[Alan3]

I'm having trouble wrapping my head around this, but tt becomes much more clear if I change the problem slightly.

Suppose you're given 2 envelopes with money in them and you are told that one contains ONE THOUSAND TIMES as much as the other (let's say they're cheques and therefore weight is not an issue). You pick one and open it up to reveal a $100 cheque. You are now offered the opportunity to switch envelopes.

I have a belief distribution that someone is not going to just give me $100,000. If I open the $100 envelope I'm going to keep it because I expect the other envelope has $0.10.

This expectation is much smaller at the 50/100/200 range. The chance that someone is going to give me $100 is very close to the chance that someone will give me $200 and I'm not going to lament the loss of $50 so much, so maybe switching is the right answer at this level.

Increasing the "amplitude" of the problem helped me understand the "Let's make a deal" problem too.