But the thing is you can’t call it “0.5 credence” and have your credence be anything like a normal probability. The Halfer will assign probability 1⁄2 for Heads and Monday, 1⁄4 for Tails and Monday, and 1⁄4 for Tails and Tuesday. Since only the guess on Monday is relevant to the payoff, we can ignore the Tuesday possibility (in which the action taken has no effect on the payoff), and see that a halfer would have a 2:1 preference for Heads. In contrast, a Thirder would give 1⁄3 probability to Heads and Monday, 1⁄3 to Tails and Monday, and 1⁄3 to Tails and Tuesday. Ignoring Tuesday, they’re indifferent between guessing Heads or Tails.
With a slight tweak to payoffs so that Tails are slightly more rewarding, the Halfer will make a definitely wrong decision, while the Thirder will make the right decision.
But the thing is you can’t call it “0.5 credence” and have your credence be anything like a normal probability. The Halfer will assign probability 1⁄2 for Heads and Monday, 1⁄4 for Tails and Monday, and 1⁄4 for Tails and Tuesday. Since only the guess on Monday is relevant to the payoff, we can ignore the Tuesday possibility (in which the action taken has no effect on the payoff), and see that a halfer would have a 2:1 preference for Heads. In contrast, a Thirder would give 1⁄3 probability to Heads and Monday, 1⁄3 to Tails and Monday, and 1⁄3 to Tails and Tuesday. Ignoring Tuesday, they’re indifferent between guessing Heads or Tails.
With a slight tweak to payoffs so that Tails are slightly more rewarding, the Halfer will make a definitely wrong decision, while the Thirder will make the right decision.