Can You Beat the Odds in the $100 Envelope Challenge?

[Tim Henry]

There are 100 envelopes in a box. Each envelope contains a different number. The numbers could be large or small, rational or irrational - anything goes as long as they are all different. Among all the envelopes in the box, the one with the largest number is the winner. If you turn it in, you will receive $100. For any other number, you get nothing. The rules for the game are as follows. You can draw an envelope out of the box and open it to read the number. If you don’t like it, you can select another envelope, but you must tear up the previous number first. You can repeat this process until you find a number you like, or you reach the last envelope in the box. Describe a strategy for this game that guarantees a 25% or better chance of winning the $100. If you can, find the expected value of your strategy. The person who submits the best strategy gets bonus points.

 

[micromass]

I suggest you read up on the secretary problem: http://en.wikipedia.org/wiki/Secretary_problem

I don't find its solution easy, however...