Garry Kasparov studies the complexity of chess programs:
The number of legal chess positions is 10 to the power of 40, the number of different possible games, 10 to the power of 120. Authors have attempted various ways to convey this immensity, usually based on one of the few fields to regularly employ such exponents, astronomy. In his book Chess Metaphors, Diego Rasskin-Gutman points out that a player looking eight moves ahead is already presented with as many possible games as there are stars in the galaxy. Another staple, a variation of which is also used by Rasskin-Gutman, is to say there are more possible chess games than the number of atoms in the universe. All of these comparisons impress upon the casual observer why brute-force computer calculation can't solve this ancient board game. They are also handy, and I am not above doing this myself, for impressing people with how complicated chess is, if only in a largely irrelevant mathematical way.
[Typos now corrected, thanks to many readers. Apologies.]
The Dish 