My attempted condensation, in case it helps future generations (or in case somebody wants to set me straight): here’s my understanding of the “pay $0.50 to win $1.10 if you correctly guess the next flip of a coin that’s weighted either 40% or 60% Heads” game:
You, a traditional Bayesian, say, “My priors are 50⁄50 on which bias the coin has. So, I’m playing this single-player ‘game’:
“I see that my highest-EV option is to play, betting on either H or T, doesn’t matter.”
Perry says, “I’m playing this zero-sum multi-player game, where my ‘Knightian uncertainty’ represents a layer in the decision tree where the Devil makes a decision:
“By minimax, I see that my highest-EV option is to not play.”
...and the difference between Perry and Caul seems purely philosophical: I think they always make the same decisions.
My attempted condensation, in case it helps future generations (or in case somebody wants to set me straight): here’s my understanding of the “pay $0.50 to win $1.10 if you correctly guess the next flip of a coin that’s weighted either 40% or 60% Heads” game:
You, a traditional Bayesian, say, “My priors are 50⁄50 on which bias the coin has. So, I’m playing this single-player ‘game’:
“I see that my highest-EV option is to play, betting on either H or T, doesn’t matter.”
Perry says, “I’m playing this zero-sum multi-player game, where my ‘Knightian uncertainty’ represents a layer in the decision tree where the Devil makes a decision:
“By minimax, I see that my highest-EV option is to not play.”
...and the difference between Perry and Caul seems purely philosophical: I think they always make the same decisions.