The results of Aumanning can't be determined from just the initial probabilities. For example, suppose that Nick knows for a fact that an undetectable ninja rolled a 20-sided die and gave the twenty to Nick with probability 15%, and Nick also knows that neither Nick nor Eliezer has made any observations that would help them determine which person the ninja gave the money to. Eliezer, on the other hand, just made a wild guess. Nick will keep saying 15% no matter what, so their estimates can't converge to anything other than 15%.

So Aumanning can't be equivalent to any choice of either f or g.