  In this note, we give an explicit polynomial-time executable strategy for
Peter Winkler's hat guessing game that gives superior results if the
distribution of hats is imbalanced. While Winkler's strategy guarantees in any
case that $\lfloor n/2 \rfloor$ of the $n$ player guess their hat color
correct, our strategy ensures that the players produce $\max\{r,b\} - 1.2
n^{2/3} -2$ correct guesses for any distribution of $r$ red and $b = n - r$
blue hats. We also show that any strategy ensuring $\max\{r,b\} - f(n)$ correct
guesses necessarily has $f(n) = \Omega(\sqrt n)$.
