 Consider the following modification of the two examples from section 3.1.5. In the first case, Sophia is presented with a weathered and irregularly shaped coin–it was just discovered in an archeological dig of an ancient city. By probabilism, Sophia must have a precise real-valued credence that it will land heads on the next spin. By the principle of indifference, her credence in Heads must be precisely .5. In the second case, she is presented with a Euro coin that she is certain is fair–this has been confirmed by extensive experimentation. Probabilism and the principal principle require her credence in Heads to be precisely .5 in this case as well. As we have already seen, there is something unsatisfactory about treating ignorance (in the first case) in the same way as certainty about chances (in the second case).