A lot of guys are out here thinking a gamer girl is the best type of girlfriend to go for, when it's absolutely the contrary. My ex-girlfriend had no previous gaming exposure, so when I dated her, I got to introduce her into my passion for video games, and I got her to play all my favorite games, and it's a joy helping your girl through a game, especially one you love, for her first time.
Gamer girls will probably feel patronized if you try to teach them a game of yours, as if they don't know how to play a game. Or it's a game they'll already know, and if you're playing it together, that's when it becomes competitive for her, and it's not as rewarding because whenever you play, it's a competition now rather than enjoying the game and your time together.
The last few times playing video games, it often ended up with me wishing she would focus on the game, as she kept looking over at me with pleading eyes and eventually led into makeout sessions. Granted, not much game progress got done during the last few times, but still, it's a perk of dating a girl whose NOT a gamer.
So gentlemen, who are gamers, it's best to get a girl who's not one. So you can share such a new experience with her.