The problem isn't guessing a random number, it's narrowing down the search range to more probable keys. Thank you for posting the percentages; this way we can see that after 54, none have fewer than 40% of bits as 1 or 0, nor more than 60%. I believe we can accept this as a fact.
with all due respect. You tried to do at least something, but you have a basic gap in the logic.
You can see - but you cannot say that this rule will work for the next puzzle..
Try to understand it.
Literally - what happened before - does not affect what happens after. What happens after has nothing to do with what happened before.
Take it as an axiom.
Narrowing the range is so non-critical - that it will not put any pressure on the puzzle