Let's say I'm playing a game that works likes this: I have n bowls that are each filled with a different number of marbles, and I know how many marbles are in each bowl. At each round, the dealer goes to each bowl one at a time, and decides to add or remove some number of marbles from that bowl. He decides how much to add or remove from each bowl based on a set of rules that only take into account the number of marbles currently in each bowl, though I have no idea what those rules are. I am able to see the changes he makes. After he has made his changes, I have to make a decision: I can either have him give me a dollar for each marble in each of the bowls, or I can have him undo all the changes he just made to the bowls. After I have made my decision and the dealer has either paid me or undid his changes to the number of marbles in each bowl, I begin the next round with the bowls as they currently are. My goal is to maximize the average amount of dollars I get per round.
My question is, what's the optimal strategy for playing this game?