Interesting way of thought but you make one mistake, your starting point is the very Western notion of "Free-Will". Indeed we as westerners think individually and want to be different from others and state that as a fact, however Asian people most of the time do not want to stand out and adhere to the group and hence would feel less frustrated by the predictability of their outcome, they would probably feel reassured that they are not very much different from other people.
I am not sure about other groups of people since I don't study them, most of my time is taken up by Asia, but if their are people versed in African cultures or Central European or Latin American or even Oceanian I think you might find quite some differences in the the results of this "experiment".