These days I work at playing quickly, carving off a couple slices of analysis and putting the rest in the "yeah, things might get messy there" bucket. It's not always easy just-letting-go, and sometimes I have to roleplay reasons that I'm not going to work hard at being clever.
For example, playing Lanterns, I limit myself to a one-minute turn, and the last game I played when it felt like I might be making a mistake, I said something like "Well, we dropped the oars and were scrabbling around in the bottom of the boat when we should have been lighting lanterns. So we've gotta dump the lanterns overboard before the boat catches on fire, now!"
Playing Commands & Colors: Samurai Battles for the first time a couple months ago, I played from the beginning saying that my commander was nursing a bad hangover. Did a good job of roleplaying that too, since I ended the game by charging disastrously with the wrong unit, snatching defeat from victory. Ee ja nai ka!
Playtesting new games with skilled designers and tournament players, I sometimes run into a variant of the same problem. Even in their first game, players who don't really understand the rules yet tend to want to analyze everything instead of just-playing-through.
So I've recently been starting introductory boardgame and testing sessions with roleplaying advice: "Pretend we're drunk! We're not going to get everything right. You don't know the system and I'm not gonna do a perfect job explaining things all the way through, so you won't make the right decisions, let's just plow through and if something goes wrong, well, it's my fault, what the hell!"
[[art by By Kawanabe Kyōsai - National Diet Library Digital Collections, Public Domain, https://commons.wikimedia.org/w/index.php?curid=2183868
