  We give a sufficient condition for a random sequence in [0,1] generated by a
$\Psi$-process to be equidistributed. The condition is met by the canonical
example -- the $\max$-2 process -- where the $n$th term is whichever of two
uniformly placed points falls in the larger gap formed by the previous $n-1$
points. This solves an open problem from Itai Benjamini, Pascal Maillard and
Elliot Paquette. We also deduce equidistribution for more general
$\Psi$-processes. This includes an interpolation of the $\min$-2 and $\max$-2
processes that is biased towards $\min$-2.
