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?
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?