Do you prefer games with a light story or with a deep story?

The reason why I'm asking this is because there's a good difference between playing games with no or barely a story or a deeper story.

For me it depends on the genre a lot. For strategy games I prefer no story (like Civilization V) so that I can think up one myself while playing, which is pretty fun. Though it might seem so, I don't think a genre can define if a game has a story or not. Professor Layton is a puzzle game, but it has an all right story. (And it could be considered adventure/puzzle, I guess) Minecraft is sort of an adventure game but it doesn't have a story at all and so on. In general I prefer a light story, though. This is because it doesn't require a lot of attention or anything so I can just sit back, but I can still enjoy the story.

What about games with light stories that have deeper meanings?

Occasionally I don't mind a premise to excuse my further action in said world. I don't tend to care much about the details and I always get frustrated when there is so much cutscene and dialogue that I feel it's okay to put down the controller. Even when it's great I don't care because the tale that I am weaving through gameplay should be more engaging if it's well designed. I go to Netflix to watch things and come to a game to play things.

Oh, that's interesting. I mean, it still counts as a light story to me but I see where the problem is. :/

Well, regarding your question, I like both. If I have to pick one, I'd guess I'll go with the deep story (as long as that doesn't mean something else is compromised, like gameplay).

I prefer games that have a story that fits with the style and intent of the game. Sometimes that means no story at all, like bejeweled, and sometimes that means a deep and immersive story.

It depends on the genre. If It's an action game, I prefer a light story, Adventure, Action-Adventure, and RPG's with deep stories, and platformers and shooters with no stories.

depends on the game, but most of the time i prefer a deeper story.

I like it deep, REAL DEEP 

Depends on the genre. Deep stories for RPGs, but I really hate shooters with deep stories. It's just creepy when shooting thousands of guys makes sense.