A number that makes your mind spin
Chess looks like a neatly defined game: 64 squares, 32 pieces, two players. But behind that calm facade lies a combinatorial monster. If you try to count all the possible chess games that can arise from the initial position, you arrive at a number so large that it far surpasses even the cosmic standard of “all the atoms in the observable universe.”
And that’s not an internet myth. It’s based on a classical scientific estimate.
First: what do we mean by “possible chess games”?
An important detail: we’re not talking about “all legal positions” on the board, nor about “all good games.” We mean something else:
A possible chess game is a complete sequence of moves, from start to finish, where every move is legal. When you have multiple choices on each turn, the game branches like a tree: each choice creates a new path, and all these paths together form a gigantic network of possible games.
This is called the game tree.
The famous estimate: the Shannon value
In 1950, Claude Shannon published a groundbreaking article on how a computer could play chess. To demonstrate why brute force is unfeasible, he made a rough but influential estimate of the size of that game tree.
His reasoning, in plain language:
- In an average position, there are roughly dozens of legal moves.
- Over an entire game, this adds up to an explosion of ramifications.
- This increases the number of possible game progressions to about 10^120.
That’s a 1 with 120 zeros. This is known as the Shannon number, a conservative lower bound for the complexity of possible chess games.
Okay, so how many atoms are there in the observable universe?
That’s also an estimate, but one that often appears in science and popular astronomy: the number of atoms in the observable universe is around 10^80 (with uncertainty margins depending on assumptions).
That’s a 1 with 80 zeros.
So even if you were to have each atom “store” a unique chess game, and you were to empty the entire observable universe into one gigantic memory warehouse of atoms, you’d still come up short. By an absurdly large factor.
Why that comparison is actually correct
The statement “more possible chess games than atoms in the observable universe” is therefore not a poetic exaggeration, but a comparison of two estimates:
- Possible chess games: approximately 10^120
- Atoms in the observable universe: approximately 10^80
The difference between 10^120 and 10^80 is 10^40. That’s a 1 with 40 zeros more.
In other words: it’s not close. It’s not “about the same.” It’s ridiculously much larger.
The truly mind-blowing part
This means something your intuition doesn’t readily accept: even a game you can play on a table can reach a scale of possibilities greater than what we consider “cosmically large.”
And chess isn’t even unique in this respect. It’s simply a wonderful example because everyone knows the rules, and because there’s a historically robust, well-documented estimate.
So chess isn’t just a duel of two minds. It’s also a maze of possibilities that, purely as a number, is larger than the observable universe in atoms.
