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?

I think it has been long enough since the last post that a hint is merited.

There is a theorem concerning optimal stopping problems like this, which states that under certain conditions the optimal strategy is to stop only when it is at least as good as continueing for one more round and then stopping.

Posted by Daniel on 2010-09-11 12:44:50