In AlphaGo, the value network is one of two neural networks that act as a heuristic functions to guide a Monte Carlo tree search of game positions. The value network takes a board position and estimates the likelihood of a win. It is used in conjunction with a policy network. While introduced in AlphaGo, the same principle can be applied generally in game playing.
Defined on page 237
Used on Chap. 11: pages 237, 238