(adsbygoogle = window.adsbygoogle || []).push({}); The "Deal or no Deal" dillemma

The problem below combines the familiar quiz show with a dash of Monty Hall.

Deal or No Deal.

22 boxes hiding money prizes.

11 blue (low). 11 red (high).

You chose one box at random.

Obviously you want it to be red.

The other boxes are revealed one by one

The game follows the normal rules of "Deal or No Deal", with the following caveat:

With every box you open, the host will always reveal one of the opposite colour. He has been told which boxes have reds and which have blues, but he does not know the values.

Thus, at every stage of the game (after the host opens a box) the number of blues and reds unopened is exactly equal.

You've just played to the end, refusing all deals.

Twenty boxes have been opened.

There are two remaining.

For the sake of drama, lets say these are 1c and $1,000,000.

The banker has offered you a swap.

Do you accept it?

Does it matter which boxes you or the host opened?

Or are the odds 50/50 regardless?

Typical example:

Say, in the course of the game you opened 7 blues and 3 reds.

The host complimented each occasion with 7 reds and 3 blues.

Should you stick or swap?

Or does it make no difference?

Simon

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# The Deal or no Deal dillemma

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