The fallacy that became itself a fallacy
Even specialists can fall prey to cognitive errors
I have been tossing a fair coin, and it has come up heads six times in a row. The chance of either heads or tails is 1 in 2, but for this to happen six consecutive times is 1 in 2 to the power 6, or 1 in 64. What is the probability that the next toss will turn up a seventh consecutive head?
The correct answer is of course 1 in 2. Coins don’t have a memory. What happened before cannot influence the current result. We all know that — yet our intuition sometimes leads us to believe differently.
On 18 August 1913, the ball at one of the roulette tables in the Monte Carlo casino had been ending up in a black slot for nearly 20 times in a row. Several gamblers started taking an interest and started putting money on red: after such a long streak of black, red was surely due to come up. And still the ball kept falling on black. People put more and more money on red at each successive turn of the wheel — and kept on losing it, as black kept on coming up. Let’s face it, where would you put your money if you happened to be there, having seen black come up 25 times in a row? Eventually, after an unbroken series of 26 blacks (likelihood: 1 in more than 136 million) the ball finally landed on red.
