Deep.

If your envelope contains 1 dollar, then tossing the coin once gives you 1.5 which is more than 1 so switching will give you an envelope with a positive number different from 1, which is by def. greater than 1. So it works for the smallest case.

If your envelope contains 2 dollars, then there is a chance that the other one contains 1 dollar, but (on the face of it) a bigger chance that there is more in the other envelope. However, there is a 50% chance of a head on the first throw and therefore there's a 50% chance you'll not switch.

Goodness this is making my head hurt ... I'd need to think about it harder and dig out some of the probability maths that I've forgotten.