'Two-envelope' money problem cracked

Published: Wednesday, August 5, 2009, 13:05 [IST]

Melbourne, Aug 5 (ANI): A long-standing problem about how an individual decides between two envelopes containing different amounts of money may have been solved.

In the journal Royal Society Proceedings A, Dr Mark McDonnell of the University of South Australia and Dr Derek Abbott of the University of Adelaide have reported their new solution to the two-envelope problem, reports ABC Online.

A person is presented with two envelopes in the problem, and informed that one contains twice the amount of money as the other. They are invited to open the envelope but then must decide if they'd like to switch it with the other. The trouble is they could double their money - but they could also halve it.

According to current beliefs, people have an equal chance of gaining or losing no matter whether they decide to switch or stay put with the original envelope, says McDonnell.

However, now he and Abbott have now worked out a formula they say can be used to increase the chance of winning the envelope game, if it's played repeatedly with different amounts of money every time.

The formula relates a particular amount of money (y) found in the first envelope to the probability (P) that you should switch envelopes to gain in the long term.

The formula calculates a smaller probability of switching the larger the original amount (y) is.

McDonnell says the key to this strategy is that the decision when exactly to switch must be random.

McDonnell says their solution is different to those that have gone before because of this random element.

"Our solution is to switch randomly," he says.

"Each time you are offered two envelopes, you observe the amount in one envelope, and then the larger the amount observed, the less likely it is that you should switch, but the choice is still random.

"The key result is that this kind of random switching leads to a long-run financial gain in comparison with either (i) never switching or (ii) switching randomly in a manner that ignores the observed amount in the opened envelope," he adds. (ANI)

 

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