Comment by steerablesafe

This method generates approximately

  log_2(sqrt(1/(2*pi*p*(1-p))) - 1000*log_2(p^p * (1-p)^(1-p))

bits of entropy from 1000 coin flips, where "p" is the probablity of flipping heads.

Neumann's method generates 1000/(p(1-p)) bits of entropy from 1000 coin flips. The theoretical maximum is

  -1000*log_2(p^p * (1-p)^(1-p))

but it requires knowing "p" exactly. This method is close to the theoretical maximum. I didn't plug in numbers, or analyise further, but it's far better than Neumann's method.

One obvious drawback is that you have to flip the coin a 1000 times to produce the first unbiased random bit, while Neumann's method starts producing bits much earlier.