Informal Fallacy: Gamblers Fallacy

This fallacy is committed when we believe that our fortune is soon to change because it follows that bad luck should eventually bring good fortune because over a long period of time things eventually even out.

When a person assumes that a departure will occur from what has previously happened for the sole reason that the law of averages demands it.

X happened

X departs from what is expected to occur on average or over the long term

Therefore, X will come to an end soon

One toss of a coin does not affect the next toss. I may get 7 heads in a row but that does not mean that the next coin toss will bring a tails because of the previous results being heads. There is still a 50-50 change that it will either be heads or tails. To assume that a tails is due because of the previous tosses being heads is to commit the Gamblers fallacy. The results of the previous tosses have no bearing on the next toss.

If a boxer has won 50% of his fights in the last 3 years and has lost the last 7 fights and has 7 fights remaining, we would be wrong to get the idea that he would automatically win the next 7 because he is due for some wins.

Not all predictions are fallacious. If a person has good evidence for his predictions, then they will be reasonable to accept. If someone tosses 9 heads in a row it would be reasonable to conclude that he will not toss another 9 in a row. This is not fallacious because there is an understanding of the laws of probability; 9 successive tosses is unlikely again, not impossible but we can estimate the probability as low. If he concluded that he would not get another 9 in a row because the odds of getting 9 in a row are lower than getting fewer than 9, then his reasoning would be sound. To discern when this fallacy occurs and when it does not comes down to understanding the laws of chance.

Example:

Ben and David are talking:

Ben: “You see that cat over there? It has lost the last 10 races. I will bet that he wins today.

David: “Why? He probably will lose.”

Ben:  “Nah, it’s in the bag. He has won 50% of his races in the last 3 years. This year, he has lost his first 3 races and he has three left. That means he will win the next three. So count it as money in the bank.”

David: “C’mon, are you sure?”

Ben: “Sure, man! He’s due!”

David: “He’s a cat, man?!”

Norman and Demeter are playing Axis and Allies:

Norman has been wiping out Demeter’s airplanes like cake. The die rolls have been good for Norman. Demeter decides that he will risk his remaining planes in one final assault. He thinks that Norman’s luck has to change after all these good rolls. Demeter’s planes are destroyed.

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