I’ve often heard the Baltimore stockbroker parable told as a true story, but I couldn’t locate any evidence that it’s ever really happened. The closest thing I found was a 2008 reality TV show — reality TV being where we go for parables nowadays—in which British magician Derren Brown pulled off a similar stunt, mailing various horse-racing picks to thousands of Britons with the result of eventually convincing a single person that he’d devised a foolproof prediction system. (Brown, who likes dispelling mystical claims more than he does promoting them, exposed the mechanism of the trick at the end of the show, probably doing more for math education in the UK than a dozen sober BBC specials.)

But if you tweak the game, making it less clearly fraudulent but leaving unchanged the potential to mislead, you find the Baltimore stockbroker is alive and well in the financial industry. When a company launches a mutual fund, they often maintain the fund in-house for some time before opening it to the public, a practice called incubation. The life of an incubated fund is not as warm and safe as the name might suggest. Typically, companies incubate lots of funds at once, experimenting with numerous investment strategies and allocations. The funds jostle and compete in the womb. Some show handsome returns, and are quickly made available to the public, with extensive documentation of their earnings so far. But the runts of the litter are mercy-killed, often without any public notice that they ever existed.

Now it might be that the mutual funds that make it out of the incubator did so because they actually represented smarter investments. The companies selling the mutual funds may even believe that. Who doesn’t, when a gamble goes right, think their own smarts and know-how are in some way due the credit? But the data suggests the opposite: the incubator funds, once the public gets their hands on them, don’t maintain their excellent prenatal performance, instead offering roughly the same returns as the median fund.

What does this mean for you, if you’re fortunate enough to have some money to invest? It means you’re best off resisting the lure of the hot new fund that made 10% over the last 12 months. Better to follow the deeply unsexy advice you’re probably sick of hearing, the “eat your vegetables and take the stairs” of financial planning: instead of hunting for a magic system or an advisor with a golden touch, put your money in a big dull low-fee index fund and forget about it. When you sink your savings into the incubated fund with the eye-popping returns, you’re like the newsletter getter who invests his life savings with the Baltimore stockbroker; you’ve been swayed by the impressive results, but you don’t know how many chances the broker had to get those results.

It’s a lot like playing Scrabble with my eight-year-old son. If he’s unsatisfied with the letters he pulls from the bag, he dumps them back in and draws again, repeating this process until he gets letters he likes. In his view this is perfectly fair; after all, he’s closing his eyes, so he has no way of knowing what letters he’s going to draw! But if you give yourself enough chances, you’ll eventually come across that Z you’re waiting for. And it’s not because you’re lucky; it’s because you’re cheating.

The Baltimore stockbroker con works because, like all good magic tricks, it doesn’t try to fool you outright. That is, it doesn’t try to tell you something false — rather, it tells you something true from which you’re likely to draw incorrect conclusions. It really is improbable that ten stock picks in a row would come out the right way, or that a magician who bet on six horse races would get the winner right every time, or that a mutual fund would beat the market by 10%. The mistake is in being surprised by this encounter with the improbable. The universe is big, and if you’re sufficiently attuned to amazingly improbable occurrences, you’ll find them. Improbable things happen a lot.

This is an extract from Jordan Ellenberg's How Not To Be Wrong published by Penguin Press