In this game, you have an infinite deck of cards. Each time you draw a card it's value is a uniformly distributed integer on the interval [0,C]. The game lasts for R rounds. You start the game by drawing a card and adding its value to your running total. At each round you have two choices: 1) draw another card from the deck and add its value to your total 2) add the value of the highest card previously drawn to your total What strategy, based on the constraints R and C, gives you the optimal total at the end of the R rounds?

(In reply to re: a hint by Steve Herman)

very good work, I rather enjoyed reading your approach to the solution as it is slightly different (although gives same strategy) to my approach.  While you solve for what rounds to draw at based on highest card, I solved for a similar table that told you for what highest card value to stop at for each round.  In other words I solved the same inequality for H instead of r like you did.  I like your solution better because it solves a linear inequality instead of a quadratic one.

Posted by Daniel on 2010-09-12 04:53:50