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Gambler’s Fallacy

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The Gambler’s Fallacy is committed it is concluded 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:

Premise 1: X happened.

Premise 2: X departs from what is expected to occur on average or over the long term.

Conclusion: Therefore, X will end soon.

There are two common ways this fallacy is committed. In both cases it is inferred that a result must be “due” because what has previously happened departs from what would be expected on average or over the long term.

The first version involves events whose probabilities are independent of one another. For example, one toss of a coin does not affect the next toss. So, each time the coin is tossed there is a 50% chance of heads and a 50% chance tails. Imagine someone tosses a coin 6 times and gets a head each time. If  they concludes that the next toss will be tails because tails “is due”, then they will have committed this 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 version 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 they have won 50% of their matches this year, that they have lost their last six fights and they have six remaining. If a person believed that the boxer would win the next six fights because they have “used up” their losses and are “due” for a victory, then this would be a fallacy. After all, the person would be ignoring the fact that the results of one match can influence the results of the next. For example, the boxer might have been injured in one match which would lower their chances of winning the last six fights.

Not all predictions about what is likely to occur are fallacious. If a person has good evidence for a prediction, then they will be reasonable to accept. For example, if a person tosses a normal coin and gets nine heads in a row it would be reasonable for them to conclude that they will probably not get another nine in a row again. This reasoning would not be fallacious if the conclusion is based on an understanding of the laws of probability. In this case, if it were concluded that they 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 this reasoning would be good, and this conclusion would be justified. Hence, determining whether the Gambler’s Fallacy is being committed can requires some basic understanding of the laws of probability.

The Gambler’s Fallacy is commonly self-inflicted and can lead people to make poor decisions. It can also be inflicted on others, to encourage them to make bad decisions. For example, a person who has been losing at a casino might be encouraged by others that they “are due” to win a hand and they could also convince themselves of this unsupported claim.

Defense: Because of its psychological power, this fallacy can be difficulty to defend against. Logically, the defense against it is having a grasp of basic probability and knowing when the outcome of a previous event can impact the next event and when it cannot. The obvious problem with this is that it is math defense going up against what can often be a strong feeling.

Example #1:

Bill is playing against Doug in a tabletop WWII tank battle game. Doug has had a great “streak of luck” and has been killing Bill’s tanks left and right with good 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 has been so good, Doug must be due for some bad dice rolls. Bill launches his attack and is shocked when Doug wipes him out.

Example #2:

Jane and Bill are talking:

Jane: “I’ll be able to buy that car I always wanted soon.”

Bill: “Why, did you get a raise?”

Jane: “No. But you know how I’ve been playing the lottery all these years?”

Bill: “Yes, you buy a ticket for every drawing, without fail.”

Jane: “And I’ve lost every time.”

Bill: “So why do you think you will win this time?”

Jane: “Well, after all those losses I’m due for a win.”

Example #3:

Joe and Sam are at the racetrack betting on horses.

Joe: “You see that horse over there? He lost his last four races. I’m going to bet on him.”

Sam: ‘Why? I think he will probably lose.”

Joe: “No way, Sam. I looked up the horse’s stats and he has won half his races in the past two years. Since he has lost three of his last four races, he’ll have to win this race. So, I’m betting the farm on him.”

Sam: “Are you sure?”

Joe: “Of course, I’m sure. That pony is due, man…he’s due!”

Originally appeared on A Philosopher’s Blog Read More

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