[BobAllinSki]

Proving the correct ranges is near enough impossible as a hand that is of a rank X wins with a % time Y, X & Y are not linearly related and are also not evenly distributed (X is, Y isnt)

It would be a much simpler game if you just both got dealt 1 card and the highest card wins, I'm sure a correct answer could be found for that as you know your % chance of winning, getting a bettter card, and that the chances of a better card are evenly distributed.