How are Pool(8 Ball) , Snooker , Rummy , Backgammon players' 
ratings (in online gaming websites) is actually calculated?

I am interested in finding out the **mathematical details / formulas**
(as opposed to vague / high-level information) behind each
rating system (each player is assigned a rating; by beating a higher
rating than yourself you score more points than if you beat a lower
ranked player, etc.).

Again, mathematical details required.  I want to be able to calculate
ratings based on the information found.


I.e :  for backgammon , FIBS formula is commonly used
http://www.fibs.com/ratings.html#explained.