This game, also known as Egyptian War, Bloodystump or Slap is currently popular in the USA. It is related to the English children's game known as "Beggar My Neighbour" or "Beat Your Neighbour Out Of Doors".
For the rules, please refer to Oxymoron's Egyptian Ratscrew Page.
A computer version of Egyptian Ratscrew is avaiable for download from Chris Allen's web site.
Fedil Grogan has produced a Ratscrew app for iPhone or iPad.