  The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to
perform the security analysis of many two-player quantum protocols. This game
specifies two Boolean functions whose outputs have to be computed to determine
success or failure. It also specifies the measurement bases used by each
player. In this paper, we generalize the CHSH game by considering all possible
non-constant Boolean functions and all possible measurement basis (up to
certain precision). Based on the success probability computation, we construct
several equivalence classes and show how they can be used to generate three
classes of dimension distinguishers. In particular, we demonstrate how to
distinguish between dimensions 2 and 3 for a special form of maximally
entangled state.
