It seems that the 1/3 each is what the recursive buck ends with, anyhow. Upon learning that Zaire claims half for him/herself and Xannon insists on averaging fairness algorithms, Xannon and Yancy merely update their claims to equal Zaire's at all times. That way, the average of the three desires will always turn out 1/3 a piece. Perhaps an argument for why an equal share is most fair. If not, Zaire could just wait until the other two had stated their desires and claimed the whole pie for him/herself, thus always skewing the final average in his/her favor.