Ply (game theory)

Short description: Game theory term

In two-or-more-player sequential games, a ply is one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn".

The word "turn" can be a problem 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.

In poker with n players the word "street" is used for a full betting round consisting of n plies -each dealt card may sometimes also be called a "street". For instance in heads up Texas hold'em a street consists of 2 plies, with possible plays being check/raise/call/fold: the first by the player at the big blind, and the second by the dealer, who posts the small blind; and there are 4 streets: preflop, flop, turn, river -the latter 3 corresponding to community cards. The terms "half-street" and "half-street game" are sometimes used to describe, respectively, a single bet in a heads up game, and a simplified heads up poker game where only a single player bets.[1]

The word "ply" used as a synonym for "layer" goes back to the 15th century.[2] Arthur Samuel first used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959,[3] but with a slightly different meaning: the "ply", in Samuel's terminology, is actually the depth of analysis ("Certain expressions were introduced which we will find useful. These are: Ply, defined as the number of moves ahead, where a ply of two consists of one proposed move by the machine and one anticipated reply by the opponent"[4]).

In computing, the concept of a 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.[5]

## Contents

* 1 See also
* 2 References
* 3 Further reading
* 4 External links

## See also

* Minimax algorithm

## References

1. ↑ Chen, Bill and Ankenman, Jerrod. The Mathematics of Poker, p110
2. ↑ Online Etymology Dictionary, "ply" (cited 24 April 2011)
3. ↑ A.L. Samuel, March 3, 1959: Some Studies in Machine Learning Using the Game of Checkers (cited 25 August 2006)
4. ↑ A.L. Samuel, March 3, 1959: Some Studies in Machine Learning Using the Game of Checkers, p. 601 (cited 2 May 2018)
5. ↑ Campbell, Murray; Hoane, A.Joseph; Hsu, Feng-Hsiung (2002). "Deep Blue". Artificial Intelligence 134 (1–2): 57–83. doi:10.1016/S0004-3702(01)00129-1. https://www.sciencedirect.com/science/article/pii/S0004370201001291.

## Further reading

* How Computers Play Chess, Computer Science Press, 1991, ISBN 978-0-7167-8121-9

## External links

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