[GolDDranks]

Besides the point about a need to generate a large number of random numbers, there's another thing: you don't know the distribution of the true random generator exactly. You know it's random, but in addition to that, the distribution needs to be flat. That's why you use a PRNG with a known-to-be flat distribution to further process the entropy. As an interesting sidenote, though, Mersenne Twister doesn't have a particularly good distribution by modern standards. For this, I would use a cryptographically secure PRNG.

[tpxl]

You can generally turn any random binary distribution into a uniform binary distribution by generating two bits, then if they're different, output the first bit, and if they're the same, ignore the result.

[londons_explore]

01 01 01 01 00 01 01 01 11 01

Doesn't seem to work... It depends on odd bits and even bits having the same distribution, which in many cases they won't.

[MauranKilom]

Yes, the draws from the random distribution must be uncorrelated. But the mentioned algorithm does indeed a "flat" output in this case.