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As for what relaxes me the most in a game, I think that I'd have to second exploration. It feels really nice and visceral to just think about how a player character relates to a world and find ways, either through game exploits or just cleverly-implemented mechanics, to break boundaries established earlier on in the experience, and feel something new. On the other hand, games that also just give you a wider world to explore from the outset are especially enjoyable just because you can let yourself fall into the game's world.
Running around is great.
But I also find game mechanics that try to relax-ify an otherwise stressful experience to be really interesting. Cassette tapes in MGSV come to mind.