Dexter Kozen. Optimal coin flipping. Technical Report http://hdl.handle.net/1813/12869, Computing and Information Science, Cornell University, June 2009.

This paper studies the problem of simulating a coin of arbitrary real bias q with a coin of arbitrary real bias p with minimum loss of entropy. We establish a lower bound that is strictly greater than the information-theoretic bound. We show that as a function of q, it is an everywhere-discontinuous self-similar fractal. We provide efficient protocols that achieve the lower bound to within any desired accuracy for (3-sqrt(5))/2 < p < 1/2 and achieve it exactly for p=1/2.