Some of you might be familiar with a show called Deal or No Deal. For those you are not familiar, a simplified version of the show is as follows,

* There is a host, a player, and 40 suitcases of money.
* The host informs the player that there are 39 empty suitcases and 1 case with 1 million dollars. The suitcases are closed and the player has no idea how much each specific suitcase contains. At the beginning of the game, the player is requested to choose 1 suitcase at random. Let's call this the Chosen Suitcase
* At the beginning of each turn, the player is requested to choose 1 suitcase from the remaining Non-Chosen Suitcases, reveal the contents, and put this case and contents in a discarded pile. After this, the player has the choice of quitting the game and keep the content of his unopened Chosen suitcase, or switching his Chosen Case for one of the remaining Non-Chosen Cases and play on.

Let's say that the player goes through 38 turns, opening and discarding suitcases without ever switching his original Chosen Case. The 38 opened cases are all empty. There are now only 2 unopened cases left, and 1 of them is currently chosen by the player. Should he switch his original Chosen Case for the remaining Suitcase for the best chance to win 1 million dollars? Assuming optimal strategy, what is the player's probability of winning the 1 million dollars in this situation?

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Here's a twist on the Monty Hall problem.

Some of you might be familiar with a show called Deal or No Deal. For those you are not familiar, a simplified version of the show is as follows,

* There is a host, a player, and 40 suitcases of money.

* The host informs the player that there are

39 empty suitcasesand1 case with 1 million dollars. The suitcases are closed and the player has no idea how much each specific suitcase contains. At the beginning of the game, the player is requested to choose 1 suitcase at random. Let's call this the Chosen Suitcase* At the beginning of each turn, the player is requested to choose 1 suitcase from the remaining Non-Chosen Suitcases, reveal the contents, and put this case and contents in a discarded pile. After this, the player has the choice of quitting the game and keep the content of his unopened Chosen suitcase, or switching his Chosen Case for one of the remaining Non-Chosen Cases and play on.

Let's say that the player goes through 38 turns, opening and discarding suitcases without ever switching his original Chosen Case. The 38 opened cases are all empty. There are now only 2 unopened cases left, and 1 of them is currently chosen by the player. Should he switch his original Chosen Case for the remaining Suitcase for the best chance to win 1 million dollars? Assuming optimal strategy, what is the player's

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