The Gambler's Fallacy

You're at a Roulette table, and no matter what you do you can't seem to catch a break; Lady Luck has left the building. But there is something you've noticed: for the last 8 turns in a row the ball has come to rest on black. Now you have an edge on luck, you think, feeling an almost scientific certainty that the chances of the next throw landing on red are very high. I mean, what are the chances of landing on black 9 times in a row? You put all your money on red....

You've been had by the gambler's fallacy - the mistaken idea that because the same thing has happened for an unlikely number of turns, it must be very likely that the next turn will produce something different.

But this isn't the case. On turn #9 the odds of landing on black are still 50/50. Sure, the chances of 9 black throws in a row are pretty low, but on each individual throw the odds are the same. There is no administrator of luck who notices that for the last 8 times the ball has come to rest on black so now it must land on red.

And then there is the inverse gambler's fallacy. This is a different view of the same thing.If you walked in on someone rolling dice and saw that the last throw was three 6's, you might assume that there must have been more throws before you came in, because the chances of rolling three 6's on the first toss are slim. But this is wrong - every combination of numbers is equally likely on each throw.

I doubt that these are the only two fallacies gamblers commit. The reasoning of a gambler is not intended to lead to the cold hard truth, but to whatever truth is most encouraging. Luck is not seen as spontaneous chance but as something born out of mythology; something with a will; something that attaches to some people and abandons others. But, while somebody might see chance 'favour' them for a stretch, nobody is lucky by their nature, no matter how tempting it is to think in those terms.