My thoughts.
    
      Randomness should be whitened.  Anything feed into an randomness pool, 
should be mixed in and run through SHA256.
                    pool = SHA256(pool || new-randomness)
    
Pseudorandomness of the output has been a design goal/requirement only in SHA-3 
family. Any prior hash function’s exhibition of this property is coincidental.

Therefore I suggest using SHA3 instead.
 

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