The Gambler's Fallacy is committed when a person assumes that a departure from what occurs on average or in the long term will be corrected in the short term. The form of the fallacy is as follows:
X has happened.
X departs from what is expected to occur on average or over the long term.
Therefore, X will come to an end soon.
There are two common ways this fallacy is committed. In both cases a person is assuming that some result must be "due" simply because what has previously happened departs from what would be expected on average or over the long term.
The first involves events whose probabilities of occurring are independent of one another. For example, one toss of a fair (two sides, non-loaded) coin does not affect the next toss of the coin. So, each time the coin is tossed there is (ideally) a 50% chance of it landing heads and a 50% chance of it landing tails. Suppose that a person tosses a coin 6 times and gets a head each time. If he concludes that the next toss will be tails because tails "is due", then he will have committed the Gambler's Fallacy. This is because the results of previous tosses have no bearing on the outcome of the 7th toss. It has a 50% chance of being heads and a 50% chance of being tails, just like any other toss.
The second involves cases whose probabilities of occurring are not independent of one another. For example, suppose that a boxer has won 50% of his fights over the past two years. Suppose that after several fights he has won 50% of his matches this year, that he his lost his last six fights and he has six left. If a person believed that he would win his next six fights because he has used up his losses and is "due" for a victory, then he would have committed the Gambler's Fallacy. After all, the person would be ignoring the fact that the results of one match can influence the results of the next one. For example, the boxer might have been injured in one match which would lower his chances of winning his last six fights.
It should be noted that not all predictions about what is likely to occur are
fallacious. If a person has good evidence for his predictions, then they will be
reasonable to accept. For example, if a person tosses a fair coin and gets nine
heads in a row it would be reasonable for him to conclude that he will probably
not get another nine in a row again. This reasoning would not be fallacious as
long as he believed his conclusion because of an understanding of the laws of
probability. In this case, if he concluded that he would not get another nine
heads in a row because the odds of getting nine heads in a row are lower than
getting fewer than nine heads in a row, then his reasoning would be good and his
conclusion would be justified. Hence, determining whether or not the Gambler's
Fallacy is being committed often requires some basic understanding of the laws
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 Doug's luck at rolling has been great Doug must be due for some bad dice rolls. Bill launches his attack and Doug butchers his forces.Jane and Bill are talking:
"The roulette ball has landed on odd numbers eight times in a row. Therefore, it's more likely to land on an even number next time."