So probability theory can’t possibly answer whether I should take free money, got it.
No, that’s not what I said. You just need to use a different probability space with a different event—“observing Red in any particular day of the experiment”.
You can do this because for every day probability to observe the color is the same. Unlike, say, Tails in the initial coin toss which probability is 1⁄2 on Monday and 1 on Tuesday.
It’s indeed a curious thing which I wasn’t thinking about, because you can arrive to the correct betting odds on the color of the room for any day, using the correct model for technicolor sleeping beauty. As P(Red)=P(Blue) and rewards are mutually exclusive, U(Red)=U(Blue) and therefore 1:1 odds. But this was sloppy of me, because to formally update when you observe the outcome you still need an appropriate separate probability space, even if the update is trivial.
So thank you for bringing it up to my attention and, I’m going to talk more about it in a future post.
No, that’s not what I said. You just need to use a different probability space with a different event—“observing Red in any particular day of the experiment”.
You can do this because for every day probability to observe the color is the same. Unlike, say, Tails in the initial coin toss which probability is 1⁄2 on Monday and 1 on Tuesday.
It’s indeed a curious thing which I wasn’t thinking about, because you can arrive to the correct betting odds on the color of the room for any day, using the correct model for technicolor sleeping beauty. As P(Red)=P(Blue) and rewards are mutually exclusive, U(Red)=U(Blue) and therefore 1:1 odds. But this was sloppy of me, because to formally update when you observe the outcome you still need an appropriate separate probability space, even if the update is trivial.
So thank you for bringing it up to my attention and, I’m going to talk more about it in a future post.