Hmm. I'm a fan of examining repeated interactions, and of trading off explore/exploit time and energy, for thinking about improvements to things that are most valuable to improve.
But I'm curious about the game example. Presumably there are LOTS of changes you could make to increase success chance here (including just using the default settings, or uninstalling the app and choosing an easier one). Why was your friend's change (in some framings, "cheat" would be an appropriate term) surprisingly effective?
(including just using the default settings, or uninstalling the app and choosing an easier one).
I feel like this was meant to be in jest, but if you were serious: my goal was to beat the stage with certain self-imposed constraints, so relaxing those constraints would've defeated the purpose of the exercise.
Anyways, it wasn't my friend's specific change that was surprising, it was the fact that he had come up with an optimization at all. My strategy was technically viable but incredibly tedious, and even though I knew it was tedious I was planning on trying it as-is anyways. It was like I was committed to eating a bowl of soup with a fork and my friend pointed out the existence of spoons. The big realization was that I had a dumb strategy that I (on some level) knew was dumb, but I didn't have the "obvious" next thought of trying to make it better.
It was jest-ish. Reductio ad absurdum. Your friend found a setting that made your chosen difficulty level less difficult. I'm not sure how different that is from just playing an easier game.
For activities where you care about the result, not about the activity itself, it makes tons of sense to change the approach to be more successful with less effort. For games where you're specifically challenging yourself more than necessary, I think the case is a lot weaker about how to optimize.
AKA: If it's stupid but it works, it's still stupid.
TL;DR: It's easy to slip into a routine which accomplishes some task but is inconvenient or annoying. Sometimes, there's a trivial change that makes the task significantly easier. The trick is noticing that you're stuck in such a routine.
I play this mobile game called Arknights, which is a tower defense where your towers are anime characters. There's a seasonal event called Contingency Contract, where you're given infinite attempts at a stage that you can make more difficult by modifying with "risks", and you're rewarded based on the highest-risk run you complete. The "intended" risk level, at which you can collect all of the rewards, is easy enough that some players challenge themselves by playing with self-imposed rules such as beating the stage at maximum possible risk, only using characters with cat ears, etc.
I am one such player. I was attempting to clear Contingency Contract with a strategy that was in theory fine, but in practice bottlenecked on three fiddly timing bits so difficult that they may as well have been coin flips. So I had a 1/8 chance of doing all three parts correctly, and then a nonzero chance of messing up somewhere else, but I thought it was good enough to be worth trying.
I spent a few hours grinding away without success, discussed the strategy for a bit with a friend, and then went to bed, intending to grind more the next day. I woke up to the friend messaging me with a success of his own, building off of my strategy. In particular, he made one trivial change - moved one unit two grid tiles over - which completely eliminated one of the coin-flip-bottlenecks.
For some reason, this particular incident was the one that catalyzed the thought of "what kind of failure mode led to this mistake, and how can I avoid it in general?"
I think this is a problem similar to cached thoughts, so I'll call it "cached actions". A cached thought is something that your brain autocompletes when you start thinking about something, and analogously a cached action is one your body defaults to when you start doing something. It's useful to develop automatic routines for things you do often, because consciously thinking about brushing your teeth is a waste of brainpower when it's the same thing twice a day forever.
However, precisely because you don't think about cached actions, you also don't notice when they could be improved. You start the task, you autopilot the actions, and then you move on. You don't consider if you could spend five minutes now to shave five seconds off the task because the thought literally never occurs to you.
Sometimes you get lucky: somebody else catches you in the act and points out the easy optimization, and you're left wondering how you never realized it before. Think about your mother asking you why you don't hold the knife like this when you're chopping vegetables. But this kind of problem seems to crop up often enough that you should learn how to fix it on your own.
It sounds simple, but the noticing part is pretty hard in my experience. Even having applied this to my own life in some capacity, I still feel like I'm probably missing more opportunities to do it.
An example from my own life: I was mildly irritated with downloading images from Twitter, since if you middle-click a tweet's image, it'll open the image in a new tab at small size, and you have to manually add "?name=large" to the URL to view it at full size. I noticed this irritation, actually thought about it for ten seconds, and then realized that it should be trivial to set up an automatic redirect or something. And lo and behold, there's a Chrome plugin that can do exactly that.
Not every cached action is going to have an obvious easy improvement. Some may be as close to optimal as you'd like to bother with, others may have optimizations that you don't think are worth the cost. But the value of potentially cutting continuous minor irritations out of your life is well worth the cost of taking a few minutes to go through this process.