Monty has played this game so often he decides to make it a little different. Before you make your choice, he tells you that if you don't find the money, he'll let you play the same game again, but increase the amount to $2000. Perhaps it would be better to try to lose the first game. Should you switch doors?
On another day, Monty lets you know before you make your first choice that if you don't find the money, you'll play again for $2000, and if you don't find that money, you'll play one more time for $3000. When offered your first choice, should you switch doors, or stay with your first choice?
What are your best decisions to maximize your potential winnings?