The Parable of the Baltimore Stockbroker

December 19, 2020 Jordan Ellanberg

Imagine getting a mail from a little known stockbroking firm. The mail predicts that a certain stock will rise this week. You leave the mail aside, as you have seen enough such mails. But the prediction turns out to be right. Next week the Baltimore Stockbroker mails again, with another tip-this time, of a stock going south. The message turns out right too and you decide to mark the Baltimore Stockbroker as ‘not spam’.

Week Three. Another hit. And your interest is piqued.

This goes on for ten weeks. Ten accurate predictions from the Baltimore Stockbroker.

You, the guy who recently retired with a substantial gratuity in the bank, are hooked.

Week eleven, the Baltimore Stockbroker sends you an offer to invest money with him, for a substantial fee of course. There is the usual caveat of past performances not guaranteeing future success, but the Baltimore Stockbroker nudges you to consider his ten-week streak.

You do the math. Every week, the Stockbroker had a 50% chance with his prediction. Either he would be right, or wrong.

Combining the probabilities for ten weeks, the chances of the Baltimore Stockbroker to be right ten weeks in a row work out to… 1/2 x 1/2 x 1/2……ten times… =1/1024.

You consider. The Baltimore Stockbroker must be onto something. And it would be worthwhile to invest your nest egg with him.

You go in for the offer. Things, from the view of the Baltimore Stockbroker, are a bit different.

What he did, was start out with sending 10,240 newsletters!

Of these, 5120 said a stock would go up, and 5120 said otherwise.

The 5120 who got a dud prediction never heard from the Baltimore Stockbroker again.

Week Two, the Baltimore Stockbroker sent 2560 newsletters, and the following week he again halved the number, based on who got his correct prediction.

This way, at the end of week 10, he had ten people, convinced he was a financial genius.

That’s. The power of probabilities, cons, and the impact of mathematics on daily life… Just one aspect!

Borrowed from *’How Not to be Wrong: The Hidden Maths of Everyday Life’ by Jordan Ellenberg. *

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