CHSH game ($x\oplus y=ab$)

Two separated players receive uniformly random input bits $a,b$ and output bits $x,y$ without communicating after receiving their inputs. They win when $x\oplus y=ab$, with exclusive or $\oplus$. For deterministic local response functions, the four desired equalities have inconsistent parity, so at most three can hold. Shared randomness only averages such strategies, proving classical winning probability at most $3/4$. In terms of correlations $E_{ab}=\mathbb{E}[(-1{)}^{x+y}\mid a,b]$, the winning probability is $1/2+(E_{00}+E_{01}+E_{10}-E_{11})/8$, directly connecting the game to the CHSH inequality.