Monday, September 22, 2008

Experiments in Assessing Risk

Suppose you’re given a chance to bet on the toss of a coin. If it comes up heads you win $20, and if tails you lose $10. Would you take this bet? Given a chance to do it 100 times in a row would you do it? This experiment was actually performed in a coffee shop in Westwood, Los Angeles, as explained by Jason Zweig in his book, Your Money & Your Brain.

The average outcome is to win $5 every time you take this bet. But, if you do it only once, you could lose $10 instead of winning $20. What about doing it 100 times? The expected outcome is to win $500. The odds that you’ll actually lose money are less than 1 in 2000. The odds of losing $200 or more are less than one in a million. The odds of winning more than $200 are over 97%. This is an incredibly good bet.

Amazingly, two out of three people accepted the one-time bet, but only 43% said they would be willing to repeat the bet 100 times. What are the possible explanations for the 57% of people who turned this down?

1. People are spectacularly bad at assessing which risks are worth taking.

2. Some people believed it was a trick, and that the gamble wouldn’t be fair.

3. Some people have philosophical objections to gambling. (However, because almost everything in life involves some type of gamble, it must be difficult to draw the line on this one.)

4. A few of the subjects were compulsive gamblers, and they knew that if they accepted the bet, they’d go out and lose it all and more in a casino.

5. A few of the subjects were so wealthy that winning only $5 per coin toss was a waste of their time.

I suspect that the dominant explanations of the experiments’ results are reasons 1 and 2. It’s no wonder that so many people make poor investing choices given that they would turn down a near sure thing.


  1. If a stranger comes up to you and offers this bet, you have to be a (trusting) fool to accept.

    It's a guarantee that the coin is not genuine and that heads will appear much less than one time in three.

    This reminds me of a quote from a TV show of many years ago. I believe it was 'Maverick' in the late 1950's:

    "If a stranger comes to you and offers to bet you that he can pull out a deck of cards and that a one-eyed jack will spit in your eye, you can be certain that you will end up with a plug of tobacco juice in your eye if you take the bet."

  2. Mark: This line of thinking applies in most situations. But, the experimenters must have known that this would poison their results. If they were smart and interested in how people would react to a fair bet, they must have gone to great lengths to demonstrate that the bet would, in fact, be a fair one.

  3. Hmmm... my first instinct was to avoid the one-time bet and accept the 100-time one. Perhaps the odds are not enough in my favour to want to take the one-time bet.

    I've read about these studies enough that I figure out the odds to overcome my hard-wired gut reactions though, so I would take either bet.

    Perhaps to overcome Mark's valid criticism of the study, the experimenter would allow the bettor to personally flip a coin from their own stash.

  4. Gene: If the amounts were larger, say $1000 if I lose and $2000 if I win, my instincts are the same as yours: avoid the one-time bet but go for the 100-fold repetition. I never trust my instincts on these things, though. Like you, I work out the numbers.

    The book didn't give the details of how the experimenters conducted the study. They may well have let the subjects use their own coin.