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?
Note, by the way, that the strategy is not really a function of R. At any point, the correct play is determined by C, and your high card at that point, and the number of rounds remaining.
R is not a direct factor
