It seems to me that if your starting odds are 9:1 in favor of 1D12 and you know you’ll get the offer only once, the value of information is indeed zero, i.e. I wouldn’t pay even a penny. If you get multiple offers for different numbers on the sheet, the value depends on how many offers you get. If you’re uncertain about how many offers you’ll get, the value depends on your Bayesian prior for the number of offers.
It seems to me that if your starting odds are 9:1 in favor of 1D12 and you know you’ll get the offer only once, the value of information is indeed zero, i.e. I wouldn’t pay even a penny. If you get multiple offers for different numbers on the sheet, the value depends on how many offers you get. If you’re uncertain about how many offers you’ll get, the value depends on your Bayesian prior for the number of offers.