How about 1. Playing a very good an interesting game only to suddenly lose at the end or 2. Playing very poorly but winning in the end anyway.
Otherwise, with your definitions, the word fun necessarily means the option where people are having fun is the one they would chose over the game where they had no fun (unless they didn't read carefully).
1. Having a lot of fun playing a game but then losing miserably...
Or...
2. Not having much fun at all while playing, but eventually you'd sqeeze out a cheap win...
Now, which one would you choose?