Ok. You’re offered a bet that is only valid if your ball is selected. That is enough to bring updating into the situation- you don’t even need to know whether or not your ball will be selected! You say “Ok, there’s a half chance my ball is not selected, and the bet is off. The other half of the time, the bet is on, and there’s a 9/10ths chance that the coin came up heads, since I know my ball has been selected.”
As suggested earlier, this strategy only works if you throw away half of the outcome space under the assumption that you can’t impact what happens there, despite the formulation of the problem being such that you do impact what happens there.
Ok. You’re offered a bet that is only valid if your ball is selected. That is enough to bring updating into the situation- you don’t even need to know whether or not your ball will be selected! You say “Ok, there’s a half chance my ball is not selected, and the bet is off. The other half of the time, the bet is on, and there’s a 9/10ths chance that the coin came up heads, since I know my ball has been selected.”
As suggested earlier, this strategy only works if you throw away half of the outcome space under the assumption that you can’t impact what happens there, despite the formulation of the problem being such that you do impact what happens there.