I'm guessing by "never" you mean you don't let them win if they didn't earn it. In that case I might have voted "never" instead of "other". When one plays chess and go with a player of lesser rank, you give them a handicap. That way the playing field is leveled. Other games are more random, and handicaps don't work the same way but you can eliminate a few rules in advance that make playing difficult. The point is to level the playing field so both opponents are having to work as hard as they can. A bit like a running race (which, actually, my 6yo can beat me most of the time) a parent could hop on one leg, or give the kid a 3 second head start or have them run a shorter distance. This way every one competes to the best of their abilities.
If I am confident the playing field is as level as can be, I have no qualms about winning. If my daughter makes a bad decision, I might ask her if she wants to try again, but if she insists, well that's how you learn. And if it ends up being as bad a move as I think then I tell her what went wrong. DH is the better chess player, and every game is a teaching game.
So, yes, I guess "other" is the accurate vote for our family. And we, too, love cooperative games but not in exclusion to competitive ones. Good sportsmanship is expected absolutely in our house, or we don't play.