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53 fever!

One thing statisticians love is a story about people acting foolish around probability . . .

Paul Alper points us to this news article by David Robson:

Fifteen years ago, the people of Italy experienced a strange kind of mass hysteria known as “53 fever”.

The madness centred on the country’s lottery. Players can choose between 11 different wheels, based in cities such as Bari, Naples or Venice. Once you have picked which wheels to play, you can then bet on a selection of numbers between 1 and 90. Your winnings depend on how much you initially bet, how many numbers you picked and how many you got right.

Sometime in 2003, however, the number 53 simply stopped coming up on the Venice wheel – leading punters to place increasingly big bets on the number in the certainty that it must soon make a reappearance.

By early 2005, 53 fever had apparently led thousands to their financial ruin, the pain of which resulted in a spate of suicides. The hysteria only died away when it finally came up in the 9 February draw, after 182 no-shows and four billion euros worth of bets.

While it may have appeared like a kind of madness, the victims had been led astray by a reasoning flaw called the “gambler’s fallacy” – a worryingly common error that can derail many of our professional decisions, from a goalkeeper’s responses to penalty shootouts in football to stock market investments and even judicial rulings on new asylum cases. . . .

Surprisingly, education and intelligence do not protect us against the bias. Indeed, one study by Chinese and American researchers found that people with higher IQs are actually more susceptible to the gambler’s fallacy than people who score less well on standardised tests. It could be that the more intelligent people overthink the patterns and believe that they are smart enough to predict what comes next. . . .

One team of researchers recently analysed US judges’ decisions on whether or not to grant asylum to refugees. Logically speaking, the ordering of the cases should not matter. But in line with the gambler’s fallacy, the team found that the judges were up to 5.5% less likely to grant a case if they had granted the two previous cases – a serious decline from the average acceptance rate of 29%. Consciously or not, they seemed to think that the chances of having the same judgement three times in a row was just too small, and so they were more inclined to break the streak.

The researchers next analysed bank staff considering loan applications. Once again, the order of the applications made a difference: the loan officers were up to 8% more likely to reject an application after they had already accepted two or more in a row – and vice versa.

As a final test, the team analysed umpires’ decisions in Major League Baseball games. In this case, the umpires were about 1.5% less likely to call a pitch a strike if the previous pitch was also called a strike – a small but significant bias that could make all the difference in a game. Kelly Shue, one the co-authors of the study, says that she was initially surprised at the results. “Because these are professionals and they’re making decisions as part of their primary occupation,” she says. But they were still vulnerable to the bias. . . .

23 Comments

  1. Oliver C. Schultheiss says:

    “Surprisingly, education and intelligence do not protect us against the bias. Indeed, one study by Chinese and American researchers found that people with higher IQs are actually more susceptible to the gambler’s fallacy than people who score less well on standardised tests. It could be that the more intelligent people overthink the patterns and believe that they are smart enough to predict what comes next. . . .”

    Funny that David Robson mentions this and you bring it up on your blog today. Because just this morning I came across this interesting bit of information in Ocklenburg & Güntürkün’s excellent textbook on “The lateralized brain” (p. 72):

    “Experimental evidence supporting the idea of the left hemisphere as “interpreter” comes from a probability guessing experiment in split-brain patients. At the beginning of each trial, a row of arrows was presented, pointing either to the left or to the right side thereby signaling in which visual field a stimulus would occur. Two stimuli could appear: Either a green square towards the top of the screen or a red square towards the bottom of the screen. The patients had to press a button to indicate which stimulus would appear.
    After their guess, one of the two stimuli was presented. For the right visual half field, the top stimulus had a probability of 80% and the bottom stimulus a probability of 20%. For the left visual half field, the top stimulus had a probability of 70% and the bottom stimulus had a probability of 30%. The sequences of stimuli in the left and right visual fields were
    randomly generated and independent of each other.

    “There are two possible strategies to react in this experiment:
    • Frequency matching: The subject chooses the two alternatives with their respective probabilities, e.g., pressing the button for the top stimulus in 80% of the trials and the button for the bottom stimulus in 20% of the trials. This is not an optimal strategy in
    this task, leading to 68% correct guesses for the right visual field (0.8 3 0.8 1 0.2 3 0.2).
    • Maximizing: The subject always chooses the more frequent alternative, e.g., pressing the button for the top stimulus in 100% of the trials, no matter which stimulus was presented in the trial before. This is the optimal strategy in the paradigm, leading to
    80% correct guesses for the right visual field (0.8 3 1.0 1 0.2 3 0).

    “In line with the idea of the left hemisphere being an “interpreter,” the split-brain patients used a frequency matching strategy on right visual half field trials, but a maximizing strategy on left visual half field trials. This indicates that the left hemisphere seems to try to generate rules in a random series of events, while the right hemisphere sticks to a less complex (and more efficient) outcome-oriented strategy. Thus, the left hemisphere can be inferior to the right one in guessing random events. Interestingly, pigeons also choose the maximizing strategy when tested in this paradigm, thus performing better than the left hemisphere in humans.”

    Our left hemisphere frequently thinks we’re so clever, when it’s really not.

    • Kaiser says:

      Assuming that those are exact quotes from the book. I’m always impressed by how certain some researchers are of their results. Apparently there was 100% perfect matching between side of brain and those two strategies. Besides, how do they know a particular strategy was used and adhered to religiously throughout the experiment?

      • Oliver C. Schultheiss says:

        Hi Kaiser,

        if you would like to look up the details of this research, the paper Ocklenburg & Güntürkün refer to is:

        Wolford, G., Miller, M. B., & Gazzaniga, M. (2000). The left hemisphere’s role in hypothesis formation. Journal of Neuroscience, 20(6), RC64-RC64.

        and can be donwloaded here:

        https://www.jneurosci.org/content/jneuro/20/6/RC64.full.pdf

        The authors close the paper with this conclusion:

        “Although this tendency to search for causal relationships has potential benefits, it can lead to nonoptimal behavior when there is no simple causal relationship. Some of the common errors in decision making are consistent with the notion that we are prone to search for and posit causal relationships even when the evidence is insufficient or even random. We find that the search for causal explanations appears to be a left hemisphere activity, consistent with previous research on the interpreter.”

    • JM says:

      “In line with the idea of the left hemisphere being an “interpreter,” the split-brain patients used a frequency matching strategy on right visual half field trials, but a maximizing strategy on left visual half field trials. This indicates that the left hemisphere seems to try to generate rules in a random series of events, while the right hemisphere sticks to a less complex (and more efficient) outcome-oriented strategy. Thus, the left hemisphere can be inferior to the right one in guessing random events. Interestingly, pigeons also choose the maximizing strategy when tested in this paradigm, thus performing better than the left hemisphere in humans.”

      This quote perfectly (and maybe accidentally?) points out something that I think gets missed a lot in these discussions, which is the tradeoff between explore and exploit.

      When you are in exploit mode, you take whatever action you believe gives you the highest probability of reward (i.e., you act like a pigeon). Meanwhile in explore mode you want to take as many different actions as possible so that you can learn about the environment and maybe discover if there is some action you haven’t tried yet that would give you a big reward. You can’t do both of these things, so you need to find some way to balance them.

      Sure it would be fine to exploit 100% of the time in this contrived experiment, but we live in a much more complicated world and one of those complications is that it is always changing. Given that fact, taking apparently ‘sub-optimal’ decisions that might described as ‘whatever I’ve been doing, do the opposite’ looks a lot more like a feature than a bug. It also seems possible that these biases can only be considered mistakes when you are doing something TRULY random (gambling on the lottery), which is not the case for the other examples (judging refugee asylum, balls and strikes) where they could serve as a totally reasonable calibrating heuristic.

  2. jonathan says:

    My problem with these examples is, for example, that while 53 may have encouraged some more betting, it mostly displaced bets, meaning it shifted 1 losing bet to another. They wanted to bet. They would lose anyway.

    The issue with judgements is there is no clear line, so they’re not just managing yes versus no but overall systemic expectations that some will be yes and some no. In a well run system, you’d expect them to estimate how many yes and no, and then they’d tend to manage to that. But if the idea is that somehow the decisions are better, that misses the point that they could likely also say no to more without changing their standards.

    And calling strikes, assuming they see the pitches correctly, is also a management of expectations, as in give the pitcher this call but that call the other way for almost the same pitch signals ‘dont expect that to always be a strike because that is a grey area call’.

    A favorite example is the catch rule in football. They tinker with it all the time. I cant believe they’re ignorant of the fact that each tinkering shifts the edge cases to make a new or slightly new grey area where call will vary.

    The expectation you can impose certainty is absurd. And the expectation that grey areas arent managed at a higher level is also absurd. If you dont have a generalized handle on what you expect in a grey area, you would not deserve to be a judge or an umpire.

    • somebody says:

      > My problem with these examples is, for example, that while 53 may have encouraged some more betting, it mostly displaced bets, meaning it shifted 1 losing bet to another. They wanted to bet. They would lose anyway.

      I guess the argument is that long chains of events like this leads people to believe they have real information on when they’re “due” to break, and that confidence leads people to make bets they otherwise wouldn’t.

      • jonathan says:

        Yes, obviously. But so what? If people are going to lose money betting, they’ll lose money betting, and the only impacts are which numbers they lose on, which doesnt matter because losing is not winning, and the extent to which the excitement draws additional play. And that’s the same as a big jackpot drawing in casual players, so the role of 53 or some other idiotic betting notion is close to noise. There will always be such momentary exciting things and they mostly displace losing.

        And in things like catch rules or strikes, the existence of the line influences behavior, so it becomes irrational to expect that a behavior which approaches the limit line will be consistently judged.

        • somebody says:

          > If people are going to lose money betting, they’ll lose money betting, and the only impacts are which numbers they lose on, which doesnt matter because losing is not winning

          The point is that people who otherwise wouldn’t have gambled at all made bets due to spurious information. The total amount spent and lost on these bets increased as the chain lengthened; that’s not “displaced losses”, it’s new losses that wouldn’t have happened without the chain. It’s stated explicitly in the anecdotes — the total size of bets increased and then fell off when 53 finally appeared. It’s an interesting little anecdote about how people implicitly assume draws without replacement as opposed to true independence. Understanding this can help make me a better communicator or teacher. Of course, in the long run, this was a temporary trend, gambling behavior went back to normal, and this story doesn’t matter. But in the long run, what does?

          • jim says:

            “The point is that people who otherwise wouldn’t have gambled at all made bets due to spurious information. “

            Well to be perfectly honest I think most of this story is Bologna.

            How do you bet exclusively on 53 in a lottery where you have to pick multiple numbers? 53 53 53 53 53 53? That little technicality seems to have been overlooked. Also even if people were betting on a single number, it’s hard to imagine anyone with half a brain that can’t recognize that, even if 53 had been absent since 1900, it’s chances of turning up on any one spin on a wheel with 90 numbers are slim. How many people would bet a suicidal amount on such an event? You’d have to have a pretty hard core gambling addiction to make such a stupid bet. Sure, some people have that. But 53 has nothing to do with that. So I think this statement:

            “53 fever had apparently led thousands to their financial ruin, the pain of which resulted in a spate of suicides. “

            is 100% false. It’s like the Indian farmers committing suicide over GMOs. It seems more likely to reflect the aspirations of the anti-gambling proselytizers than something that happened in real life: wouldn’t it be better if (bad) gamblers were punished by fate?

            So, hey, if this is real, I’ll stand corrected. I can accept that there is a kernel of truth there. But it’s woefully short on details and refers to – apparently – mythological events.

            • somebody says:

              > How do you bet exclusively on 53 in a lottery where you have to pick multiple numbers? 53 53 53 53 53 53? That little technicality seems to have been overlooked.

              I don’t understand this objection. You don’t have to match all the numbers for a payout, there are multiple kinds of bets you can make including matching a single number, and you can make multiple bets on a single ticket as well.

              > So I think this statement:

              > “53 fever had apparently led thousands to their financial ruin, the pain of which resulted in a spate of suicides. “

              > is 100% false.

              https://www.irishtimes.com/news/what-s-in-a-number-if-it-s-53-murder-suicide-and-ruin-1.409405

              On the subject of some lady who committed suicide over gambling debts

              > Lotto receipts showed that Maria, like Franco Grassi, had gambled (and lost) consistently on 53. Gambling fever has had a less tragic but still potentially devastating effect on many other Italian families.

              https://www.repubblica.it/2005/a/sezioni/cronaca/lotto/ritardancora/ritardancora.html

              From google translate, it appears that all the previous betting/earning records were also set by long chains of a single number not appearing:

              > The number has not been drawn since May 10, 2003 and has also become one of the most played in the Lotto. According to Agicos (Competitions and Betting News Agency), in fact, the 53rd on Venice has beaten all revenue records in the country: approximately 4.2 billion euros have so far been spent by Italians in the hunt for Venetian latecomers.

              > On the other hand, one of the highest Lotto winnings ever dates back to last June, when – recalls Agicos – over 810 million euros were won thanks to the return (after 133 draws) of the 8 against Palermo. The record of the biggest winnings, however, is the number 31 on Bari, released after an absence lasting 167 rounds. On the 31st of Bari in April 2000, he brought over 900 million euros into the pockets of the Italians.

              It sure does seem like streaks have an effect on total volume of bets.

              > it’s hard to imagine anyone with half a brain that can’t recognize that, even if 53 had been absent since 1900, it’s chances of turning up on any one spin on a wheel with 90 numbers are slim. How many people would bet a suicidal amount on such an event? You’d have to have a pretty hard core gambling addiction to make such a stupid bet.

              I’m generally pretty skeptical of claims of fundamental “irrationalities” discovered by paternalistic behavioral economist types, but I do think one can design systems in which instincts fail systematically, and that lotteries are one of the oldest examples. It isn’t that anyone “bets a suicidal amount on such an event”. It’s that people notice what appears to be a trend, get excited, bet a little bit, they lose, which just makes them a little more certain that the trend has to end the next time, and eventually they’ve already sunk in so much that their only hope of recovering their money is to keep betting. That’s how a gambling addiction works, it’s not the excitement of gambling larger amounts, it’s the need to recover what they’ve already lost.

              It’s not about being an idiot. d’Alembert, of wave equation fame, argued against Bernoulli that the probability of heads increases the more times tails comes up successively, and devised a “betting system” or increasing bets on losses and decreasing them on wins.

              • jim says:

                Somebody:

                I don’t doubt that many people bet on 53. And I’m aware that there are “many ways to win”. But doesn’t the fact that there are multiple numbers in each draw decrease the value of hitting any individual number? I suspect there’s a reason most lotteries aren’t a draw of a single number: it would make winning too common. So it’s not just a bet on 53 and most people surely know that.

                “On the subject of some lady who committed suicide over gambling debts”

                I have no problem believing some people commit suicide over gambling losses. But the article claims a “spate” of suicides and that “thousands” were led to their financial ruin. This I seriously doubt.

                “It’s not about being an idiot. d’Alembert…devised a “betting system” or increasing bets on losses and decreasing them on wins. “

                I wonder if d’Alembert bet his fortune on that…

                My point is that in real life people are aware that no coin flip or number draw has 100% certainty, and they’re also aware that the uncertainty of a number draw is proportional to the number of possible draws. The bets they place are proportional to what they can afford based on that knowledge, with the rare exception of gambling-addicted people.

                “people notice what appears to be a trend, get excited, bet a little bit…”

                I’m sure that’s true for a *very* small number of people. Not enough to lead “thousands” to financial ruin much less death.

              • somebody says:

                > I don’t doubt that many people bet on 53. And I’m aware that there are “many ways to win”. But doesn’t the fact that there are multiple numbers in each draw decrease the value of hitting any individual number? I suspect there’s a reason most lotteries aren’t a draw of a single number: it would make winning too common. So it’s not just a bet on 53 and most people surely know that.

                I still don’t understand the relevance. Sure, hitting 53 is less valuable than hitting all 5 of the numbers. What does that have to do with anything? You still get a payout as long as 53 comes out once, so people who think 53 is very likely to come out will bet on it, leading to a larger total amount of money bet on tickets including 53?

                > I have no problem believing some people commit suicide over gambling losses. But the article claims a “spate” of suicides and that “thousands” were led to their financial ruin. This I seriously doubt.

                I can’t speak for the general financial ruin, but the spate of suicides tied to repeated bets on 53 is undeniable. The fact was not that “some people commit suicide over gambling losses”, it was that a number of suicides were specifically tied to increasingly large bets on the number 53 by their lottery receipts. I’m not sure why you want to doubt it so hard, but the suicides are true.

  3. jim says:

    Uh, I don’t get it. Is this The Fallacy of the 53 Fallacy Fallacy?

    Seems to me the mistake of the bettors isn’t that they’re betting on 53. 53 will come up again and in any case the worst case scenario is that it has the same odds as any number on the wheel, so there’s no less reason to bet on 53 than on 42, 7, 21, or 89.

    The mistake the bettors are making is “betting increasingly large amounts”. After all there still 89 other numbers on the wheel and even after a year or two sans 53, whether you think the overall odds of 53 showing up are increasing or not, you have to acknowledge that on any given spin the odds are still pretty low. And with any probability game, there’s no sure bet, so it’s pretty stupid to bet the farm on any give spin or flip, even if there have been 99 heads in a row.

    So for my money what we have is a fallacy wrapped in a fallacy wrapped in a fallacy. The 53 fallacy is a fallacy, because the frequency of 53s probably *will* revert to the mean but in any case that doesn’t even matter because the odds of 53 are surely no worse than any other number. The real fallacy is misunderstanding the short term odds of 53, whether or not the long term odds are increasing; and in figuring out *how much* to bet against the always present chance of losing.

  4. Navigator says:

    Would the ’53’ problem actually be a confusion b/w ‘gambler’s fallacy’ and regression to the mean (independence vs. dependence)?
    Thanks

  5. Michael Weissman says:

    I hate to defend umpires, but sometimes a home plate ump seems to be making a deliberate choice to compensate for a previous bad call, not necessarily falling for the fallacy.

    • John N-G says:

      My hypothesis is related to this: a conscious or unconscious effort to be fair to both parties when many cases fall into an indeterminate subjective gray area. The umpire wants to be fair to the pitchers and the batters, the banker wants to be fair to the applicants and the banks, the judges want to be fair to the asylum seekers and the government. For all three adjudicators, impartiality in both appearance and practice is absolutely essential. For them to have self-confidence in their impartiality, they must judge ambiguous cases evenly, and wish to avoid drifting subjectively in one direction or the other.

      In other words, human nature seems to be a better explanation of those three experiments than abstract subconscious erroneous probabilistic reasoning.

  6. Z says:

    “the team found that the judges were up to 5.5% less likely to grant a case if they had granted the two previous cases”

    Is this a case of the hot hand fallacy fallacy? If judges hear N cases a day in which X of the N should be granted, then conditional on just having used up 2 of your X in a row the proportion of grantable cases remaining may on average go down from X/N. In which case the 5% drop might be expected. I’ll have to do some simulations if I have time…

  7. Jake says:

    For the umpire example, shouldn’t there be some kind of conditioning on whether the pitch was intended to be in the strike zone?

    (Haven’t read the paper, maybe they address that)

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