  In this paper we study the small scale equidistribution property of random
waves whose coefficients are determined by an unfair coin. That is the
coefficients take value $+1$ with probability $p$ and $-1$ with probability
$1-p$. Random waves whose coefficients are associated with a fair coin are
known to equidistribute down to the wavelength scale. We obtain explicit
requirements on the deviation from the fair ($p=0.5$) coin to retain
equidistribution.
