The probability is 5/6 all the way through to the end. The two identical twins each know that they rolled six ifef the other didn't, but the pairing procedure gives them unequal measure; they do not exist to the same degree. Thus, the relation between die roll and measure acts as a piece of evidence that it is the other one who rolled six - but this is non-transferrable anthropic evidence, so they are prevented from using each others' evidence to reach agreement.

(This sort of thing is more sensible when you have a utility or preference function to embed the world-model into; this forces you to be clearer about what is being measured by probability.)