So you want to use FDT, not CDT. But if the additional data of which direction the fly is going isn’t used in the decision-theoretic computation, then Beauty will make the same choice on both days regardless of whether she has seen the fly’s direction or not. So according to this analysis the probability still needs to be 1⁄2 after she has seen the fly.
So you want to use FDT, not CDT. But if the additional data of which direction the fly is going isn’t used in the decision-theoretic computation, then Beauty will make the same choice on both days regardless of whether she has seen the fly’s direction or not. So according to this analysis the probability still needs to be 1⁄2 after she has seen the fly.