---
title: "How many possible chess games are there? about 10^120 games; a"
description: "about 10^120 games; about 4.8 × 10^44 legal positions How the figure is estimated, how confident it is, and what makes the scale graspable."
url: https://atoneplace.net/how-many/possible-chess-games/
site: "At One Place"
---

# How many possible chess games are there?

**How many possible chess games are there?: about 10^120 games; about 4.8 × 10^44 legal positions**

There are about 10^80 atoms in the observable universe. There are roughly 10^40 times more possible chess games than that — meaning you could give every atom in the universe its own universe of atoms and still not have enough.

Two different numbers get quoted and they answer different questions. The game-tree complexity — how many distinct games could be played — is around 10^120, an estimate Claude Shannon made in 1950 and which is now called the Shannon number. The number of legal board positions is far smaller and has been computed rather than estimated: about 4.8 × 10^44, calculated by John Tromp in 2021 to within 0.02%. A chess engine searches positions, not games, which is why the smaller number is the one that matters in practice.

## How the figure is arrived at

Shannon's estimate: roughly 30 legal moves are available in a typical position, a game lasts about 40 moves for each side, so the tree has about 30^80 ≈ 10^120 leaves. Tromp's position count is a genuine computation using a sampling technique over an encoding of all board configurations, testing legality on a random sample and scaling — which is why it comes with a stated error bar and Shannon's does not.

## Other numbers and possibilities counts

- [How many combinations does a Rubik's Cube have?](https://atoneplace.net/how-many/rubiks-cube-states/) — 43,252,003,274,489,856,000 — about 43 quintillion
- [How many ways can you shuffle a deck of cards?](https://atoneplace.net/how-many/possible-shuffles-of-a-deck/) — about 8 × 10^67
- [How many combinations are there in the lottery?](https://atoneplace.net/how-many/lottery-combinations/) — 292,201,338 for Powerball
- [How many digits of pi have been calculated?](https://atoneplace.net/how-many/digits-of-pi-computed/) — about 202 trillion
- [How many possible passwords are there?](https://atoneplace.net/how-many/possible-passwords/) — 6.6 quadrillion for eight characters — 540 sextillion for twelve
- [How many Sudoku puzzles are there?](https://atoneplace.net/how-many/possible-sudoku-grids/) — 6,670,903,752,021,072,936,960 completed grids
- [How many prime numbers are there under a million?](https://atoneplace.net/how-many/primes-under-a-million/) — exactly 78,498
- [How many possible positions are there in Go?](https://atoneplace.net/how-many/possible-go-positions/) — about 2.08 × 10^170

## Common questions

### How many possible chess games are there?

about 10^120 games; about 4.8 × 10^44 legal positions

### How is that estimated?

Shannon's estimate: roughly 30 legal moves are available in a typical position, a game lasts about 40 moves for each side, so the tree has about 30^80 ≈ 10^120 leaves. Tromp's position count is a genuine computation using a sampling technique over an encoding of all board configurations, testing legality on a random sample and scaling — which is why it comes with a stated error bar and Shannon's does not.

## Related pages

- [How many combinations does a Rubik's Cube have?](https://atoneplace.net/how-many/rubiks-cube-states/)
- [How many ways can you shuffle a deck of cards?](https://atoneplace.net/how-many/possible-shuffles-of-a-deck/)
- [How many combinations are there in the lottery?](https://atoneplace.net/how-many/lottery-combinations/)
- [How many digits of pi have been calculated?](https://atoneplace.net/how-many/digits-of-pi-computed/)
- [How many possible passwords are there?](https://atoneplace.net/how-many/possible-passwords/)
- [How many Sudoku puzzles are there?](https://atoneplace.net/how-many/possible-sudoku-grids/)
- [How many prime numbers are there under a million?](https://atoneplace.net/how-many/primes-under-a-million/)
- [How many possible positions are there in Go?](https://atoneplace.net/how-many/possible-go-positions/)
- [How many people are there in the world?](https://atoneplace.net/how-many/people-alive-right-now/)
- [How many stars are there in the universe?](https://atoneplace.net/how-many/stars-in-the-universe/)
- [How many countries are there in the world?](https://atoneplace.net/how-many/countries/)
- [How many bones are in the human body?](https://atoneplace.net/how-many/bones-in-the-human-body/)
- [How many grains of sand are there on Earth?](https://atoneplace.net/how-many/grains-of-sand-on-earth/)
- [How many ants are there in the world?](https://atoneplace.net/how-many/ants-on-earth/)

## Sources

- Calculated on this page — At One Place (/about/)