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:
“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)
“We didn’t come to dig in Egypt for medals. Much more is learned from studying bits of broken pottery than from all the sensational finds. Our job is to increase the sum of human knowledge of the past, not to satisfy our own curiosity.”
—John L. Balderston (1899–1954)
“As long as lightly all their livelong sessions,
Like a yardful of schoolboys out at recess
Before their plays and games were organized,
They yelling mix tag, hide-and-seek, hopscotch,
And leapfrog in each other’s way all’s well.”
—Robert Frost (1874–1963)