In incomplete information games, agents must make decisions based on partial knowledge of the game state. The Belief Stochastic Game model addresses this problem by delegating state estimation to the game model itself. This allows agents to operate using externally provided belief states, reducing the need for game-specific inference logic. In this paper, we investigate two methods for representing beliefs in games with hidden piece IDs: a constraint-based model using Constraint Satisfaction Problems and a probabilistic extension using Belief Propagation to estimate marginal probabilities. We evaluate the impact of these two representations on two different games using a general-purpose agent. Our results show that constraint-based belief provides comparable results to probabilistic inference, with minimal differences in agent performance. This suggests that constraint-based belief states alone may be sufficient for effective decision-making in many settings.
