A possible option is to investigate the success mechanic in the RPG
Cavemaster by Jeff Dee and Talzhemir Mrr.
http://unigames.us/shop/
I played this with the authors at a convention several years ago.
From what I remember, the player competes with the GM in which each separates and hides a number of skill stones between their hands. By randomly choosing the opponents' hands, a quantity of stones is revealed to determine a winner (and margin?) of the contest.
It may be possible to convert the mechanic to fit other random number generations.
Since it is supposed to be simple enough for our ancestors to play in a cave, it may be possible to adapt it to car travel. I guess it could be a bit hazardous for a driver to fiddle with sets of stones if he doesn't have an assistant . . . and may be hard to steer with fistfuls ;-)
Maybe you could somehow designate a number of "stones" in your virtual hands.