How Many Moves in a Typical Chess Game?

About 10¹²⁰

Strictly logical games, such as chess, can be characterized by how many possible positions can arise, bounding their complexity. Depending on the phase of the game, players must pick one out of a small number of possible moves, called the game’s breadth or branching factor b. If it’s White’s turn, White needs to pick one of b possible moves; Black can respond to each of these with b countermoves of his own. That is, after one turn, there are already b times b or b² moves that White needs to consider in response. Assuming that a game of chess lasts on average d moves (called the game’s depth), the complete game tree from any one starting position i.e. the list of all moves, countermoves, counter-countermoves and so on until one side or the other wins - contains about b times b times b..., d times in a row, or b^d end positions. This is the so-called terminal nodes or leaves of the search tree. Given that a typical chess game has a branching factor of about 35 and lasts 80 moves, the number of possible moves is vast, about 35⁸⁰.

35⁸⁰ is only an estimation. Claude Shannon, a mathematician in the 1950s, invented information theory and also wrote the first paper on how to program a machine to play chess. Shannon’s number, at 10¹²³, is huge, in particular considering there are only about 10⁸⁰ atoms in the entire observable universe of galaxies, stars, planets, dogs, trees and people, etc.