The Monty Hall problem is a counter-intuitive statistics puzzle loosely based on the American television game show Let's Make a Deal and named after its original host, Manty Hall.
The Game:
Do you stick with the original guess or switch to the other unopened door?
Surprisingly, the odds to win the car ar 1/3 if you stick with the original one but goes to 2/3 if you switch the door.
The game is about re-evaluating your decisions as new information emerges.
Initially you can pick up one of three doors. Only one with the car. Assume that the door with the car is W and the other two are B and C. Let's enumerate the possible cases:
As you can see from the evidence: If you don't change your choice you loose 2/3 of the times. If you change your choice you win 2/3 of the times.
The problem can be generalized to N doors. Where only one has a car behind.
If you stick with the original choice the odds to win are just 1/N, but if you change your mind, after that Monty has removed N-2 goats, then the odds to win magically becomes (N-1)/N. Pretty impressive.
To better understand why this works, another, alternative, approach to the problem is needed: If you change your initial choice is like if, initially, you are not trying to pick the door with the car but a door with a goat, which has probability (N-1)/N). Then Monty will always make you the favour of removing the other N-2 bad cases and what is left is, eventually, the fortunate case.
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