You are given the option to purchase or sell a stock for today. You are also told that the stock will either double in value or halve in value tomorrow. In addition to buying or selling the stock, you may bet on the outcome of the value of the stock in a casino. If you bet dollars on the correct outcome, you will receive dollars, otherwise you will lose your bet. Given this information, come up with the optimal solution to always profit. Report your guaranteed profit when .