description

The Gambler's Fallacy is the belief that departures from the average will be corrected. For example, that if I have flipped heads ten times in a row, that tails is much more likely to turn up this time, because it's overdue.

This is something of a mathematical blind spot in the human mind: if I have flipped a coin to get fifty heads in a row, there is a 50% chance that I will flip heads again.

I have personally observed people in casinos whose strategy is to watch other people on slot machines, and if they see somebody leave a machine that hasn't paid out in ages, they jump onto it before anybody else does. I'm pretty certain this is their reasoning: it's due.

Another name for this fallacy is the regression to the mean fallacy. Regression to the mean is a legitemate mathematical concept, but it relates to having an individual outlier, rather than unlikely patterns.

Paradoxically, I have also watched people operate with exactly the opposite philosophy: they believe that some numbers get 'hot'. They pick the same lottery numbers, because they've won for them in the past.

examples

Bill is playing against Doug in a WWII tank battle game. Doug has had a great "streak of luck" and has been killing Bill's tanks left and right with good die rolls. Bill, who has a few tanks left, decides to risk all in a desperate attack on Doug. He is a bit worried that Doug might wipe him out, but he thinks that since DougÕs luck at rolling has been great Doug must be due for some bad dice rolls. Bill launches his attack and Doug butchers his forces.

T,F,T,T,? - Everybody guesses F for the 5th question if they don't know the answer, because they believe the Fs should even out as much as possible.