The Language of Argument

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C H A P T E R 1 2 ■ C h o i c e s

Expected Overall Value

Given that lotteries usually have an extremely unfavorable expected

monetary 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 any-

way. People fantasize about what they will do with the money if they win,

and fantasies are fun. Furthermore, if the bet is only $1, and the person mak-

ing the bet is not desperately poor, losing is not going to hurt much. Even

if the expected 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?

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