Opponent-Limited Online Search for Imperfect Information Games

In recent years, online search has been playing an increasingly important role in imperfect information games (IIGs). Previous online search is known as common-knowledge subgame solving, which has to consider all the states in a common-knowledge closure. This is only computationally tolerable for medium size games, such as poker. To handle larger games, order-1 Knowledge-Limited Subgame Solving (1-KLSS) only considers the states in a knowledge-limited closure, which results in a much smaller subgame. However, 1-KLSS is unsafe. In this paper, we first extend 1-KLSS to Safe-1-KLSS and prove its safeness. To make Safe-1-KLSS applicable to even larger games, we propose Opponent-Limited Subgame Solving (OLSS) to limit how the opponent reaches a subgame and how it acts in the subgame. Limiting the opponent's strategy dramatically reduces the subgame size and improves the efficiency of subgame solving while still preserving some safety in the limit. Experiments in medium size poker show that Safe-1-KLSS and OLSS are orders of magnitude faster than previous common-knowledge subgame solving. Also, OLSS significantly improves the online performance in a two-player Mahjong game, whose game size prohibits the use of previous commonknowledge subgame-solving methods.