[Q_is_4_Quantum]

Given access to repeated uses of a coin of unknown bias "p" (which is not 0 or 1) you can (eventually) always generate a new coin flip with bias given (exactly) by:

1. 1/2 (i.e fair - von Neumann)

2. p^2

3. p^2/(p^2+(1-p)^2)

4. sqrt(p)

Number 4 really surprised me, I learned it from this paper: http://www.math.chalmers.se/~wastlund/coinFlip.pdf

But you can never generate the biases:

5. 2p

6. 4p(1-p)

Although... if you change the game to allow a quantum coin then 5. and 6. are possible (a paper of mine: https://arxiv.org/abs/1509.06183)