Monte Carlo Fallacy

Here goes a popular mathematical joke: If you are fearful of the small risk of boarding the same plane as a bomb-crazy terrorist, make the odds even tinier by packing along a bomb in your luggage!

Known as the gambler’s fallacy or Monte Carlo fallacy, the most spectacular example of this type of flawed thinking took place in the eponymous casino in 1913, when the ball in a roulette wheel landed on black 26 times in a row, taking away millions from players believing that it was more likely to give red after each lengthy sequence of blacks. Like these players, many people tend to believe that after the same event has happened multiple times or after a single unlikely event has taken its course, the likelihoods of events of an opposite nature will rise as part of some compensatory mechanism of the universe. Yet, in reality, if each event occurs independently, such that an outcome does not alter the conditions under which the next event takes place, the probabilities of the events should remain constant, regardless of how unlikely the previous results are.

If there is any compensatory effect, it manifests by having abnormal outcomes or patterns of outcomes diluted with regular ones—rather than “balanced” by opposing outcomes—over large numbers of events to give the statistical averages we are familiar with. Hence, a streak of ten heads in a series of coin tosses will not necessarily be followed by a predominance of tails. Instead, as statistician David J Hand explains, the subsequent tosses still have 0.5 probabilities of heads and the most common numbers of heads per ten tosses are around five. After a long series of trials containing the more common outcomes, the initial streak of ten heads becomes insignificant in the overall results. Now, what does that say of She Was Pretty, which tries out a note of tension as it meanders to its finale by prognosticating that good times are apt to be succeeded by bad and vice versa?

Lest we are too quick to sneer at the writer’s apparent lack of statistical literacy—even as research has shown that high cognition actually predisposes one to the Monte Carlo fallacy—the interdependency of non-mechanical, real-life events outside of clean experimental setups is not always clear-cut. Human psychology is one particular factor that can turn originally independent events into dependent ones. An initial outcome may change the mindset of people such that, buoyed by the sweetness of success, they produce more excellent results or, demoralized by a setback, they continue delivering weak performances. Depending on individual personalities, the patterns may be reversed too: initial success lowers their guard, which results in subsequent poor performance, and initial failure ignites their competitive spirit, leading to eventual success. Both reversed cases would prove the drama correct, except that it would be the mind, not some unknown force of the universe, that upholds the patterns.

When events are truly independent, there is still a condition that can lead them to the same outcome: a rigged system. A wheel of fortune may be loaded so that it keeps stopping at one particular slot. A person, similarly, may bring the same set of skills and attitude to his endeavors. The challenge here is to keep the system stable. With a biased wheel of fortune, the extra weight attached to it may dislodge over time if the designer or owner is not careful. With humans, the uncertainty is greater since neither mind nor body is guaranteed to stay constant over the years. It would obviously be unwise to assume that winning streaks predominantly dependent on personal effort will last forever, which is why seizing opportunities is ever so important.

Choi Siwon as Kim Shin-hyuk (Caution: Spoiler below)

So powerful is the role of the mind while it lasts that it can harness benefits from the Monte Carlo fallacy, if we care to. Knowing that many people are susceptible to the fallacy, we can study such behavioral patterns in the activity concerned and strike against competitors just when they are falling into the trap. That is what neuroscientists are suggesting after discovering that although goalkeepers direct their defense to another side more than 70% of the time after experiencing three repeated ball directions in penalty shootouts, kickers do not make use of this tendency. However, they also note that awareness of the fallacy may have backfired by making goalkeepers believe that kickers will change direction by the fourth kick. Successful manipulation of the fallacy therefore depends on relative levels of strategic thinking and perceived cognitive statuses of opponents.

Mind games are part and parcel of mystery plots as well, and after reuniting its headlining childhood lovers way before the finale, She Was Pretty‘s real source of suspense lies in the secret identities of various side characters. Television serials, unfortunately, have to contend with huge armies of eagle-eyed viewers with the luxury to scrutinize and theorize about plot details over extensive periods of time before releases of official answers. The Internet age aggravates this with an abundance of public avenues for brainstorming and sharing of theories. No matter how intricate a mystery is, unless it lasts for only one episode, the answer is likely to be sifted out and spread far and out before the planned reveal.

Hence, with the exception of truly expert puzzle builders, rational screen writers wishing to preserve an element of surprise should be particularly incentivized to withhold all real clues until the last minute and, perhaps, plant (logically coherent) red herrings over the course of the series for viewers to discover. Such misleading clues are not necessarily manifestations of insincerity, but rather, illustrations of the deceptive power of reality. Alternatively, for dramas aired while scripting is still in process, the relevance of earlier clues can be made tentative, linking to answers only when hardly any spectator has successfully deciphered their logic. If, instead, the correct interpretations have spread virally, the scriptwriters can render the clues redundant and choose answers unassociated with these clues. However, upon observing these storytelling habits, rational viewers would stop examining clues and instead make speculations solely based on writing motives, relative conspicuousness of characters (for identity-related mysteries) and potential shock factors. To continue confusing viewers and sustain more interest in the plot itself, writers should then switch tactics from time to time, using concrete clues for one production and indefinite or fake ones for another. This is where the Monte Carlo fallacy and counter-tactics and counter-counter-tactics for it would take over.

On the flip side, screenwriting is perhaps part commercial enterprise and part self-expression. Like penalty kickers, production teams, which react to responses of audiences (the goalkeeper) separately, have also been disadvantaged by the difficulty of coordinating moves. Whether dramas have been or should be the kind of single-minded and harmonious automatons that would simplify a game theorist’s work is an open question. But that leaves a portion of the audience to play possibly one-sided Monte Carlo games on the basis of perceived incompetence.

The first leads: Hwang Jung-eum (left) as Kim Hye-jin and Park Seo-joon (right) as Ji Sung-joon

More than a few so-called “thrillers” have displayed actual clues in disappointingly obvious ways. So when a romantic comedy discloses early on the presence of an unidentified undercover chaebol heir among its characters and hints at its second male lead’s possession of wealth (secretly making a luxurious hotel suite his home, being chauffeured in an expensive car, unfamiliarity with street food, etc.) incommensurate with his rank-and-file position at a magazine office, it is easy to dismiss how serious its theme of giving supporting cast a chance in the limelight can be—especially for audience members overcompensating for the fallacy. Besides, a spiffy-looking colleague has been contrasted as an obvious red herring.

Only some way into the show is another secret character, a world-famous author named Ten, introduced. For this other mystery person, clues are carefully tied to the garishly dressed chief editor, who shamelessly ditches work to play shopaholic all day but reveals signs of wisdom at critical moments, making one wonder if her flaws are just an elaborate cover-up for some other side of her life. In a scene ostensibly about her disparaging the titular character’s looks, she is even briefly shown using a fountain pen which has appeared in Ten’s photograph—a hint spotted only by sharper netizens.

It goes without saying that the second male lead is eventually revealed to hold no other identity than Ten, a nom de plume he chose for its nonsensical quality but may be tied to the idol actor Choi Siwon’s nickname among fans in China: ten yuan (a phrase with Mandarin pronunciation similar to that of Chinese characters for “Siwon”). The chief editor’s pen was a gift from him. But apparently so convinced of Choi’s identity as the prized chaebol heir a fellow cast member was that he claimed to be shell-shocked when he found out from the script during the live shoot that his minor supporting character Kim Poong-ho, a disheveled man with itch issues and neglected by everyone in the office, was the true heir, who was to become the company vice-chairman. The stunned reactions of viewers were certainly genuine when a dressed-up Poong-ho walked up to the podium during the investiture, complete with a corsage on his backscratcher. Yet, if the drama had not contradicted its title and supporting-character-as-the-lead premise by giving the heroine a mid-show makeover, more viewers might have enough faith in the drama to look beyond the false clues. The plot’s victory appears satisfying, but the basis it was built on probably slightly less so.

Wonderfully, the mind may still let us have the last laugh by making the best of past experiences. As some good old piece of advice would go, turn failures into lessons where possible, and for other experiences, remember only what little beauty and joy they hold. When a positive side is identifiable from each past event, the distinction between positive and negative events on which statistical games build their foundations somewhat vanishes, lessening regrets. Notwithstanding its more debatable issues, She Was Pretty is, in its finest moments, a moving tale about first love, friendship and the invisible people among us.

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