So, I'm having a pretty lazy day and decided to do some thinking. And, while this usually turns out to be a splendid idea, today it resulted in me hurting myself. Psychically. So yeah. I've been through a lot of toy games trying to figure out a way to reconcile this all in my brain box, but here's the basic gist of it: Part 1) I tell you to pull out a $100 bill from your pocket and put it on the table. I'm going to make you a proposition and you can either accept or decline. If you accept, I will flip a fair coin and you will call it in the air. If you win, you're forced to trade your $100 for $200 of mine that I will give to you in exchange. If you lose, you have to trade your $100 for $50 of mine. What is the value of accepting? Part 2) I have two envelopes, one containing twice the amount of money as the other, and both containing some positive amount of money. I hand you one of them. You can switch anywhere from 0-100 times. If you ran it 101 times choosing a different number of switches each time, in which instance(s) would you do best? Part 3) Same as Part 2, but this time you look inside before being given the option to switch. You find $10,000. What difference, if any, is there between Parts 1 and 3?