The Language of Argument

2 4 0

C HaP Te r 1 1 ■ C h a n c e s

assume that they are due for a run of good luck to even things out. Gambling

systems are sometimes based on this fallacious idea. People keep track of the

numbers that come up on a roulette wheel, trying to discover a number that

has not come up for a long time. They then pile their money on that number

on the assumption that it is due. They usually end up losing a bundle.

These gamblers seem to assume, “In the long run, things will even out (or

average out).” Interpreted one way, this amounts to what mathematicians

call the law of large numbers, and it is perfectly correct. When flipping a coin,

we expect it to come up heads half the time, so it should come up heads five

times in ten flips. If we actually check this out, however, we discover that

the number of times it comes up heads in ten flips varies significantly from

this predicted value—sometimes coming up heads more than five times,

sometimes coming up fewer. What the law of large numbers tells us is that

the actual percentage of heads will tend to come closer to the theoretically

predicted percentage of heads the more trials we make. If you flipped a coin

a million times, it would be very surprising if the percentage of heads were

more than 1 percent away from the predicted 50 percent.

This law of large numbers is often misunderstood in a way that leads to the

gambler’s fallacy. Some people assume that each possible outcome will occur

the average number of times in each series of trials. To see that this is a fallacy,

Mike Shiell/CSL, CartoonStock Ltd

97364_ch11_ptg01_239-262.indd 240 15/11/13 10:58 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.