This strikes me as a modified two player version of Peg Solitaire, rather than checkers.
Players alternate turns except that a player is granted additional consecutive moves (i.e., captures) during a single turn, under certain circumstances.
Players must readjust two separate pegs prior to their first move of a turn, then they must move using a ...
After a lot of searches, I finally figured out they are called "Top Trump Cards".
http://www.toptrumps.com (site appears to be down, from my side, though)
But it does appear that I have either recalled the rules incorrectly, or we made our own rules when we were kids (latter is the most probable).
I also found out where I could buy them in South Africa (...
I have never seen someone else do this but a friend of mine and I use to play a similar game to decide who is the first player in our games of Dominion especially when there are more than two players:
We choose one player who is the 0. player, all other players are then numbered according to the player order (the highest number is then [number of players]-1)...