Analyzing the dice game

Lifehacker had an interesting post today where they outlined a simple dice game where you have three distinct six-sided dice, each with a different number scheme. The neat thing was that the dice had a mutually intransitive set of win probabilities, similar to rock paper¬†scissors. So if your opponent chooses first and you choose the die that has the 5⁄9 edge over theirs, you will win about 5% more of the rolls (1⁄18).