Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over a risky prospect of equal expected value is called risk averse; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, first formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit, so, suggested Bernoulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one's possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is \(0.50 \times u(200)\), where \(u\) is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curve, respectively.) It follows from a concave function that the subjective value attached to a gain of $100 is more than 50 percent of the value attached to a gain of $200, which gives a preference for the sure $100 gain and, hence, risk aversion.
Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This gives a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. Except for prospects that involve very small probabilities, risk aversion is generally seen in choices involving gains, while risk seeking tends to hold in choices involving losses.
Based on the above passage, look at the decision situations faced by three persons: Babu, Babitha and Bablu.
Suppose the instant and further utility of each unit of gain is the same for Babu. Babu has decided to play as many times as possible before he dies. He expects to live for another 50 years. A game does not last more than ten seconds. Babu is confused about which theory to trust for making his decision and seeks the help of a renowned decision making consultant, Roy Associates. What should Roy Associates' advice to Babu be?
