The expected utility associated with choosing box A is higher than that of choosing B; therefore, you should pick A in Problem 2.
...assuming that the cost of doing said utility function evaluations is negligible. (Or rather, is less than half the difference in utility between the boxes.)
(If the cost of evaluating the difference in expected utility between the boxes is higher than half the difference in expected utility between the boxes[1], it is rational to flip a coin and choose a random box instead.)
In this particular case I doubt that that is the case; it can become relevant in many seeming-paradoxes.
...assuming that the cost of doing said utility function evaluations is negligible. (Or rather, is less than half the difference in utility between the boxes.)
(If the cost of evaluating the difference in expected utility between the boxes is higher than half the difference in expected utility between the boxes[1], it is rational to flip a coin and choose a random box instead.)
In this particular case I doubt that that is the case; it can become relevant in many seeming-paradoxes.
Of course, this assumes that this evaluation is itself of negligible utility cost...