How many different ways can a chess game unfold?

Almost nothing looks more orderly than chess pieces before a match starts. The first move, however, begins a spiral into chaos. After both players move, 400 possible board setups exist. After the second pair of turns, there are 197,742 possible games, after 3 moves 121 million. At every turn, players chart a progressively more distinctive path, and each games evolves into one that has probably never been played before.

According to Jonathan Schaeffer, a computer scientist at the University of Alberta who demonstrates A.I. using games, “The possible number of chess games is so huge that no one will invest the effort to calculate the exact number”

Some have estimated it at around 10^100,000. Out of those, 10¹²⁰ games are “typical” :about 40 moves long with an average of 30 choices per move.

There are only 10¹⁵ total hairs on all the human heads in the world, 10²³ grains of sand on the Earth, and about 10⁸¹ atoms in the universe. The number of typical chess games in many times as great as all those numbers multiplied together – and impressive feat for 32 wooden pieces lined up on a board.

Source: Popular Science January 2011…