Game theory and life in Squid Game

3rd October, 2021

If you haven't watched Squid Game yet, stop socializing or hustling your life away and park yourself in front of a screen for nine hours. Especially watch the show before reading this blog post: you'll have to in order to live with the spoilers and also evaluate what you would do if you were in the show.

The premise of Squid Game is that 456 players have been gathered on a remote island to play six games. Only one player will walk away with the prize money of 45.6 billion South Korean won (USD$39 million). The catch—as the players discover after the first game— is that the prize money accumulates with each player's death.

For each player who is "eliminated", 100 million won ($85,000) are added to the victor's pool.

Although Squid Game has been lauded for its scathing critique of capitalism through its extreme presentation of how far we would go for money — is it really extreme, the idea that every other person's death not only adds to but is necessary for the winner? There are other interesting questions it also presents and answers about human life: How much of it is chance versus under our control? What are the rules that govern our existence? Are they fair and equitable? Is "success" a zero-sum game? If yes, how should you play to win? And what does that say about human nature and society?

Fundamentally, Squid Game keeps asking its players to make life-or-death decisions with limited information. And game theory is about modelling our decision-making under uncertainty. Using some of its ideas and concepts, we can analyze whether the characters' actions make sense, what we would do in the same situation, and what that says about us.

Should you play Squid Game?

The first piece of missing information the players have to contend with is that the games are life-or-death situations (!). All 456 individuals have been lured onto the island with the promise of large sums of money in exchange for playing some games. The players are all indebted in the outside world, with millions of wons of loans to pay off and disappointed families to deal with. They are already the most likely to do anything to survive. Now here was this "game", miraculously offering them a chance to overcome their miserable lives.

Game #1 is "Red Light, Green Light", based on a popular children's pastime. You can only move under a certain condition; any movement outside of it results in immediate death. After innocuously entering what must have felt like a once-in-a-lifetime opportunity, 255 people die in five minutes—mostly for fleeing in panic, even after being told that slight movements would kill them, and otherwise for their slight movements despite grasping the rules.

Once the game ends, there is outrage among the 201 survivors. But when 25.5 billion won—an amount equivalent to the number of dead players—starts to fill a huge pig-shaped glass bowl above their heads, the survivors finally realize what they have signed up for.

This is the first point in the show where one can calculate whether it makes sense to continue playing, albeit with some assumptions. The facts I'd know now are: Squid Game is a zero-sum game. For me to win 45.6 billion won, I have to be okay with the death of 455 other human beings. Perhaps I will even be the cause of their death, directly or indirectly.

And what is the probability that I will get the expected payoff of 45.6 billion won? If P(Gx) is the probability that I will win Game #X, the probability that I will survive the rest of Squid Game is:

But at this point, with no information on what the rest of the games are, I cannot calculate my chances of winning any single game nor all of them. Knowing, however, that there are 201 players left and only one winner, the probability that I will be her is 0.005 or 0.5% (=1/201).

I now know that I have a 99.5% chance of dying in 5 days, and a 0.5% chance of winning 45.6 billion won (up from 0.2% when there were 456 of us). How good are these numbers? Are they better than my chances in the real world? I would likely not have known the answer to this if I was on the show, but I'm not, so let's look at some figures.

As of 2019, there were 354,000 people who had more than one billion South Korean won. In a population of 52 million that equals a 0.6% chance. But my chances of being worth 45.6 billion would be significantly lesser than that (especially as a South Korean woman, not because I'm less capable or deserving but because, like everywhere else in the world, I would have more institutional barriers to overcome).

Given this, 0.5% is pretty equal to or better odds than normal life. Another method of comparing the game to the outside world is checking how much a human life is worth in both. In the game, every player's life (or death) is valued at 100 million won.

In reality, the value of a human life is a calculation that policymakers and scientists have long grappled with. Although moral and social justice is founded on the idea that all lives are equal, to assume the infinite worth of each life would not help governments decide how much to spend on what. In the 1980s in the United States, the value of a stastical life (VSL) was calculated based on the medical costs of preventing one's death and the loss of earnings that would come from it; this was $300,000 per life, on average. This figure did not justify the $2.6 billion spend that came with labels that warned people about hazardous chemicals—until economists changed VSL to mean the amount people would spend on small reductions to the risk of death. They analyzed that employers in blue-collar industries paid each worker $300-400 more for a one-in-10,000 chance of dying on the job, implying a $3 million spend to hire 10,000 such workers. That calculation of VSL is why we now have labels warning us of hazardous chemicals.

This VSL figure has now appreciated to $10 million, and it also varies by country—but not by age or race within countries, in keeping with the premise that we should all be worth the same. Squid Game's valuation of a life at 100 million won or $85,000 is likely less than the VSL in South Korea. It is, however, more than double the per capita income in the nation, which is 38 million won or only $34,000.

If you, like the players, had nothing to lose and none of the above probabalistic chances at wealth because of the millions in debt you've already incurred—wouldn't you play? You might not die as easily in normal life, but the game offers odds you would never have otherwise. As the frontman supervising the games says in Episode 5, Squid Game was designed to give a fair and equal chance at victory to all players. "These people suffered from inequality and discrimination out in the world," he says, about to kill a worker for bribing one of the players with information on the games. "And we're giving them one last chance to fight fair and win."

You would most likely die if you continued playing Squid Game. But—like those who walked out after Game #1 only to return to the bloodthirsty island—there is no other way you'd be worth anything alive.

In an episode called "Hell", we are offered a glimpse into the players' lives in the outside world and the conditions that make Squid Game worth it. Gi-hun, who goes on to win the hefty prize, cannot afford to pay his old mother's hospital bills. Sang-woo, who grew up with Gi-hun and competes with him in the final round, is about to be arrested for financial fraud amounting to 900 million won. Ali, a Pakistani immigrant, has to maim his boss to get the wages he is due. And Doek-su, a thug outside and the most ruthless player in the game, has to kill an underling and escape the bosses he has robbed.

When these people return to the game, they know what they are getting into. The prize money will be won through the death of their fellow players.

Yet only some openly take up violence and manipulation as a strategy to win. Some try to maintain their virtue, either because of an innate belief in the goodness of humanity even in the direst of circumstances, or a desire to see themselves as "good", or to be perceived as such in order to have a better strategy than outrightly seeking power. After all, although Squid Game is zero-sum in totality, the players anticipate the need for alliances in order to maximize individual advancement as much as possible, and also to survive the more rule-breaking, predatory teams.

Which of these routes is best? What does the winner's character tell us about the dominant strategy to win?

Let's revisit the games. Game #1 was not zero-sum in itself, in that you did not need others to lose/die in order to win. Ali and Sang-woo help Gi-hun, with Sang-woo probably wanting to keep around a childhood friend for the remaining games.

Game #2, which is behind the Dalgona-candy craze amongst Squid Game fans across the world, was also not zero-sum. Individual players had to carve out a given shape from a piece of candy without any damage to the carved shape. Gi-hun makes no attempt to prevent several people from copying his trick, which he discovers at the (literal) last minute. Han Mi-nyeo, a loud and wily woman, also helps Doek-su the thug, hoping to win her way into his aggressive coalition. It was for good reason; later that night, his clan wipes out 27 players in a discotheque bloodbath.

Game #3 and Game#4 are zero-sum. In the latter, over a particularly melancholic game of Marbles, players are asked to obtain all their partners' marbles and unwittingly kill those closest to them. Sang-woo paired with Ali, who wins fair and square initially. But, unwilling to lose and seemingly virtuous, Sang-woo takes advantage of Ali's desire to not kill him, and tricks him into believing there is a way out for both of them. Instead, he grabs Ali's marbles and lets him die.

Gi-hun also tricks the old man he's paired with when he gets the chance. Although teary-eyed and guilt-stricken, he is more deluded about his own nature. Gi-hun later sells the same dream—of escaping together—to another player, just like Sang-woo did to Ali, even though he too has no reason to believe more than one player can leave the island. After Game #5, when Sang-woo once again kills a man who helped him advance, Gi-hun confronts him, asking if Sang-woo would kill him too. He blames Sang-woo, unable to see that he is just as culpable for the deaths of his fellow players through the very act of playing Squid Game. Drunk on his own virtue, angry and vindictive, Gi-hun almost kills Sang-woo — until he is stopped and told he's a "good person at heart".

By the last game, Doek-su and his obviously selfish, openly violent colleagues have turned on each other and died. The last two players are those who genuinely co-operated with others until they couldn't, in order to save themselves. But the difference between Sang-woo and Gi-hun is that the former sees and accepts his hypocrisy to himself. Sang-woo is thus able to wield it through the games, combining a ruthless mindset with a co-operative strategy. Gi-hun, on the other hand, insists on being perceived as good by himself and others — and succeeds.

At the end, when it's down to the two of them, a stricken Sang-woo kills himself even though he has the chance to walk away alive. And Gi-hun, for all his insistence on ending the game without the prize money, goes home with 45.6 billion won.

Gi-hun does help his friends' families when he is out, having lost his mother, and the season ends with him vowing to stop the next Squid Game. But his was perhaps the most beneficial strategy to play with: to be as immoral and culpable as anyone, but while ardently believing in your own morality. Not only did people trust him and help him advance, believing he would put them before himself, but Gi-hun is also able to live with himself at the end—unlike Sang-woo.

Ultimately, Squid Game offers not an extreme model of capitalism but a real one. In the world we've made for ourselves and that we live in today today, resources and opportunities are scarce, and power, rather than merit, may offer a better guarantee of success. When life is thus zero-sum and winners feel like they have to create losers, they perhaps need to be adept not only at deceiving others but also themselves.