Forgetting causality in the concurrent game semantics of probabilistic PCF

We enrich thin concurrent games with symmetry, recently introduced by Castellan et al, with probabilities, and build on top of it a cartesian closed category with an interpretation of Probabilistic PCF (PPCF). Exploiting that the strategies obtained from PPCF terms have a deadlock-free interaction, we deduce that there is a functor preserving the interpretation from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract, without the need for a probabilistic notion of innocence. This holds both for a sequential and a parallel interpretation of PPCF in the style of Castellan et al.