  A family of protocols for quantum weak coin-flipping which asymptotically
achieve a bias of 0.192 is described in this paper. The family contains
protocols with n+2 messages for all n>1. The case n=2 is equivalent to the
protocol of Spekkens and Rudolph with bias of 0.207. The case n=3 achieves a
bias of 0.199, and n=8 achieves a bias of 0.193. The analysis of the protocols
uses Kitaev's description of coin-flipping as a semidefinite program. The paper
constructs an analytical solution to the dual problem which provides an upper
bound on the amount that a party can cheat.
