Developed initially over several works of Vern Paulsen and co-authors, the game algebra of a synchronous non-local game $\mathcal{G}$ carries all data regarding winning strategies for the original game via representations. This object has proven to be very useful in showing when one synchronous game can be transformed into another (and vice versa). Such transformations are captured in the notion of *-equivalence between synchronous games $\mathcal{G}_1$ and $\mathcal{G}_2$, defined by the existence of unital $*$-homomorphisms between the two game algebras. This notion of equivalence preserves winning strategies in a natural way. In this talk we will give a bit of a survey of these kinds of equivalences and also look at what happens when one considers near-perfect strategies.