(A simplified hedging example) In the early 2000's, there was a casino boom in Macao. To compete with other players in the market, some casinos offered free lunch boxes to those customers who kept gambling over a suffi- cient amount of time, say several hours. Being two poor students (aged over 18!), Tony and Yau wanted to get some free lunch boxes without mak- ing/losing money. They reached a dice table where people were betting on the total point counts of three dice. There are two possible outcomes for each round of the game: (1)"Large", which refers to a total point count of II to 18, and (2) "Small", which refers to a total point count of 3 to 10. Both have a payoff of 1-to-1. "Triples" or "alls" (i.e. {1,1,1}, ..., {6,6,6}) are still counted as either "Large" or "Small", depending on the sum. a. Assume that the chance of having a "Small" is the same as that of having a "Large", how would you teach Tony and Yau to bet so that their net worth can be maintained at a constant level after one round of the game? b. Suppose that you observe that the chance of having a "Small" is 1/3, how would you teach Tony and Yau so that they will not make/loss any money over 2-3 hours of gambling?