I don't carry rope for Day Hiking unless I have a specific plan for using it. I do carry 60ft of 3/8th's inch rope when I go backpacking/camping. If for no other use, I hang my backpack from a high tree limb while I sleep. I also find occasional need to use rope to rappel and or lower or pull gear up the short bluffs we have in the south.
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QMC, USCG (Ret)
The best luck is what you make yourself!