  It is known that if $x\in[0,1]$ is polynomial time random (i.e. no polynomial
time computable martingale succeeds on the binary fractional expansion of $x$)
then $x$ is normal in any integer base greater than one. We show that if $x$ is
polynomial time random and $\beta>1$ is Pisot, then $x$ is "normal in base
$\beta$", in the sense that the sequence $(x\beta^n)_{n\in\mathbb{N}}$ is
uniformly distributed modulo one. We work with the notion of "$P$-martingale",
a generalization of martingales to non-uniform distributions, and show that a
sequence over a finite alphabet is distributed according to an irreducible,
invariant Markov measure~$P$ if an only if no $P$-martingale whose betting
factors are computed by a deterministic finite automaton succeeds on it. This
is a generalization of Schnorr and Stimm's characterization of normal sequences
in integer bases. Our results use tools and techniques from symbolic dynamics,
together with automata theory and algorithmic randomness.
