Apparently I had gestalt switched out of considering the coin. Thanks.
(Also, you double-counted the 100 you lose in reality day 2, messing up your expected value computation again.)
the double counting was intentional. My intuition was that if your on reality day 1, you expect to lose 100 today and 100 again tomorrow since you know you will give Omega the cash when he asks you. However, you don’t really know that in this thought experiment. He may give you amnesia, but he doesn’t get your brain in precisely the same physical state when he asks you the second time. So the problem seems resolved to me. This does suggest another thought experiment though.
Apparently I had gestalt switched out of considering the coin. Thanks.
the double counting was intentional. My intuition was that if your on reality day 1, you expect to lose 100 today and 100 again tomorrow since you know you will give Omega the cash when he asks you. However, you don’t really know that in this thought experiment. He may give you amnesia, but he doesn’t get your brain in precisely the same physical state when he asks you the second time. So the problem seems resolved to me. This does suggest another thought experiment though.