EXPECTED OVERALL VALUE
Given that lotteries usually have an extremely unfavorable expected mone- tary value, why do millions of people invest billions of dollars in them each year? Part of the answer is that some people are stupid, superstitious, or both. People will sometimes reason, “Somebody has to win; why not me?” They can also convince themselves that their lucky day has come. But that is not the whole story, for most people who put down money on lottery tickets realize that the bet is a bad bet, but think that it is worth doing anyway. Peo- ple fantasize about what they will do with the money if they win, and fan- tasies are fun. Furthermore, if the bet is only $1, and the person making the bet is not desperately poor, losing is not going to hurt much. Even if the ex- pected monetary value on the lottery ticket is the loss of fifty cents, this might strike someone as a reasonable price for the fun of thinking about winning. (After all, you accept a sure loss of $8 every time you pay $8 to see a movie.) So a bet that is bad from a purely monetary point of view might be acceptable when other factors are considered.
The reverse situation can also arise: A bet may be unreasonable, even though it has a positive expected monetary value. Suppose, for example, that you are allowed to participate in a lottery in which a $1 ticket gives you 1 chance in 10 million of getting a payoff of $20 million. Here, as noted above, the expected monetary value of a $1 bet is a profit of $1, so from the point of view of expected monetary value, it is a good bet. This makes it sound reasonable to bet in this lottery, and a small bet probably is reason- able. But under these circumstances, would it be reasonable for you to sell everything you owned to buy lottery tickets? The answer to this is almost
the following argument on the other side. Because the chances of winning are fifty-fifty, you will, on the average, win half the time. But notice what happens in such a case:
Win Lose Lose Win
Total $150 $90 $54 $81
So, even though you have won half the time, you have come out $19 behind. Surprisingly, it does not matter what order the wins and losses come in; if
two are wins and two are losses, you come out behind. (You can check this.) So, because you are only going to win roughly half the time, and when you win half the time you actually lose money, it now seems to be a bad idea to gamble at Fogelin’s Palace.
What should you do: gamble at Fogelin’s Palace or not? Why?