If you define your utility function such that each lottery has identical utility, then sure. However, your utility function also includes preferences based on fairness. If you think that a one-billionth chance of doing lottery A a billion times is better than doing lottery A once on grounds of fairness, then your utility function must assign a different utility to lottery #658,168,192 than lottery #1. You cannot simultaneously say that the two are equivalent in terms of utility and that one is preferable to the other on grounds of X; that is like trying to make A = 3 and A = 4 at the same time.