I agree with this answer. I believe in the question as given the answer is probably “even”, but if Omega clarifies that in a counterfactual world randomly selected from the pool of all counterfactual worlds the calculator displayed “odd”, then you should have a 50% probability each way.
The reason observational evidence works in your world but not in other not randomly selected possible worlds is that if Omega selected the world in any way other than at random, then we’re talking about a world that may have been specifically selected for being improbable.
Omega changes the test sheet in all possible worlds where the calculator shows “odd”. (A “counterfactual” is an event, not a particular possible world, which is more natural since you name counterfactuals by specifying high-level properties, which is not sufficient to select only one possible world, if that notion even makes sense.) Clarified in the post.
I agree with this answer. I believe in the question as given the answer is probably “even”, but if Omega clarifies that in a counterfactual world randomly selected from the pool of all counterfactual worlds the calculator displayed “odd”, then you should have a 50% probability each way.
The reason observational evidence works in your world but not in other not randomly selected possible worlds is that if Omega selected the world in any way other than at random, then we’re talking about a world that may have been specifically selected for being improbable.
Omega changes the test sheet in all possible worlds where the calculator shows “odd”. (A “counterfactual” is an event, not a particular possible world, which is more natural since you name counterfactuals by specifying high-level properties, which is not sufficient to select only one possible world, if that notion even makes sense.) Clarified in the post.