The Maths of Squid Game: The Challenge – Part 1: The Voting Test
The Maths of Squid Game: The Challenge – Part 1: The Voting Test
The first in a series of articles looking at strategies for the Netflix series Squid Game: The Challenge. Episode 4: The Voting Test
Fans of the original Korean TV drama Squid Game will not have failed to notice the release of the real-life version of the show that debuted on Netflix last month. The revamped real-life Squid Game sees 456 contestants (numbered from 1 to 456) try to stay in the show longer than all the others to win a jackpot of $4.56 million – the elimination of each player adding $10,000 to the prize fund. If they haven’t already binged it, many loyal viewers will be well on their way. I confess I finished the final episode within hours of its release on December 5th 2023. It is compelling viewing.
SPOILER ALERT: this series of articles contains spoilers about episodes of Squid Game: The Challenge, so if you haven’t yet watched it but plan to and you don’t want to know what happens, then you might want to avoid the rest of this article.
In the original series, praised for its macabre aesthetic, the players were whittled down, in a series of life or death “games” until just a single player remained. In an even darker twist, players realised they could add funds to the prize pot by killing each other in the communal dorm they inhabited outside of the games.
The reality show also sees players eliminated in games, but to replace the dormitory out-of-game fights-to-the-death of the original show (and as a way of controlling the numbers at each stage) the producers add a little extra jeopardy through a series of “elimination tests”. If anything, these tests create a more palpable sense of tension than the threats of warring factions in the dorms of the fictional series ever could. Many of the tests are mathematical, in the sense that logical thinking will help with developing strategies to help win the game.
One such elimination test sees players line up and ‘vote for’ their fellow contestants. The three players with the most votes after everyone has cast their ballot will be eliminated. The voting proceeds one player at a time, tapping the contestant’s number into a keypad. Although the voting is secret, as soon as a contestant receives a vote for the first time, their number comes up on the screen making it clear who the voter just voted for. Since being known to have voted for someone is likely to attract retribution via a nomination, it is dangerous to vote for someone for the first time – no matter how much you dislike them. Indeed this retribution was evident during the elimination test on the show. Players who received a vote early on later voted for their nominator when it came time for their turn to vote.
In the show, when the players formed the queue which would determine their voting order they were not fully aware of how the process would work. But in light of the full view of the game where is a good place to stand in the queue?
Being at the very front of the queue at the beginning of the game immediately seems like a terrible choice as you are forced to show your hand to everyone else in the room - running the risk of being voted for in retaliation by the person you nominated. Contestants after the first have the option to vote for the same person who is already up on the screen (although if no new face comes up it will be clear that this was their action) or to choose someone new. As soon as two players have been voted for and are consequently up on the screen everyone else has plausible deniability about which of the two they voted for.
A strong positive feedback loop, encouraged by the desire to keep their vote secret and avoid becoming a target themselves ensures that the contestants already up on the screen typically receive more and more votes. An early nomination can be an effective death sentence. Indeed, the first three players nominated on the show were the three who were eventually voted off.
So where should you stand in the queue to minimise your chances of elimination? Not being the first person in the queue seems sensible. Once a name is up on the board you can vote for that candidate without bearing the responsibility of being the nominator, but while there’s still only one name on the board everyone will know who you voted for. So perhaps being too near the front isn’t good either. Assuming, as the game goes on that more candidates go up on the board there will eventually be plausible deniability about your vote. So perhaps the further back the better?
The problem with being at the back of the queue though is that your vote effectively counts for less. As long as you’re not already up on the board this isn’t a big problem – the key is not to get voted off after all. If, however, you get nominated early on and you are at the back of the queue, then you have very little chance to wreak your revenge. Knowing this, if you do find yourself in the position of voting first, then a sensible strategy would be to nominate the person at the very back of the queue, knowing that they will have no chance to nominate you in return. Indeed a sensible strategy for anyone near the front would be to nominate a candidate near the back who will have little or no chance of retribution. Equally though, once a player has cast their vote they have no comeback, so for everyone else, nominating someone who has already voted is also a sensible strategy. Another reason for not being to near the front of the queue.
So is there an optimal strategy? Given a set of behaviours that each player consistently conforms too – like not attracting retribution - then it is theoretically possible to find an optimal strategy. As viewers of the show will have recognised though, human psychology is notoriously fickle many players will adopt sub-optimal strategies which makes predicting the outcome of any such game extremely difficult. But this, of course, is what makes the show so interesting!