Two details the judge isn’t told about are 1) you would have to pay for the former meal, but not for the latter, and 2) if you stay in the restaurant, you gain useful information you’ll be able to take in account the next time you might want to eat there.
1) is patchable by specifying that the leftovers are non-perishable, so eating them is equivalent to buying a meal.
2) Either the judge is told that the variable meal is repeatable if it’s good, or we specify in the group problem that you’re not going back there no matter what.
Two details the judge isn’t told about are 1) you would have to pay for the former meal, but not for the latter, and 2) if you stay in the restaurant, you gain useful information you’ll be able to take in account the next time you might want to eat there.
1) is patchable by specifying that the leftovers are non-perishable, so eating them is equivalent to buying a meal.
2) Either the judge is told that the variable meal is repeatable if it’s good, or we specify in the group problem that you’re not going back there no matter what.