Salkkuman: The player that is going to roll will have a 16.67% chance to win in that roll. The next player to roll has a 13.89% chance to win on his roll. However once the player that is going to roll, rolls and loses they switch places on there stitistical probability to win. Over all the first person to roll in this situation has a 9.09% beter odds of wining then the secound player to roll.

Assuming both players are positioned such that they will always have 1/6 chance for an immediate win:
p=1/6 + (1-p)5/6 --> p = 6/11, about 54.5%.

whopper: Yep exactly what I said 4.5*2=9% however you actually gave the formula so a much beter answer.