The difference between your reasoning and the reasoning of FDT, is that your reasoning acts like the equality of the number in the big box and the number chosen by Omicron is robust, whereas the setup of the problem indicates that while the number in the big box is sensitive to your action, the number chosen by Omicron is not. As such, FDT says you shouldn’t imagine them covarying; when you imagine changing your action you should imagine the number in the big box changing while the number chosen by Omicron stays fixed. And indeed, as illustrated in the expected utility calculation in the OP, FDT’s reasoning is “correct” in the sense of winning more utility (in all cases, and in expectation).
The consequences of not having enough time to think.
winning more utility
more money.
EDIT: It’s not clear what effects the amount of time restriction has. ‘Not enough time to factor this number’ could still be a lot of time, or it could be very little.
The difference between your reasoning and the reasoning of FDT, is that your reasoning acts like the equality of the number in the big box and the number chosen by Omicron is robust, whereas the setup of the problem indicates that while the number in the big box is sensitive to your action, the number chosen by Omicron is not. As such, FDT says you shouldn’t imagine them covarying; when you imagine changing your action you should imagine the number in the big box changing while the number chosen by Omicron stays fixed. And indeed, as illustrated in the expected utility calculation in the OP, FDT’s reasoning is “correct” in the sense of winning more utility (in all cases, and in expectation).
The consequences of not having enough time to think.
more money.
EDIT: It’s not clear what effects the amount of time restriction has. ‘Not enough time to factor this number’ could still be a lot of time, or it could be very little.