
see... no clue at all! that's embarrassing;
You've got the machine running backwards.
Mutation is the random part. Selection is the part whose entire definition is non-random, it keeps what survives and discards what doesn't.
That's not ad hoc; it's the thing Darwin's whole theory is built on, and it's been the answer to this exact objection since 1859.
A sieve isn't random because the gravel was. Your probability argument only works if every step has to happen at once by chance, and selection is precisely the mechanism that means it doesn't, each gain is locked in before the next is tried.
You didn't find randomness hiding in selection. You just don't know which half does which job!!
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