# Incentive

In combinatorial game theory, the **incentive** of a move measures how much the player making it gains by it. It is thus the difference game in favour of that player between the abstract game in which the move is made and the option to which they move. The sets of all incentives for either player are called the **Left** and **Right incentives** of the game.

Formally, given a game ``G = { G^L | G^R }`` the incentive of the move to a particular ``{:G^L:}_i`` or ``{:G^R:}_j`` is ``{:G^L:}_i - G`` or ``G - {:G^R:}_l`` respectively, and the Left and Right incentives of ``G`` are the sets ``G^L - G`` and ``G - G^R`` respectively.^{[1]}

## See also

- Gain — In Go, the number of points by which a move shifts the count in favour of its player. When positions are numbers, this is equivalent to the incentive.
- Value — Various ways of measuring the value of various things in go and CGT

## Notes

[1] *On Numbers and Games* (2``""^"nd"`` edition 2001) page 207. *Winning Ways* (2``""^"nd"`` edition 2000/2001) page 148.