how could you update a non accurate a priori hypothesis?

Suppose you know a coin is unfaqir, now, you must infer how much unfair it is

You can predict a 10% advantage to heads(60/40) , you generate a new test , you set 2 standard deviations as a confidence to be close to doublecheck you hypothesis.

Your new test shows less advantage, we must find the appropiate trials with +2sd in favor to heads to determine you were right

Truth might be +5% or +15%, how would be the steps to find it out?