Chess Has More Possible Games Than There Are Atoms in the Universe

A Universe Hidden in 64 Squares: The Staggering Math of Chess

Somewhere in a wooden box in your closet sits an object stranger than anything cosmology has ever produced. It has 64 squares. It has 32 pieces. And it holds more possible futures than there are atoms in everything you can see: every star, every galaxy, every speck of dust drifting between them.

That is not a metaphor. It is a number.

Push a single pawn forward against a friend, and you have already stepped onto a decision tree larger than physical reality. Somewhere past the tenth move, the count of paths the game could take blows straight through the total atom count of the observable universe, and keeps climbing for another forty powers of ten after that. Chess, it turns out, is not just a game. It is one of the strangest math problems humans have ever accidentally invented.

Let's figure out how something this small got this big.

Who Was Claude Shannon?

Long before anyone worried about artificial intelligence, Claude Shannon was busy inventing the mathematics that would eventually make it possible. Working at Bell Labs in the 1940s, he wrote a single 1948 paper, "A Mathematical Theory of Communication," that founded an entire field almost by itself: information theory. Every text you send and every video you stream still traces back to it. People call him the father of information theory for good reason.

But Shannon had a second obsession, and it was much smaller than the internet. It was chess.

In 1950, he published "Programming a Computer for Playing Chess" in the Philosophical Magazine, after first presenting the idea at a conference the year before. It became the first serious technical paper ever written on teaching a machine to play. Shannon never actually built a working chess program. What he built instead was a framework: an evaluation function, a search method called minimax, the basic architecture that nearly every chess engine since has leaned on in some form.

And buried inside that paper is one calculation that still stops people cold. Chess, Shannon estimated, contains something like 10^120 possible games. Mathematicians and programmers now call it the Shannon number.

 How Big Is 10^120, Actually?

Numbers like this stop meaning anything past a certain point. Our brains compare apples. They do not compare exponents. So let's ground it in something real: atoms.

Scientists estimate the observable universe contains somewhere around 10^80 atoms. The real figure sits between about 10^78 and 10^82 depending on the assumptions, but 10^80 is the standard shorthand. That number already breaks intuition on its own. It is every particle in every star astronomers have ever detected.

Now compare it to 10^120.

The gap between those two exponents, 120 minus 80, is 40 zeroes. That means the number of possible chess games is not merely bigger than the atom count of the universe. It is bigger by a factor of 10,000,000,000,000,000,000,000,000,000,000,000,000,000, a multiplier so large that the word "trillion" barely registers as a useful unit for it.

Here is one way to feel that gap. Picture every atom in the observable universe. Now imagine that each one of those atoms secretly contained its own hidden universe, packed with galaxies, stars, and its own trillions upon trillions of atoms. That image, a universe folded inside every atom of our universe, gestures at something close to the scale we're talking about. And it still undersells it. Chess keeps going past where most nested-universe thought experiments run out of room.

You are not playing a board game. You are holding a number that makes the cosmos look small.

 How Shannon Actually Did the Math

Here's the part I love: the calculation itself is almost embarrassingly simple. Shannon didn't need a supercomputer. He needed a napkin.

Start with the length of an average game: about 40 moves per player. Since both sides move, that's 80 total half-moves, or plies, from the first pawn push to the final handshake.

At each of those 80 turns, a player typically has around 30 legal moves available. Not always. Sometimes it's 2, sometimes it's 40. But 30 is a solid working average, and Shannon leaned on real tournament games gathered by the psychologist Adriaan de Groot, who had spent years studying how chess masters actually perceive a position.

So the math becomes 30 choices, repeated across 80 turns: 30 raised to the 80th power.

Run that exponent out and you land almost exactly on 10^120. A small number, multiplied by itself enough times, quietly turns into something bigger than physical reality.

It gets worse if you try to brute-force it. Even a machine checking a million variations every single second would need something on the order of 10^90 years just to work through the branches hiding behind a single opening move. The universe itself is about 1.4 times 10^10 years old. You would need to run through the entire current age of the universe roughly ten thousand trillion trillion trillion trillion times over, just to finish analyzing move one.

 The Tree That Never Stops Branching

Every move in chess forks the game into a new set of possibilities, and every one of those forks again. Programmers call this a game tree, and it grows faster than almost anyone expects.

Look at what happens in just the opening handful of moves. After both players have moved three times each, six plies in, the game has already generated over 9 million distinct board positions. Push two moves further, to five full pairs of moves, ten plies total, and the tree has already forked into more than 69 trillion possible games, built from over 85 billion distinct positions. Ten moves. Sixty-nine trillion futures.

This explosive branching is exactly why brute-force computing cannot solve chess, not now, and not with any hardware realistically on the horizon. It's worth separating two related numbers here. The 10^120 figure describes possible games: complete move sequences from start to finish. The number of distinct legal positions on the board is far smaller, since many different move orders land you on the same arrangement of pieces. A 2021 computational study by researcher John Tromp pinned the true count of legal chess positions at around 4.82 times 10^44.

Still bigger than the number of atoms in the Earth. Still nowhere close to 10^120.

Human Intuition Versus the Machine

So how does anyone actually play this game?

Grandmasters do not calculate 10^120 of anything. Nobody does. Human chess mastery runs on something closer to pattern recognition than arithmetic. Years of study compress into an instinct for which parts of a position matter and which don't. A strong player glances at a board and quietly discards most of the legal moves without consciously working through a single one. That's intuition doing the pruning brute force never could.

Machines took a different path, and it evolved across two very different eras. In 1997, IBM's Deep Blue defeated world champion Garry Kasparov 3.5 to 2.5 in their rematch, a year after losing to him 4 to 2 in their first encounter. Deep Blue played the way Shannon originally imagined, just scaled up enormously: 256 processors working in parallel, evaluating roughly 200 million positions every second through deep alpha-beta search. It was raw calculation at a size no human brain could match.

Then, twenty years later, something stranger arrived. In December 2017, DeepMind unveiled AlphaZero, a program given nothing but the rules of chess and the freedom to play itself, over and over, with no human games and no opening books fed in. After roughly four hours of self-play training, DeepMind's researchers found it was already outplaying the world's strongest conventional engine, Stockfish 8. By nine hours, it beat Stockfish outright across a hundred-game match: 28 wins, 0 losses, 72 draws.

AlphaZero didn't win by searching more positions than Deep Blue. It searched far fewer. It won by developing something that looked, unsettlingly, like intuition: a learned sense for which branches of that impossible tree were even worth glancing at.

What the Chessboard Really Holds

Chess emerged somewhere in northern India roughly a millennium and a half ago, as a game about kings and horses and castles. Nobody who first carved those pieces could have known they were building a doorway into combinatorics deep enough to rival cosmology.

That's the strange truth sitting inside your closet. Every time you set up the board, you are not arranging thirty-two pieces. You are opening a structure with more branching futures than there are atoms to build a universe out of. The pawn in your hand carries more possibility inside it than physical reality does.

And here is the part that never quite resolves. In 2007, a team led by computer scientist Jonathan Schaeffer finished a project that took nearly two decades: they proved, exhaustively, that checkers is a draw with perfect play from both sides. Checkers fell. Its state space, while still enormous, was finally small enough for modern computing to corner completely.

Chess has not fallen. Nobody knows, with anything close to certainty, whether the starting position is a forced win for White, a forced win for Black, or, like checkers, a draw neither side can escape. The tree is too large, the branches too many, and no computer on any realistic horizon can search all the way down to the bottom of it.

Somewhere inside that first, ordinary-looking move, the pawn to e4, sits an answer nobody alive has ever seen.

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