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The Professor's Bet

Updated: May 3, 2020

Say we are having dinner and I start a bet. I'll toss a coin once and if head comes I'll pay you $200 but if it is tails, you'll pay me $100.

Would you take the odds?

If you think mathematically you have an expected value of $50 and those are good odds, so you ought to take it.

But a professor from MIT said no. This was Professor E Cary Brown, who was given this question by Professor Paul Samuelson.

Now Samuelson was much intrigued by Brown's decision and changed his bet.

He said if I were to toss the coin a hundred times instead of one, would you take it.

Professor E Cary Brown thought of the Law of Large Numbers and saw that he can win up to $5000 practically for sure and agreed.


So Samuelson concluded that E Cary Brown is irrational. Because if you took 1 of them, you should take 100 of them right?

But what's of key importance here is that in the second case E Cary Brown saw that he would have a chance to redeem his losses. A common man unaware of the Law of Large numbers might also take the same decision.


This is something which is called the Prospect Theory, a key concept in behavioural economics. According to this theory, human psychology works such that, the gains seem much larger than the losses. In other words, when I am betting large amounts and losing, my risk appetite increases even though the risk also increases continually because I am looking at the prospect of winning back all the money and this is what E Cary Brown saw in the second case.

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