Ply (game theory)
Encyclopedia
In two-player sequential game
s, a ply refers to one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn".
"Turn" is problematic since it means different things in different traditions. For example, in standard chess
terminology, one move consists of a turn by each player; therefore a ply in chess is a half-move. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black. In the game of Go, by contrast, a ply is the normal unit of counting moves; so for example to say that a game is 250 moves long is to imply 250 plies.
The word "ply" used as a synonym for "layer" goes back to the 15th century. Arthur Samuel
used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959.
In computing, the concept of ply is important because one ply corresponds to one level of the game tree
. The Deep Blue chess computer which defeated Kasparov
in 1997 would typically search to a depth of between six and sixteen plies to a maximum of forty plies in some situations.
Sequential game
In game theory, a sequential game is a game where one player chooses his action before the others choose theirs. Importantly, the later players must have some information of the first's choice, otherwise the difference in time would have no strategic effect...
s, a ply refers to one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn".
"Turn" is problematic since it means different things in different traditions. For example, in standard chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
terminology, one move consists of a turn by each player; therefore a ply in chess is a half-move. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black. In the game of Go, by contrast, a ply is the normal unit of counting moves; so for example to say that a game is 250 moves long is to imply 250 plies.
The word "ply" used as a synonym for "layer" goes back to the 15th century. Arthur Samuel
Arthur Samuel
Arthur Lee Samuel was an American pioneer in the field of computer gaming and artificial intelligence. The Samuel Checkers-playing Program appears to be the world's first self-learning program, and as such a very early demonstration of the fundamental concept of artificial intelligence...
used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959.
In computing, the concept of ply is important because one ply corresponds to one level of the game tree
Game tree
In game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; the complete tree is the same tree as that...
. The Deep Blue chess computer which defeated Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....
in 1997 would typically search to a depth of between six and sixteen plies to a maximum of forty plies in some situations.