Resolving the impossible lottery

In a previous post, I have posed a question which seems to admit of two contradictory explanations. Go read that post before this one or this post won't make a whole lot of sense!

Coincidences surprising and inevitable

Kitler photographed by Amy Halligan

Why is it that we might have no problem suspending our disbelief when watching a movie about an alien invasion, but we would find it ridiculous if the writers of a realistic soap opera suddenly started a storyline involving aliens?

This is actually a question that has interested me for some time, even if I seldom gave it much thought.

I will be getting back to the lottery paradox I posed in my last post, but first I have some things to say about the nature of coincidences and improbable events, and this is one of the questions I will attempt to answer.

Winning the impossible lottery

Photo: Nick See

I wanted to call this post 'The Lottery Paradox', but it turns out that title is already taken by a very similar idea. The version I'm going to discuss is a bit more extreme and has a different focus.

It is inspired by some thoughts I've been having related to the validity of the Anthropic Principle (the subject of my last post), inspired by the comments left by Callum J Hackett on that post.

Suppose the nation of Foobar has a national lottery, but the way it works is that every single day, one of the citizens is chosen at random to win a big prize.

Now suppose that the nation of Foobar has an arbitarily huge number of citizens (say a Googolplex).

I'm going to try to persuade you to believe two completely opposing conclusions about the possibility of believing that you have won this lottery. One of these conclusions is true, and one of them is false. See if you can tell which is which.