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:
“The sum of the whole matter is this, that our civilization cannot survive materially unless it be redeemed spiritually.”
—Woodrow Wilson (1856–1924)
“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestley’s footsteps....To all eternity, the sum of truth and right will have been increased by their means; to all eternity, falsehoods and injustice will be the weaker because they have lived.”
—Thomas Henry Huxley (1825–95)
“The rules of drinking games are taken more serious than the rules of war.”
—Chinese proverb.