Category Archives: probability

How can the “Gambler’s Fallacy” help penalty takers score?

Nooooo, Ashley Cole!

The World Cup might be over, but researchers from University College, London, are still sifting through video data in an effort to understand goalkeepers’ behavior during penalty shoot-outs.

After analysing spot kicks from World Cups and European Championships between 1976 and 2012, researchers discovered that goalkeepers were falling prey to a form of “gambler’s fallacy”–an enduring psychological mistake involoving random events that seems to have plagued human thinking for time immemorial. Continue reading


What use is the binomial theorem?

Still remember the binomial theorem? It’s the formula for generating the coefficients of a “binomial”–a fancy word for any two-term piece of algebra e.g. (1 + x) or (a + b)–raised to any power you like. As it happens, the coefficients turn out to be the numbers in the appropriate row of Pascal’s triangle. For example if we square the following binomial . . .

(x + y)2 = x2 + 2xy + y2

. . . we get the coefficients 1 2 1.

Continue reading