Answer to Game Show Problem

It is definitely in the contestant's interest to change their choice. At the first stage they have only a one in three chance of winning, but if they change their choice at the second stage they have a two in three chance. If the contestant has chosen an empty box at the first stage, the host has no choice as to which box he opens at the second stage, and so the remaining box will always contain the money.

The table below shows the outcomes in each of the eighteen possible cases. Work through them all if you care to.

Money in	1st choice	Stay put	Change
*
**Box A	**Box A	**Win	**Lose
**Box A	**Box B	**Lose	**Win
**Box A	**Box C	**Lose	**Win
*
**Box B	**Box A	**Lose	**Win
**Box B	**Box B	**Win	**Lose
**Box B	**Box C	**Lose	**Win
*
**Box C	**Box A	**Lose	**Win
**Box C	**Box B	**Lose	**Win
**Box C	**Box C	**Win	**Lose

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