I don’t think I understand the problem. While reading the Numerical Lottery (NL) paragraph, I decided choosing only box B was the obvious answer, which led me to think I’ve misunderstood something.
In box B is $1,000, a composite number. If I pick a composite number, the NL gifts me $2 million it-doesn’t-really-matter-what-currency
Oh, I misread the problem. In box A is $1,000. Well, now I think I’ve understood the problem, and chosen the right answer for mistaken reasons.
If the NL pays “[me] $2 million if it has selected a composite number, and otherwise [...] $0,”* and the number it has selected goes in box B, then regardless of the number shown I can only profit from the NL by choosing box B. I’m guaranteed a profit by signalling to Omega that I will only choose box B.
Even in a scenario where box B contains the lesser amount, ‘tis still the most rational choice, considering I can apparently play the game an infinite number of times—or at least three thousand and one times. Considering that I will always choose box B when reasoning from the provided information (unless I’m still not understanding something), by this point I have at least $3,001,000,000 dollars; if I ever choose otherwise, Omega will no longer have reason to predict I will only one-box, and I lose my guarantee. The word ‘Ultimate’ makes me think I’m drastically wrong.
I don’t think I understand the problem. While reading the Numerical Lottery (NL) paragraph, I decided choosing only box B was the obvious answer, which led me to think I’ve misunderstood something.
In box B is $1,000, a composite number. If I pick a composite number, the NL gifts me $2 million it-doesn’t-really-matter-what-currency
Oh, I misread the problem. In box A is $1,000. Well, now I think I’ve understood the problem, and chosen the right answer for mistaken reasons.
If the NL pays “[me] $2 million if it has selected a composite number, and otherwise [...] $0,”* and the number it has selected goes in box B, then regardless of the number shown I can only profit from the NL by choosing box B. I’m guaranteed a profit by signalling to Omega that I will only choose box B.
Even in a scenario where box B contains the lesser amount, ‘tis still the most rational choice, considering I can apparently play the game an infinite number of times—or at least three thousand and one times. Considering that I will always choose box B when reasoning from the provided information (unless I’m still not understanding something), by this point I have at least $3,001,000,000 dollars; if I ever choose otherwise, Omega will no longer have reason to predict I will only one-box, and I lose my guarantee. The word ‘Ultimate’ makes me think I’m drastically wrong.
* Emphasis added.