(a) Assuming you are perfectly rational and that money has logarithmic VNM utility, checking the lottery ticket is not worth the time spent. However, System 1 doesn’t understand very low probabilities, so it will probably distract you by wondering whether you won. Given bounded rationality, it’s probably worthwhile to check just to make the distraction go away.
(b) There is a ~1 in 1000 chance that I would read the numbers wrong. If misreading the numbers and actually having won are the only possibilities, there is about a 1 in 100k chance that I’ve won. Depending on the specific circumstances of how I came to posses the ticket and how legitimate it and the website look, I would also entertain the possibility that it’s a scam or a prank.
(c) I would expect banks to be pretty careful about confirming large deposits, so I would be pretty confident that I had won (p > 0.5) when the deposit was confirmed. A few weeks later if the bank had not reported any issues with the deposit, I would be very confident (p > 0.99) that I had won.
The prior improbability of this whole scenario would cause me to update in favor of the simulation hypothesis, because a simulator would probably have a greater propensity to simulate people receiving large windfalls than a natural world is to generate them.
I consider the hypothesis “I am living in a simulation where I just won an extremely large amount of money” to be a subset of “I just won an extremely large amount of money”.
2.
(a) Assuming you are perfectly rational and that money has logarithmic VNM utility, checking the lottery ticket is not worth the time spent. However, System 1 doesn’t understand very low probabilities, so it will probably distract you by wondering whether you won. Given bounded rationality, it’s probably worthwhile to check just to make the distraction go away.
(b) There is a ~1 in 1000 chance that I would read the numbers wrong. If misreading the numbers and actually having won are the only possibilities, there is about a 1 in 100k chance that I’ve won. Depending on the specific circumstances of how I came to posses the ticket and how legitimate it and the website look, I would also entertain the possibility that it’s a scam or a prank.
(c) I would expect banks to be pretty careful about confirming large deposits, so I would be pretty confident that I had won (p > 0.5) when the deposit was confirmed. A few weeks later if the bank had not reported any issues with the deposit, I would be very confident (p > 0.99) that I had won.
The prior improbability of this whole scenario would cause me to update in favor of the simulation hypothesis, because a simulator would probably have a greater propensity to simulate people receiving large windfalls than a natural world is to generate them.
I consider the hypothesis “I am living in a simulation where I just won an extremely large amount of money” to be a subset of “I just won an extremely large amount of money”.