Does Blitzball in FFX count? Because at one point I just stopped playing FFX and just focused on playing Blitzball over and over again, using pretty much the same team, I think I was too young to understand all the bullshit surrounding it. Just a fun little weird sport game thing.
I also got hooked on Blitzball in a big way. I probably couldn't go back, but I've got fond memories of poaching all the best players from other teams and playing tons of Blitzball with my Patriots-esque juggernaut.
My answer for this question would probably be the SNES game E.V.O. The loop in that was grindy--you had to run around and eat a lot of other animals to get the points you spent on upgrades--but I was totally willing to put up with it to build, like, tanky armored amphibians or pteranodons with T-rex teeth.
More recently, the get money --> die --> buy hereditary upgrades loop of Rogue Legacy was also really addictive.
You've done a great job of teasing out my exact worry about Overwatch--I love, love, love the world and the characters, but I'm not sure I'll enjoy the actual format of the game quite so much. I never had much fun trying to get into the competitive side of TF2 (though I did dig the wave-based mode). So if Overwatch has more cooperative modes in it, cool; if not, that'll be a bummer.
I'm starting to think Fallout 4 might be my answer to the end question. I really love games where you can build yourself a town, but the weird, clunky settlement interface is kind of dragging my enjoyment of it down in Fallout. I'm still pretty early on, so I'm not writing it off just yet, but it's been rough.
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