Betting on Lotteries

Because of this phenomenon of diminishing marginal value, betting on lotteries is an even worse bet than most people suppose. A lottery with a payoff of $20 million sounds attractive, but it does not seem to be twenty times more attractive than a payoff of $1 million. So even if the expected monetary value of your $1 bet in a lottery is the loss of $0.50, the actual value to you is really something less than this, and so the bet is even worse than it seemed at first.

In general, then, when payoffs are large, the expected overall value of the payoff to someone is reduced because of the effects of diminishing marginal value. But not always. It is possible to think of exotic cases in which expected overall value increases with the size of the payoff. Suppose a witch told you that she would turn you into a toad if you did not give her $10 million by tomorrow. You believe her, because you know for a fact that she has turned others into toads when they did not pay up. You have only $1 to your name, but you are given the opportunity to participate in the first lottery described above, where a $1 ticket gives you 1 chance in 20 million of hitting a $10 mil- lion payoff. We saw that the expected monetary value of that wager was an unfavorable negative $0.50. But now consider the overall value of $1 to you if you are turned into a toad. Toads have no use for money, so to you, as a toad, the value of the dollar would drop to nothing. Thus, unless some other, more attractive alternatives are available, it would be reasonable to buy a lottery ticket, despite the unfavorable expected monetary value of the wager.