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:
“but Overall is beyond me: is the sum of these events
I cannot draw, the ledger I cannot keep, the accounting
beyond the account:”
—Archie Randolph Ammons (b. 1926)
“but Overall is beyond me: is the sum of these events
I cannot draw, the ledger I cannot keep, the accounting
beyond the account:”
—Archie Randolph Ammons (b. 1926)
“Criticism occupies the lowest place in the literary hierarchy: as regards form, almost always; and as regards moral value, incontestably. It comes after rhyming games and acrostics, which at least require a certain inventiveness.”
—Gustave Flaubert (1821–1880)