Why are there more possible chess games than atoms in the universe?

Because choices multiply. In a typical chess position, White and Black together have about a thousand ways to play their next pair of moves, and a typical game lasts about 40 such pairs. Multiply a thousand by itself 40 times and you get a 1 followed by 120 zeros, 10^120 possible games. The observable universe, by comparison, holds roughly 10^80 atoms. That estimate is called the Shannon number, after the mathematician Claude Shannon, who worked it out in a paper published in 1950.

The explosion starts almost immediately. After each player has made just five moves, there are already 69,352,859,712,417 different games that could have been played, about 69 trillion. Each new move multiplies the count again, which is why it races past anything physical so quickly.

Shannon was not trying to impress anyone with a big number. He wanted to show that a computer could never play perfect chess by simply checking every possible game: there would never be enough time. Instead, in his paper "Programming a Computer for Playing Chess", which launched the field of computer chess, he proposed scoring positions and looking only at a limited set of promising moves. That approach laid the foundations for the chess programs that followed.

The number is a rough lower bound, and it counts silly games too. If you allow only about three sensible moves at each turn, the count drops to around 10^40 games, still far more than anyone could ever play. Shannon, a juggler and unicyclist who also built a machine to solve the Rubik's Cube, would have enjoyed that the answer is still unimaginably large.