Some games get less fun as you get better at them. Tic-tac-toe, for example, turns out to be simple enough that two player who know the game well will always draw.
Team Fortress 2 (a team-based first person shooter) is one of my most played computer games, and getting better at it has led me to expect to do well. When I play badly, then, I get more frustrated than I would have when I was still new to the game. However, when I'm playing well (and competitively) at my current skill level, it's a lot more fun than anything I experienced as a beginner.
Is there a way I can experience the good without the bad? So far, the answer in TF2 seems to be focusing on the teamwork aspect of the game. When I play as a medic, a relatively weak class that heals teammates, I don't necessarily expect to do well, since even a skilled medic dies easily. The fun comes in getting the rest of the team to work with and protect me, which results in everyone doing better. My favorite experiences so far in TF2 have been joining losing teams, convincing the players to work together, and ultimately winning through much effort.