Question

There are two envelopes in front of you each with a non-zero number. You will receive an amount of money equal to the final envelope you choose. You are informed one has twice as much money as the other. You are then allowed to select either envelope. After you select one and before opening it you are given the option to change your mind and switch to the other one?

You think to yourself that if your envelope has x dollars there is a 50% chance the other one has 1/2x dollars and a 50% chance it has 2x dollars.

The expected return, you compute, is 1/2(1/2x+2x)=1.25x which seems like a favorable gamble.

Do you switch and why? Assume you are neither risk averse nor risk prone, in other words you will take any good gamble and avoid any bad one.

Answer 1