  We generalize the problem of coin flipping to more than two outcomes and
parties. We term this problem dice rolling, and study both its weak and strong
variants. We prove by construction that in quantum settings (i) weak N-sided
dice rolling admits an arbitrarily small bias for any value of N, and (ii)
two-party strong N-sided dice rolling saturates the corresponding
generalization of Kitaev's bound for any value of N. In addition, we make use
of this last result to introduce a family of optimal 2m-party strong n^m-sided
dice rolling protocols for any value of m and n.
