There's the famous "Truth or Consequences" problem. You have three doors. Behind one of them is a big prize, behind the other two are booby prizes. You get to pick one door. The host reveals a booby prize behind one of the other doors, and you get a chance to switch. Should you? Most people think it doesn't matter but they suspect the host is trying to trick them into switching away from the big prize, so they won't switch. Also, a problem I remember from grade school. The teacher gave two scenarios about borrowing [say] $100 for a year with $5 interest to be paid: (1) You prepay the interest, or (2) you pay the interest when you pay off the loan after a year. He had the students stand in two lines, one who said the two scenarios were equal, and the other who said one was more advantageous. I seem to remember being the only one on the latter line, and being disappointed that there was no opportunity to explain. And here's an interesting anecdote from real life. A friend was talking to her stockbroker near the end of last year because she had some long term capital gains she didn't want to pay taxes on (even though the current tax rate for them is only 20% (15% fed, 5% state)). So she wanted to take some offsetting losses. He told her he would sell some stuff, wait 31 days (to avoid the wash rule that prevents you from taking a loss if you buy it back too soon), and buy it back. She worried that she might pay more in commissions than she would save in taxes, but he assured her that it wasn't a problem, because his commission was only 1% while the tax rate was 15%. [Here I invoke the advice "Never ascribe to malice what can be adequately explained by incompetence."] As the readers on this list will instantly recognize, the 1% is on the value of the asset being sold, not the amount of the loss, and it has to be doubled to 2% if the asset is being rebought. [Problem left to the reader: what percentage loss leads to break-even between commission and tax savings.] --ms James Propp wrote:
I'm teaching a course on quantitative reasoning for an audience of nearly two hundred math-averse students, and one of the ways I'm hoping to "sell the product" to them is to pitch the course as a kind of self-defense art that helps you not get ripped off by used car dealers, cell-phone companies, credit-card companies, banks, etc.
For instance, I'll talk about the scam wherein the scammer sends free investment advice to 1024 people (half of whom get one piece of advice and half of whom get a conflicting piece of advice), then sends free advice to the 512 who got good advice on the first round (again splitting his advice half-and-half), then sends free advice to 256 people, and so on, and finally starts to ask a small number of people to pay a lot of money, hoping that they'll reason that someone who's been right so often must be onto something.
I'll also show the class the grifting scene in "Paper Moon".
Can any of you think of other good mathematical cons, or good resources for finding out about them?
("Ricky Jay's Big Book of Math Hustles" would be perfect if such a book existed!)
Jim
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