An individual, who has zero initial wealth, has been offered a free gambling opportunity by the Casino. This opportunity allows him to receive 60 of free gift money and plays in a binomial game. This binomial game returns twice the amount of any correct bet and nothing for any wrong bet, and the probability of winning and losing a bet in each round is 18/37 and 19/37, respectively. The minimum bet in each round is 50p (or 0.5) with no upper limit. The Casino requires the individual to continue playing until he has either increased his wealth to 64 or lost all the 60 free gift money.

1. Calculate the probability that the individual will lose all 60 before increasing his wealth to 64, if his betting strategy is to bet
   1. a fixed amount of 50p in each round (unit-betting strategy)
   2. a fixed amount of 1 in each round (double-betting strategy)
   3. a fixed amount of 2 in each round (quadruple-betting strategy)

2. Provide the details of a varying-bets betting strategy which minimizes the probability of ruin, and calculate the probability that the individual will leave the game with 64 if he uses such a strategy. Explain intuitively why this strategy can increase his chance of success.

3. Assume that the individuals utility function is given by UW=W0.5 and assume that he sticks to the double-betting strategy defined in a). Treating the individuals two possible outcomes (i.e. going home taking either 0 or 64 from the Casino) as a binomial gambling situation, calculate his Actuarial Value of the gamble, Certainty Equivalent Wealth, Markowitz Risk Premium, and Cost of the Gamble.

4. Under the same assumptions in c), suppose that before the individual accepts this free gambling opportunity, an experienced gambler offers to buy this opportunity from him for the price of 40. Explain whether the individual will accept the deal.