For randomisation in the "ancient game": there was none, as the game that Murray based his idea on had all pieces the same colour. The game was called "leap-frog", but I've not been able to find any reference to it outside Murray's own "History of Board-Games Other Than Chess".
(hide) If you want to find an opponent with similar playing skills to your own look in the Ratings page of the type of game you want and find a player with a similar BKR. (pauloaguia) (show all tips)