How Many Moves in a Typical Chess Game?

About 10^{120}

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 b^{2}
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
35^{80}.

35^{80} 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 10^{123}, is huge, in particular
considering there are only about 10^{80} atoms in the entire observable
universe of galaxies, stars, planets, dogs, trees and people, etc.