You bet a number, R, chosen from the set of integers [1, N]. R is proportional to the amount of money at stake. With probability P

_{R}you will win back 2R. With probability 1- P

_{R}you win back nothing (so you lose R). P

_{R}is dependent on R but you do not know what it is.

You know the following:

- The maximum and minimum values in the set of all P are 0.9 and 0, respectively.

- For all k != j, |P

_{k}- P

_{j}| > 1/(2N)

- After X bets, the probabilities are shifted cyclically such that P’

_{k}= P

_{k-1}, and P’

_{1}= P

_{N}.

- After 10N bets, the entire system resets, and a new set of probabilities is generated that satisfies the above conditions.

Suppose N = 100, X = 10, and you have a lot of money. Can you game the system? What is the best strategy?

My current strategy (not sure if optimal):

1. Set some confidence counter to 0. Set current bet to 1.

2. Bet 10 times.

3. If those 10 bets yielded net profit, increase confidence by 1. If they yielded net loss, decrease confidence by 1.

4. If confidence is negative, set it to 0. If confidence is positive, increase bet by 1.

5. Go back to Step 2.