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:
“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has wished, drawing the sum of one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
—Friedrich Nietzsche (1844–1900)
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—Henry David Thoreau (1817–1862)
“The rules of drinking games are taken more serious than the rules of war.”
—Chinese proverb.