6. (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 11 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 Smal 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? 6. (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 11 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 Smal 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