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Book review: Winning the lottery is like being struck by lightning


A wise man once said, “never tell me the odds” but are you calculating your chances of successfully navigating an asteroid field (3,720:1), shouting “Shazam” and letting whether it works twice in a row (9 million: 1), or winning the state lottery (42 million: 1 in California), probability affects the outcome in our daily lives for events. equally large and small. But given their widespread role in our lives, your average person is usually pretty fine with accurately calculating them. As we see in the excerpt below from James C. Zimring’s latest headline, Part truth: How fractions distort our thinkingOur expectations about the likelihood of an event can vary, depending on how the question is asked and what part is focused on.

partially concealed truth

Columbia University Press

Taken from Part truth: How fractions distort our thinking by James C. Zimring, published by Columbia Business School Publishing. Copyright (c) 2022 James C. Zimring. Used under agreement with Publisher. Copyright Registered.


The Mistake That Seems Impossible: Underestimating Quantity

The more unlikely an event seems, the more attention it will hold when it happens and the more obligated we feel to explain why it happened. This just makes good sense. If the world doesn’t behave according to the rules we understand, we’ve probably misunderstood the rules. We should pay attention to the unlikely because new knowledge comes from our efforts to understand contradictions.

Sometimes what seems impossible can actually happen. A famous example of this is found with playing the lottery (i.e. the lottery fallacy). It is also understood that it is highly unlikely that a particular person will win the lottery. For example, the chance of a ticket winning the Powerball lottery (the specific lottery analyzed in this chapter) is 1/292,000,000. This explains why so many people pay attention to the winners. Where did they buy their tickets? Did they see a fortune teller before buying a ticket, or do they have a history of displaying psychic abilities? Do they perform any special rituals before buying tickets? It is a natural tendency to try to explain how such an unlikely event could have happened. If we can identify the reason, perhaps understanding that reason will also help us win the lottery.

The lottery fallacy is not limited to good things happening. Explanations are also sought to explain bad things. Some people are struck by lightning more than once, which seems too hard to accept as a random chance. There must be some explanation. Inevitably, it is speculated that the person may have some strange mutated trait that makes them attract electricity, or that they carry some metal on them or have titanium prostheses in their bodies. Perhaps they were cursed by a mystical force or God had abandoned them.

Lottery error can be understood as a form of confusing one probability with another, or to continue our topic from part 1, confusing one fraction with another. One can express the odds of winning the lottery as a fraction (1/292,000,000), where the numerator is the only combination of numbers that will win and the denominator is all possible combinations of numbers. The fallacy arises because we tend to only notice someone who has a ticket that has won the lottery. However, this is not the only person playing the lottery and it is not the only ticket. How many tickets were purchased for any given drawing? The exact number varies, because more tickets are sold as the jackpot gets higher; however, a typical drawing consisting of about 300 million tickets has been sold. Of course, some of the tickets sold must be duplicates, as there can only be 292 million possible combinations. Furthermore, if every possible combination was purchased, then someone would win in each draw. In fact, about 50 percent of the drawings have a winner; so we can infer that on average 146 million different combinations of numbers are purchased.

Of course, the news doesn’t give us a list of all the people who didn’t win. Can you imagine the same weekly headline, “299,999,999 again no lottery winners!” (names are listed online at www.thisweekslosers.com). No, the news only tells us that there is a winner, and sometimes who wins. When we ask ourselves, “What’s that person’s odds of winning?” we are asking the wrong question and referring to the wrong fraction. That particular person’s odds of winning are 1/292,000,000. By chance, that person will win the lottery once in the 2,807,692 years they play continuously (assuming two draws per week). What we should be asking is “What is the odds of any person winning?”

In probability, the chance of one thing or another happening is the sum of the individual probabilities. So, assuming there are no duplicate tickets, if there is only one person playing the lottery, the probability of someone winning is 1/292,000,000. If two people are playing, the odds of having one winner are 2/292,000,000. If 1,000 people are playing, the odds are 1,000 / 292,000,000. When we consider that 146 million different combinations of numbers are bought, the top part of the fraction (the numerator) will become extremely large and the odds that someone will win is quite high. When we marvel at the fact that someone has won the lottery, we mistake the real fraction (146,000,000 / 292,000,000) for the fraction (1 / 292,000,000) – meaning we are misjudging the numerator. What seems like an extremely unlikely event is actually possible. This tendency for people to make mistakes is related to inherent discoverability, as described in chapter 2. Only winners are “available” in our minds, and not all who did not win.

Similarly, the odds of being struck by lightning twice in a person’s lifetime is one in nine million. Since there are 7.9 billion people living on Earth, it’s likely that 833 people will be struck by lightning twice in their lifetime (at least). As with the lottery example, our attention is focused only on those who were struck by lightning. We can’t look at how many people are never attacked. Just as it is unlikely that any particular person will win the Powerball lottery, it is also highly unlikely that no one will win the lottery after a few spins, just given the number of players. Likewise, it is very unlikely that someone will be struck by lightning twice, but much less likely, given the number of people in the world.

So when we explain great things like someone wins the lottery or gets struck by lightning twice, we’re really trying to explain why a highly probable thing happens, this really no need to explain anything. The rules of the world are working exactly as we understand them, but we are mistaking high probability for virtually impossible.

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