Abstract. Kriegspiel is a Chess variant similar to wargames, in which players have to deal with uncertainty. Kriegspiel increases the difficulty typical of Chess by hiding from each player his opponent’s moves. Although it is a two person game it needs a referee, whose task consists in accepting the legal moves and rejecting the illegal ones, with respect to the real situation. Neither player knows the whole history of moves and each player has to guess the state of the game on the basis of messages received from the referee. A player’s try may result legal or illegal, and a legal move may prove to be a capture or a check. The paper describes the rationale of a program to play basic endgames of Kriegspiel, where a player has left only the King. These endings have been theoretically studied with rule-based mechanisms, whereas few researches exist on a gametree-based approach. We show how the branch of game tree can be reduced in order to employ an evaluation function and a search algorithm. Then we deal with game situations dependent on stochastic element and we show how we resolve them during the tree visit. 1

We describe a novel approach to incomplete information board games, which is based on the concept of metaposition as the merging of a very large set of possible game states into a single entity which contains at least every state in the current information set. This merging operation allows an artificial player to apply traditional perfect information game theory tools such as the Minimax theorem. We apply this technique to the game of Kriegspiel, a variant of chess characterized by strongly incomplete information as players cannot see their opponent’s pieces but can only try to guess their positions by listening to the messages of a referee. We provide a general representation of Kriegspiel states through metaposition trees and describe a weighed maximax algorithm for evaluating metapositions. We have tested our approach competing against both human and computer players. 1

Abstract. This paper presents a Phantom Go program. It is based on a Monte-Carlo approach. The program plays Phantom Go at an intermediate level. 1