In combinatorial game theory, the sum of combinatorial games is a combinatorial game in which two players take turns, on each turn making a move on a single game out of a specified collection of combinatorial games. The new game is said to be a sum of the collection of games.
The sum operation was formalized by Conway (1976). It can be used to give combinatorial games an arithmetic structure that extends the arithmetic of the real numbers (see surreal number) and to model game play in games like Go and Amazons in which late stages of games tend to split up into disconnected regions of the board that do not affect each other.
Famous quotes containing the words sum of, sum and/or games:
“And what is the potential man, after all? Is he not the sum of all that is human? Divine, in other words?”
—Henry Miller (1891–1980)
“The sum of the whole matter is this, that our civilization cannot survive materially unless it be redeemed spiritually.”
—Woodrow Wilson (1856–1924)
“In 1600 the specialization of games and pastimes did not extend beyond infancy; after the age of three or four it decreased and disappeared. From then on the child played the same games as the adult, either with other children or with adults. . . . Conversely, adults used to play games which today only children play.”
—Philippe Ariés (20th century)