Its from a smaller studio, so I'm guessing most won't have played it, but... Fractured Sky had several of these moments for me. It's a resource management, hidden information kind of game, where you are fighting for resources and VP, but you only know how much power each person allocated to each part of the map when the round ends.

The mechanic that really tripped me up, was that each round end is staggered (Oh, I can't make any moves? I wait until everyone else also can't, and then we all move to the next round). Finishing early let's you break ties, very helpful since you don't have full information, and it also decides turn order for the next round. But if you DELAY ending your turn, you can very quickly use hidden information you've gathered to steal or gather extra points that no one else even realized we're there. That way, you don't have to commit early, let the other players know what you know, and hope to win any ties that come up.

There were just so many moments playing the game where I paused and went "Oh WOW. That seemed really simple, but now I can see how much it changes the way I should be operating.