  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 many
commonly studied imperfect information games like poker, 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.
