Cows in the Maze

Mathematics is SO SERIOUS, that we all need to chill out a bit, and stop getting so uptight about decimal points and fractions and parallelograms." (Ian Stewart)

I just received a copy of Ian Stewart's "Cows in the Maze, And Other Mathematical Explorations" to review from Michelle Rafferty at Oxford University Press. I haven't read it all yet. I'm saving that for the long trip back to England this Friday, but I did thumb through it and got distracted repeatedly by interesting topics. The book is from Stewart's articles in Scientific American. I will save a fuller review, but will advise at the onset that it looks like a wonderful gift for a math student graduating from high school this month.



I do want to mention a topic(game) from the first chapter, which is on dice and dice games. I read a lot of math books, and yet I had never seen the game mentioned. I am going to slightly alter the game (Me altering Stewart's games is like telling Ichiro to try a different stance at the plate to improve his hitting, but hey, here I go)
So here is the idea, and a challenge. A point target is determined, say 15, or 21, or any number that sounds good to you; and a single die is rolled (it doesn't matter by whom). The number showing is the starting value for the running total. Each player in turn will give the die a quarter rotation in any of the four possible directions (for example, if a 1 is on the face, a quarter roll might bring up a 2,3,4, or 5, but not the six on the bottom).This number is added to the running total. The first person who goes over the set target value is the loser (alternate game, make him the winnner).

And my question is... given that each player plays intelligently, is there an advantage to one or the other player based on the value of the opening roll?