Consider the following game: You have a random number generator that produces in every round an integer number from
to
with equal probability. You play 3 rounds and have to decide at which position of a 3 digit number you want to place the random digit. Your goal is to form the largest possible (decimal) number. Formulate this game as a Markov decision process and find an optimal policy. Also analyze the case where the numbers are drawn *without replacement*, i.e. if the digit
appears in the first round, it cannot appear anymore in the remaining two rounds.

Haeusler Stefan 2013-01-16