about what this number is: a deliberately rough, lower-bound estimate for typical, sensible-length games — not an exact count, and not the absolute mathematical ceiling. Some later estimates, factoring in the full range of legal (if bizarre) games chess actually allows, put the true figure even higher, around 10^123.
How many legal positions actually exist
This is a genuinely different — and more precisely answered — question. In 2014, computer scientists John Tromp and Peter Österlund calculated the number of legal chess positions with high confidence at approximately 4.82 × 10^44. That's the number that actually matters for the dream of one day fully "solving" chess the way tic-tac-toe or checkers has been solved — and even at "only" 10^44, it's still far beyond what any computer can hope to brute-force through directly, which is exactly why modern chess engines rely on smart evaluation and selective search rather than checking every possibility.
Why this actually matters, beyond trivia
This math is the entire reason chess engines work the way they do. No computer, now or in any realistic future, checks every possible game — that's precisely Shannon's point, dressed up as a numbers problem. Instead, engines like the ones powering chess AI opponents today search selectively, pruning away branches that look clearly bad and spending their computation on positions that matter. The sheer size of these numbers is the reason chess remains a rich, unsolved game — and, more practically, why even a well-designed AI engine still has to guess intelligently rather than calculate perfectly.
Frequently asked questions
What is the Shannon number in chess? The Shannon number is the widely cited estimate of roughly 10^120 possible chess games, calculated by Claude Shannon in 1950 as a rough lower bound based on typical move counts — it's a scale marker for chess's complexity, not an exact count.
Are there more possible chess games than atoms in the universe? Yes, by an enormous margin. There are an estimated 10^80 atoms in the observable universe, while the Shannon number estimate for possible chess games is around 10^120 — chess's complexity outstrips the physical universe's atom count by roughly 40 orders of magnitude.
Has anyone actually counted every legal chess position? Not exhaustively enumerated one by one, but researchers have calculated a very precise estimate — about 4.82 × 10^44 legal positions — using mathematical techniques that don't require checking each one individually.
Will a computer ever solve chess completely, the way it solved checkers? Not with current or foreseeable technology. Checkers has roughly 5 × 10^20 positions, already at the edge of what took years of dedicated computing to fully solve; chess's position count is roughly 24 orders of magnitude larger, putting a full solution far beyond realistic computing power for the foreseeable future.
Want to add a few more branches to that game tree yourself? Play a game and see how quickly your own choices multiply the possibilities.