Imagine you are in a casino at a roulette table waiting to gamble. You have been following the game for a while and you’ve noticed that the last six outcomes were black. Well, it is quite remarkable, isn’t it? The probability to get six outcomes of the same color at the roulette is 1/64, approximately 1,6%. The chance to get seven consecutive blacks is the half, 1/128 or better 0,8%. Figures never lie! You must be very unlucky to obtain seven black shots. Therefore you put all your paycheck on red. But… wait a second. Is that right?
Obviously not! What you are missing is something fundamental which is the fact that consecutive outcomes at the roulette table are independent events which means that knowing the outcome of one provides no useful information about the outcome of the other. This involves that the probability to get seven consecutive blacks is truly 1/128 but the probability to obtain a seventh black after the first six ones is no more that 1/2, as there is nothing preventing the ball to stop either on a red or a black spot.
That’s the gambler’s fallacy. That’s it! Cool, isn’t it?Francesco Pochetti