Thursday, February 21, 2013

Winning Bar Bets With Mathematics

Benford's law is pretty neat. I first came across this phenomenon while watching a silly Internet TV show related to bar bets. The bar bet that exploits Benford's law is a little complicated, and relies (of course) on the law of large numbers.

The premise is that you challenge your fellow bar patrons to a bet: that humans are no good at generating random numbers. It makes sense intuitively since people tend to pick numbers that have a special meaning, and there's a finite number of numbers that have meaningful connotations (i.e. 3's a charm, lucky number 7, etc.). To add to the challenge, you'll throw in some randomness. Each person will come up with two randomly chosen quantities based on some data, such as the population of pet birds in the US and the volume of water in the Dead Sea in cubic feet. Then, multiply the two numbers to get a third number. The bet will be that even the first digit of *that* number is not uniformly distributed. On the surface, it seems counter-intuitive. But Benford's law will give you an edge in this silly bar game.