Answer to Guess and make a fortune game

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The answer is that the contestant is better off making a switch.

It is very difficult to articulate the answer is such questions, but let me make a try. If people dont get it, then I will make more tries from different angles

Here goes the argument:
1. When the player chooses the box in the beginning of the game, the probability of him getting the fortune is 1/3.
2. Let us divide the boxes into two sets. One contains the box that the player has choosen and the second set contains the two boxes that the player has not choosen.
3. The probability that the fortune is in the second set is 2/3.
4. Now the host comes and removes an empty box from the second set. Now if the player is given a chance, he is better off choosing the second set because the probability of winning is 2/3

If you are still confused and half convinced, think that there were 100 boxes and fortune behind one. Now you choose one box and the host eliminates 98 empty boxes out of the rest 99. Wont you make a switch?

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