Don’t box yourself in when making decisions
Monty Hall, the quiz show host who bemused many FT readers a year ago by trying to persuade them to switch boxes in the hope of winning a car, has a new game. There are only two boxes and one contains twice as much money as the other. When you choose one, he shows you that it contains ￡100. Will you stick with your original choice, or switch to the other box?
This problem is real. Anyone who has changed jobs, bought a house or planned a merger has encountered a version of the two-box game; keep what you know, or go for an uncertain alternative. But familiar problems are not necessarily easy to model. Monty points out that you can lose only ￡50 but might gain ￡100. He says he does not know which box has the bigger prize. If untrue, is he trying to save his employer money, or trying to help you win? You have no way of judging whether the ￡50 loss is more or less likely than the ￡100 gain.
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Decision theory tells you there is an expected gain of ￡25 from an equal chance of winning ￡100 or losing ￡50. But many people do not see the problem this way. They dislike the prospect of losing ￡50 more than they like the prospect of gaining ￡100. This, decision theorists claim, is irrational. If you accepted 100 gambles like this, you are virtually certain to end up with a substantial gain.
But, you may say, I am not playing this game 100 times. I am only playing it once and you cannot guarantee a gain in a single trial. That is true, but it illustrates “the fallacy of large numbers”. On the 100th trial, you are in the same position as someone who is offered the chance to do it once. So you should not do it the 100th time. But then you should not do it the 99th time, or the 98th
