This problem throws many people, even a number of ‘expert’ mathematicians. Suppose you first choose envelope A:
| Round-the-world tickets are in | Host opens | If you stick | If you switch |
|---|---|---|---|
| Envelope A | B or C | Star prize | Booby prize |
| Envelope B | C | Booby prize | Star prize |
| Envelope C | B | Booby prize | Star prize |
The star prize is equally likely to be in any of the three envelopes. You therefore have a 2 in 3 chance of winning the round-the-world tickets if you change your mind, compared to a 1 in 3 chance if you stick. Consequently, you are better off opening the envelope you didn’t choose first.