$10000 is distributed into 5 envelopes. One envelope, the "bomb", remains empty. In the basic version the player knows how much is put into each envelope, let's say $1000, $2000, $3000, $4000, and 0. Then the envelopes are shuffled and in each round you, the player, can either choose to get one of the remaining envelopes or keep the money you have collected so far and quit. If you ask for a new envelope, randomly one of the remaining envelopes is selected and handed to the player. If this envelope contains nothing (the bomb), the player you lose all the money you collected in the previous envelopes, otherwise you add the money to the money taken so far.
How much would you "expect" to win when you were playing the game? Would you expect to win more or less if the $10000 were differently distributed on the envelopes, say as $2000, $2000, $2000, $2000, and 0? What if it were distributed as $100, $500, $2600, $7000, and 0? What about other distributions? Would you play different then? And what exactly does "expectation" mean?
Version b: In another version, you, the player can distribute the money into the envelopes (using the requirement that one of them, the bomb, has to remain empty) before starting to play. How would you distribute the money, and how would you play?
Version c: In still another version, the distribution of the money on the 5 envelopes is not known to the player. It is just known that exactly one envelope is empty and that the other four contain all the 10000 Dollar. How would expected value and strategy change? Would they change?