[Offtopic] IBM Monthly Puzzle

[stephen at melbpc.org.au]

IBM Research: Welcome to our Monthly Puzzles

 <http://www.research.ibm.com/ponder/>

You are cordially invited to match wits with some of the best minds in 
IBM Research.

Seems some of us can't see a problem without wanting to take a crack at 
solving it. Does that sound like you? Good. Forge ahead and ponder this 
month's problem. 

We'll post a new one every month, and allow two to three weeks for you to 
submit solutions (we may even publish submitted answers, especially if 
they're correct). We won't reply individually to submitted solutions but 
every few days we will update a list of people who answered correctly. 
Towards the end of the month, we'll post the answer.

Ponder This Challenge:

Puzzle for February 2007.

Consider the following two person game.

Each player receives a random number uniformly distributed between 0 and 
1. Each player can choose to discard his number and receive a new random 
number between 0 and 1. This choice is made without knowing the other 
players number or whether the other player chose to replace his number.

After each player has had an opportunity to replace his number the 
numbers are compared and the player with the higher number wins. 

What strategy should a player follow to ensure he will win at least 50% 
of the time?

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Cheers people
Stephen Loosley
Victoria, Australia