Eeesh, start up a topic, then get sidetracked by fun games and family dinners.
Number of rules & mechanics in a game sounds like a good definition for complexity to me. Pulling the math book out on it doesn't look like something that would help us think about the issues. (THIS time.)
Really? You think that someone (who wasn't schizophrenic) could start playing Mario Kart and come to believe, if only briefly, that they existed in that world, that the game world was real, and that it was jarring to return to the real world and find they did not in fact exist in the game world?
That's beyond what I would call immersive, too. I never find it jarring to stop playing. (Standing up afterward if I've been playing too long is another story.) However, what I can do is internalize all those rules and make and make... jeez, what words to use? "Imaginary world" is wrong, especially with board games. There's no world, it's still just the board with pieces on it. More like a reality overlay with all those rules. For chess, the overlay says that bishops move diagonally. If one doesn't, it's WRONG. Once I can get this overlay figured out, then I can start figuring out strategies/tactics and get really immersed. When I get to the point that I barely even think about the things the rules don't allow, I would consider myself completely immersed.
That leads to something I think
@BeardyHat reminded me of - it takes time to internalize those rules. Sometimes, too much time. Games can help out by not requiring that you know every bit of complexity right away, but sometimes that's not really possible. In fact, some games are happy to toss you in the deep end and let you re-load your game until you figure out how to swim.
Oh frak, it's tomorrow here, I need to get to sleep! OK, one more quick thing: I think adding PvP automatically adds a lot of depth, often TONS of depth. Playing poker against a simple computer program is going to be pretty shallow and, once you get a feel for how commonplace the various hands are, it's likely to get really boring. Playing against real people, though, introduces bluffs, trying to read facial expressions, and all sorts of psychology. (Que
Vizzini, finding all manner of depth in the simplest of games.)