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I experience similar, but I'm pretty sure it's just rest and a fresh mind, not overnight learning/thinking. When I'm bashing my head against a wall, I'm stuck in a local optimum, and sleeping lets me reset and try something new that often works better (and I execute it better since I'm not as tired).
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It's both. Sleep is when trained skill get delegated into the muscle memory. Not sure if it relates to dreaming.

https://en.wikipedia.org/wiki/Muscle_memory#Sleep_effects_on...

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Sometimes called the "cold controller" effect as well, and not necessarily requiring sleep but rather just a break from the game.
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That’s so on point. One time I was stuck on One Reborn from Bloodborne for a whole evening. While I was sleeping I figured out the optimal path to best the Chime Maidens. I woke up and beat the boss in 5 mins.

Very real phenomenon. Happened so many times

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