But you are ignorant - you know the probabilities well enough, but you're ignorant of which numbers will be drawn, which is the most important part of the whole operation. If I said for whatever reason "If I ever buy a lottery ticket, my numbers will be 5, 11, 17, 33, 36, and 42", and those numbers come up next Friday, you will have been retrospectively wrong not to have bought, even if "Never buy a ticket" is statistically the best strategy. We cannot make decisions retrospectively, of course, but if you randomly took a flier and bought a ticket for Friday's draw, then...well, I'd sound pretty stupid if I made fun of you for it, you know?
you will have been retrospectively wrong not to have bought
Not really; Before you know the outcome, saying "my numbers will be 5, 11, 17, 33, 36, and 42" is privileging the hypothesis. (unless you had other information which allowed you to select that specific combination)
And even if those numbers, by pure chance, were correct, there is still a reason it was a bad decision (in the 'maximizing expected utility' sense) to buy a ticket. Which is what I meant when I said that you can't have expected to win.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: