  It is well-known that the higher-order language PCF is not fully abstract:
there is a program - the so-called parallel or tester, meant to test whether
its input behaves as a parallel or - which never terminates on any input,
operationally, but is denotationally non-trivial. We explore a probabilistic
variant of PCF, and ask whether the parallel or tester exhibits a similar
behavior there. The answer is no: operationally, one can feed the parallel or
tester an input that will fool it into thinking it is a parallel or. We show
that the largest probability of success of such would-be parallel ors is
exactly $8/27$. The bound is reached by a very simple probabilistic program.
The difficult part is to show that that bound cannot be exceeded.
