Monty Hall Marathon

Monty Hall offers you the choice of three doors. Behind one is $1000. Behind the others are nothing. He'll let you choose one door, then he'll open one of the remaining doors to show nothing. He'll then allow you to choose if you want to keep your original door selection or switch to the remaining door.

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?

Source: Original.

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