That’s not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
It’s totally important. The knowledge that you get paid for guessing T in the cases you’re never asked the question is extremely relevant here. It changes the EV from 1⁄3 * 3 = 1 to 1⁄3 * 3 + 1⁄4 * 3 = 1.75.
No, it doesn’t. There is no 1⁄4 chance of anything once you’ve found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?
That’s not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
It’s totally important. The knowledge that you get paid for guessing T in the cases you’re never asked the question is extremely relevant here. It changes the EV from 1⁄3 * 3 = 1 to 1⁄3 * 3 + 1⁄4 * 3 = 1.75.
No, it doesn’t. There is no 1⁄4 chance of anything once you’ve found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?