I don’t see the problem, and I suspect you’re ignoring that the anthropic probability (2/3 probability for A1) is _ONLY_ in those worlds where you get to bet. Your payout is reduced whether you’re in B or you’re in A and bet wrong.
I _think_ that “always bet T” maximizes each agent’s payout.
There are only 3 coins, so 8 possibilities (some of which collapse into the same case, but that doesn’t matter). Payouts are for agent A (meaning 1+1 is 1 for A’s bet and 1 for B’s bet, paid to A). Agent B is symmetrical, so not shown. PayoutHiffA1 is if the strategy is to bet H in room A1 and T in A2. Total is for the rules as given, Agent pay is ONLY the agent’s contribution, with no cross-agent payments.
I don’t understand what you are saying. If you find yourself in Room A1, you simply eliminate the last two possibilities so the total payout of Tails becomes 6.
If you find yourself in Room A1, you do find yourself in a world where you are allowed to bet. It doesn’t make sense to consider the counterfactual, because you already have gotten new information.
I don’t see the problem, and I suspect you’re ignoring that the anthropic probability (2/3 probability for A1) is _ONLY_ in those worlds where you get to bet. Your payout is reduced whether you’re in B or you’re in A and bet wrong.
I _think_ that “always bet T” maximizes each agent’s payout.
There are only 3 coins, so 8 possibilities (some of which collapse into the same case, but that doesn’t matter). Payouts are for agent A (meaning 1+1 is 1 for A’s bet and 1 for B’s bet, paid to A). Agent B is symmetrical, so not shown. PayoutHiffA1 is if the strategy is to bet H in room A1 and T in A2. Total is for the rules as given, Agent pay is ONLY the agent’s contribution, with no cross-agent payments.
I don’t understand what you are saying. If you find yourself in Room A1, you simply eliminate the last two possibilities so the total payout of Tails becomes 6.
If you find yourself in Room A1, you do find yourself in a world where you are allowed to bet. It doesn’t make sense to consider the counterfactual, because you already have gotten new information.