Value Functions for Depth-Limited Solving in Imperfect-Information Games beyond Poker

Depth-limited look-ahead search is an essential tool for agents playing perfect-information games. In imperfect information games, the lack of a clear definition of a value of a state makes designing theoretically sound depth-limited solving algorithms substantially more difficult. Furthermore, most results in this direction only consider the domain of poker. We propose a domain and algorithm independent definition of a value function in general extensive-form games, formally analyze its uniqueness, structure, and compact representations. In an empirical study, we show that neural networks can be easily trained to approximate value functions in three substantially different domains. Furthermore, we analyze the influence of the precision of the value function on the quality of the strategies produced by the depth-limited equilibrium solving algorithm using it.