Wednesday 28 May 2014

The Two Envelopes Paradox

A mathematical problem that has nothing to do with chess.
Two envelopes are placed in front of you. You are told that one envelope contains a sum of money, and the other, twice the amount. You are asked to choose one. But before you open the envelope you are told that you can swap your envelope for the other one.
Question 1: Should you swap?

Assuming you know a little about calculation expected outcomes, your reasoning might go like this.
I have a 1/2 chance of choosing the smaller envelope and a 1/2 chance of choosing the larger envelope. My expectation from swapping is therefore (1/2*x+2*x)/2 or 1.25x
So swapping envelopes increases my return by 25%
Question 2: Is this a valid way of making your choice?

and Question 3: Can I infinitely increase my expected outcome by swapping again and again!


Anonymous said...

That sounds very much like the Monty Hall problem:


Anonymous said...

The Monty hall problem would require more than two envelopes. Every choice you make (first pick and any subsequent swaps) is simply choosing between two, ie 50% chance. No amount of swapping will change that.