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Comment by FredBrach | Hacker News Reader

This paradox looks easily resolvable to me: keeping the same door can be seen as choosing a new door - but the same.

The host eliminates an "incorrect" door only after you first choose one. The monty hall problem is about using the new information that the host is obligated to give you. if you use it you increase your chances to 1/2, if you do nothing with the new information you remain at 1/3. Consider an alternative scenario with the same concept: you have 100 doors, and after you choose a door the host eliminates 98 wrong doors. you can now choose the 1 other door or keep your original choice. Its obvious the other one is a better choice

> if you use it you increase your chances to 1/2,

I may be misreading you here, but if I'm not, then you are incorrect. If you switch, you win 2/3 of the time, not 1/2. This is one of the many "doesn't make sense" conclusions of this problem, which makes it so great.

Consider this:

There are 2 people playing simultaneously, and you both have to agree on the same door initially. Monty then reveals one of the other losing doors. Because of your personalities, you switch every time, the other person never switches.

Since Monty always reveals a loser, one of you HAS to win. Since the other person never switches, his chance of winning remains at 1/3. Since someone ALWAYS wins, and he wins 1/3 of the time, you, the switcher, are left with the remaining 2/3.

Another alternative scenario that sometimes helps people have their "ah-ha" moment is to change it so that Monty doesn't actually open a door, but instead says "Do you want to keep your door, or would you like to switch and take BOTH remaining doors?".

Yes you have to do something: choosing a new door - but it can be the same. Do you get me? The action of making a new choice is either visible if you are choosing a new door, but you can also say that you are making a new choice by choosing the same door.

By the way, it is simpler: the probability the door you've choosen at first hide the car is just increasing when the host is eliminating one. You don't have to do something for that.

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