[typicalset]

In the general case, you can compress a sequence of N biased coin flips with arithmetic coding. For a coin with known bias, this compression is (essentially) optimal and will therefore produce ~N*(Shannon information) unbiased bits.

[dragontamer]

In the "even more general case", the Shannon Theorem suggests that random_code(message) -> reaches the Shannon Limit. :-)

The problem is that perfectly-random codes can't be decoded very easily... so this little factoid is kind of worthless in most cases. Fortunately, we don't actually care what the information looks like when flipping coins. We usually just want "some random message", so no need to decode in this application!

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Cryptographers assume hash-functions are perfect random codes (they aren't in theory, but they are in practice... at least until they're cracked. Kinda funny how that works out). As such, the cryptohash(message) methodology should also reach the Shannon-limit, as long as your cryptohash remains secure... and you stay within the blocksize restrictions of the hash.