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Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown

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Statistical Games

I have noted earlier that this problem is very special for the type of randomness under consideration. The solution would not make sense if the bet concerned the weather, for example. If I bet it would rain on at least 7 of the next 13 days, and the bet is interrupted after 6 rainy and 5 sunny days, it does not necessarily make sense to award me three-fourths of the stake. If the 6 rainy days came at the beginning of the period and it has been cloudless since, you might even be the favorite at this point. In any case, an arbiter awarding the stake should at least look at the sky and listen to the weather forecast. But the problem is very special in another way as well. We're trying to resolve a game for money. Consider the same question with one player having promised to marry the other if she lost, in return for the other player promising to go to war in place of the first player's brother if he lost. Should the first player marry one quarter of the second player, while the other three-quarters of the second player goes to war along with one-quarter of the first player's brother? The only possible way to decide this case is to pick randomly, with the first player having a three-fourths chance of winning. This means continuing the game. And you don't need such far-fetched dramatic examples. Any time the stakes cannot be converted to a divisible common unit—that is, if the gamble is not for money—Pascal and Fermat have nothing useful to tell us.

To see how unusual ...

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