Probabilistic combinatory logic

In an ongoing attempt to formulate a Quantum combinatory logic, User:Hppavilion1 started by formulating probabilistic combinatory logic.

Difference from traditional combinatory logic
Probabilistic combinatory logic adds one new combinator:. accepts two arguments via currying and returns one of them at random (with 50/50 probability).

Derived Combinators
The author's first idea, the  combinator was really just stupid:. However, if one needs to use it, it maybe can easily be derived from the  combinator from the B,C,K,W system; however, the author is too stupid to figure that  out. To define it, you simply need to define the  combinator that tells if its arguments are equal, then to do some conditionals mumble mumble and voila! You have the R combinator!

Computational Class
PCL is clearly TC by trivial reduction to combinatory logic; however, additionally, PCL is equivalent to a Probabilistic Turing Machine, if the author is correct, by nature.