I'm not sure your argument of the benefits of this actually works.
Taking myself as an example: I play a lot of card and board games; I am very good at learning new games; I have been that annoying person who picks up a game after a quick five minute explanation and beats everyone else who's played it multiple times. But I don't feel like it's given me any extra insight into situations beyond board games. It could be that the problem is too much compartmentalisation, but my instincts tell me that the problem is that board games are just too tidy compared to real life. In real life there are just too many variables and the rules are often implicit or outright wrong, and without understanding how all the variables interact I have trouble working out how to improve my position.
I will say, however, that your plan sounds like a lot of fun. Just not necessarily that useful
I used to annoy my little sister by reading up on simple games with mathematically perfect strategies, then beating her every single time. Now she refuses to play with me. (E.g. Nim, and variations thereof. If you don't know how to play Nim, it's actually a pretty good example for this thread. The perfect strategy requires a certain amount of mental arithmetic and is non-obvious, so if you don't know it the game is pretty playable.)
Edit: In retrospect, I'm a jerk.
I've always wanted to be a Jernau Morat Gurgeh.
By the way, isn't Go a good example of a game that is hard to improvise and do well in? Just a reminder that domain knowledge usually trumps all else.
Diplomacy. Best played with exactly seven players. Playing time 4-12 hours face-to-face; can be played by email over the internet.
Obligatory warning: Playing this with friends is not advised unless you and your friends are very thick-skinned. I have never encountered another game that is as likely to destroy friendships.
You don't need a group of people to be in on this with you -- just find a local group of board gamers, and hang out with them every once in a while. I guarantee they will have so many games that you will be playing new ones all the time.
http://www.boardgamegeek.com/ is where it's at, I gather.
No one mentioned Dominion yet? It seems to crowd out Magic Playing groups, which I take as a quality sign. Each game is very different from the other, but so far the same guy of my playing group consistently wins.
Chinese chess, surprisingly rare in many Western countries, but has very in depth strategy.
Settlers of Catan (the original. Most of the expansions just make things more complicated)- warning is a bit addictive.
Sprouts- an amusing game due to Conway.
Illuminati- A very amusing game by Steve Jackson. Can take a bit long.
Ninja Burger- another fun Steve Jackson game.
Note that some other Steve Jackson games aren't necessarily worth it (for example Munchkin is a lot of fun but is deliberately unbalanced and so isn't going to work well for the purposes discussed...
I don't know about board games, but after 15 years of playing video games with varying levels of intensity/time spent, I've gotten a lot better at quickly picking up new ones. I assume others have the same experience.
I've wondered whether a computer program which could deduce competent strategy and tactics from game rules would be a good step toward AI.
I don't really play the type of games getting mentioned here. But I'd be interested in seeing what four LW regulars would do with Bridge. Much of the game consists of conventions of play and well known strategies (and nearly everyone learns these strategies and conventions while learning the rules). I'd be interested to see how much would be duplicated and what alternative conventions new but very intelligent players would come up with.
Earlier today I had an idea for a meta-game a group of people could play. It’d be ideal if you lived in an intentional community, or were at university with a games society, or somewhere with regular Less Wrong Meetups.
Each time you would find a new game. Each of you would then study the rules for half an hour and strategise, and then you’d play it, once. Afterwards, compare thoughts on strategies and meta-strategies. If you haven’t played Imperialism, try that. If you’ve never tried out Martin Gardner’s games, try them. If you’ve never played Phutball, give it a go.
It should help teach us to understand new situations quickly, look for workable exploits, accurately model other people, and compute Nash equilibrium. Obviously, be careful not to end up just spending your life playing games; the aim isn't to become good at playing games, it's to become good at learning to play games - hopefully including the great game of life.
However, it’s important that no-one in the group know the rules before hand, which makes finding the new games a little harder. On the plus side, it doesn’t matter that the games are well-balanced: if the world is mad, we should be looking for exploits in real life.
It could be really helpful if people who knew of good games to play gave suggestions. A name, possibly some formal specifications (number of players, average time of a game), and some way of accessing the rules. If you only have the rules in a text-file, rot13 them please, and likewise for any discussion of strategy.