Here's how I see it - the important unstated variable is how big a budget does the host of the game have? If you know that you're playing with a billionaire who

Here's how I see it - the important unstated variable is how big a budget does the host of the game have? If you know that you're playing with a billionaire who loves this party trick, and is probably willing to give away a million dollars on this, then the $20 you found in you envelope is probably the smaller value. If your envelope contains $800,000 it's probably the bigger one. The host has chosen a number randomly between 1-N, and they're not neccessarily going to tell you what N is. But in the long run you'll find that values closest to N/2 are more common than values further from N/2.