Have some Omega thought experiments been one shot, never to be repeated type deals or is my memory incorrect?
Yes I wasn’t thinking through what would happen when the ith digit wasn’t 0. You can’t switch to one boxing in that case because you don’t know when that would be, or rather when you see an empty box you are forced to do the same as when you see a full box due to the way the game is set up.
Have some Omega thought experiments been one shot, never to be repeated type deals or is my memory incorrect?
Yes, and that’s the intent in this example as well. Still, it can be useful to look at the expected distribution of outcomes over a large enough number of trials that have the same structure, in order to infer the (counterfactual) probabilities that apply to a single trial.
Have some Omega thought experiments been one shot, never to be repeated type deals or is my memory incorrect?
Yes I wasn’t thinking through what would happen when the ith digit wasn’t 0. You can’t switch to one boxing in that case because you don’t know when that would be, or rather when you see an empty box you are forced to do the same as when you see a full box due to the way the game is set up.
Yes, and that’s the intent in this example as well. Still, it can be useful to look at the expected distribution of outcomes over a large enough number of trials that have the same structure, in order to infer the (counterfactual) probabilities that apply to a single trial.
Yes, they have. And most can be formulated as such as long as p(Omega is honest) is given as ‘high’ somewhere.