The negative of loss is sometimes referred to as utility. Consider a gambling game very unlike most in that you are bound to win·at least £2, and accordingly in order to be allowed to play, you must pay an entry fee of £e. A coin is tossed until it comes up heads, and if this occurs for the first time on the nth toss, you receive £2ⁿ. Assuming that the utility to you of making a gain of £x is u(x ), find the expected utility of this game, and then discuss whether it is plausible that u (x) is directly proportional to x. [The gamble discussed here is known as the St Petersburg Paradox. A fuller discussion of it can be found in Leonard and Hsu (2001, Chapter 4).]