I can’t prove what I’m going to do and I can’t prove that I and the twin are going to do the same thing, because of the Boltzmann Bits in both of our decision-makers that might turn out different ways. But I can prove that we have a 1−2ε+2ε2 chance of doing the same thing, and my expected utility is (1−ε)2⋅10+ε2⋅5, rounding to 10 once it actually happens.
I can’t prove what I’m going to do and I can’t prove that I and the twin are going to do the same thing, because of the Boltzmann Bits in both of our decision-makers that might turn out different ways. But I can prove that we have a 1−2ε+2ε2 chance of doing the same thing, and my expected utility is (1−ε)2⋅10+ε2⋅5, rounding to 10 once it actually happens.