Carrom
I was quite surprised to know that the game of carrom was something unfamiliar to folks outside of the Indian subcontinent.
Apparently, the Indian Carrom Federation is actually from Chennai, where I was born and spent many of my young years. But though that is the case, I learned to play this when I was much younger and I think living in Thiruchirapalli (Trichy).
The game's like a flattened version of billiards. You have two teams, with each team's players sat opposite each other. A set of black and white carrom men are racked in the middle with a queen in the centre. Your objective is to knock all of your men into the pockets (the queen needs to be covered by one of the other men).
Just like mahjong, the game appears to have numerous variants. The one we played seems to be different from the one that is official and if I'm honest, I don't know if that's for a good reason or only because I was playing with my younger brother and we'd often just make up rules.
In any case, the differences in our version and the official version are:
1. When you foul (pocket the striker, or opponent's men) you deliver one of your men to the centre, but you stack them on top of each other, excepting the queen which must always be accessible.
2. When we play points, we play for black (5), white (10), queen (25).
3. No thumbing!
4. You can't hit any men directly that are on the arrowed circles nearest you.
5. You can't hit any men directly that are not past the two red circles adjacent to you.
Some number of these rules (no thumbing, for instance) are clearly intended for us to make the game more interesting since missed shots are easy to thumb.
Another, less interesting, difference is that we'd call it carroms for some reason. But that might just have been because we were kids.
Overall, pretty fun game, quick, and you can get a passing ability in it quite quickly.