You select one. Then Santa removes one of the other ones. He also promises you that the one he removed was in fact one of the empty ones. You have now the chance to either stick to the one you selected or switch to the remaining one still on the table (giving the one you currently hold back to Santa).

How are your chances if you stick to the parcel you selected at the start? How are your chances if you switch to the one Santa has left on the table?

Old problem, beaten to death long before the internet existed.

The classical answer is to switch.

However, there's more to say. With your wording of the problem, there isn't enough information to say whether you should switch or not. See, only after you've picked it's revealed that Santa offers you a choice. Which means that Santa may be biased -- perhaps he only offers you a choice if you've picked the top prize, assuming you know about Monty Hall and switch (the financial crisis has reached the North Pole after all).

Now, if it's a given that Santa will always reveal an empty price after your first choice, it's better to switch, increasing your chance of winning from 1/3 to 2/3. But if we do not know what Santa's strategy will be, we cannot know whether switching will increase our chance to win is.

In reply to Re: Holiday parcel puzzle by JavaFan
in thread Holiday parcel puzzle by cavac

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