Dice known to have existed in Roman times include 6 sided cubed dice with pips similar to modern d6, 4 sided dice (numbered 1,3,4,6) made from bones and rectangular in shape, and 20 sided dice having an appearance similar to a modern d20. "One curious dice found in Viking Dublin is a cubic dice, much like most modern dice, but has the curious number combination of 3, 4, 4, 5, 5, 6." (From regia.com)
With regards to the d6 dicing, a player would roll two dice (sometimes three) and the highest total among the players won.
Tali (knucklebones) rules: Summary of rules.
Some notes about these rules are covered here.
The first text describing the nature and the rules of the dice game in medieval Europe was the Codex of King Alfonso (1283). (From here. An English language translation of the text can be found here.
Possible gaming system using "high roll" and "as many on one as on two" for inspiration.