1) You are given a choice of $100 or an envelope that has a 50% chance of having half that amount and a 50% chance of having double that amount. Which would you pick? Is there an advantage to switching to the unknown envelope?

2) Another guy had arrived just before you and saw two unopened envelopes, one of which was selected in a random process that had an equal chance of opening either envelope. Upon opening, its contents was $100 which gave you more information to base your choice on. You are both truthfully told the other envelope has a 50% chance of having half that amount and a 50% chance of having double that amount, since nobody knows the contents of either envelop but know that one has twice as much as the other. Which should the guy who saw two unopened envelopes pick? Is there an advantage to switching to the unknown envelope for either participant and if so why would seeing an envelope opened to reveal the $100 make a difference?

3) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. One is randomly selected as above and is opened revealing $100. The random process has an equal chance of opening either envelope. Which action would you choose if you were one of the two people that selected one of these envelopes?
a) Should you keep the envelope you chose?
b) Should you switch to the one you didn't choose?
c) Should you take the $100?
d) Should you take the amount in the unopened envelope?
Is there an advantage to any of the switching strategies once the contents of one envelope is known?

4) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. You each pick a different envelope. You each pick an envelope but neither is opened. Would you switch if you were one of the participants?

What made the answer to any of these 4 different? If there was no difference then why wouldn't you take the envelope in puzzle #1.