If I take only box B I will either make 1M$ or 2M$. Omega, with its 99,9% accuracy, will likely have selected a prime number. Expected utility is 0.999 1M + 0.001 2M $ = 1M+1K $.
If I take both, I will either get 1M+1K $ or 2M +1K $. Already I’m grabbing both boxes, because the expected utility is clearly higher. Omega would likely have selected a composite number. Expected utility is therefore 0.999 2001 K + 0.001 1001 K = 2M $.
In cases where the Lottery number doesn’t match Omega’s, I have a number of general strategies available, most of which might get me hit by the trolley depending on how it defines factoring. Does checking whether the ones digit is even or the number 5 count? Does summing the digits (and then the digits of the sum recursively if needed) and checking if the result is 3, 6 or 9 count? Using these two strategies would improve my odds significantly, but risks the wrath of the trolley.
Posting before checking the comments.
If I take only box B I will either make 1M$ or 2M$. Omega, with its 99,9% accuracy, will likely have selected a prime number. Expected utility is 0.999 1M + 0.001 2M $ = 1M+1K $.
If I take both, I will either get 1M+1K $ or 2M +1K $. Already I’m grabbing both boxes, because the expected utility is clearly higher. Omega would likely have selected a composite number. Expected utility is therefore 0.999 2001 K + 0.001 1001 K = 2M $.
In cases where the Lottery number doesn’t match Omega’s, I have a number of general strategies available, most of which might get me hit by the trolley depending on how it defines factoring. Does checking whether the ones digit is even or the number 5 count? Does summing the digits (and then the digits of the sum recursively if needed) and checking if the result is 3, 6 or 9 count? Using these two strategies would improve my odds significantly, but risks the wrath of the trolley.