> 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.
    
    Is pseudorandomness a requirement?  Or is it the "50% chance of a bitflip"?

For [P]RNG?! In one word: yes. 

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