This paper provides a complexity analysis for the game of reconnaissance blind chess (RBC), a recently-introduced variant of chess where each player does not know the positions of the opponent's pieces a priori but may reveal a subset of them through chosen, private sensing actions. In contrast to commonly studied imperfect information games like poker and Kriegspiel, an RBC player does not know what the opponent knows or has chosen to learn, exponentially expanding the size of the game's information sets (i.e., the number of possible game states that are consistent with what a player has observed). Effective RBC sensing and moving strategies must account for the uncertainty of both players, an essential element of many real-world decision-making problems. Here we evaluate RBC from a game theoretic perspective, tracking the proliferation of information sets from the perspective of selected canonical bot players in tournament play. We show that, even for effective sensing strategies, the game sizes of RBC compare to those of Go while the average size of a player's information set throughout an RBC game is much greater than that of a player in Heads-up Limit Hold 'Em. We compare these measures of complexity among different playing algorithms and provide cursory assessments of the various sensing and moving strategies.

Monte Carlo tree search has brought significant improvements to the level of computer players in games such as Go, but so far it has not been used very extensively in games of strongly imperfect information with a dynamic board and an emphasis on risk management and decision making under uncertainty. In this paper we explore its application to the game of Kriegspiel (invisible chess), providing three Monte Carlo methods of increasing strength for playing the game with little specific knowledge. We compare these Monte Carlo agents to the strongest known minimax-based Kriegspiel player, obtaining significantly better results with a considerably simpler logic and less domain-specific knowledge.