Analyzing the probability of "Squid Game- The Challenge" Finale
Manjish Naik
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This article has been corrected since it was first published as I made an error in adding probabilities of C winning.
If you are a huge fan of Squid Games, the Korean TV show on Netflix, I am sure you have been following the reality TV show "Squid Games- The Challenge", where real people play games similar to the TV show, obviously without any bloodshed.
Spoiler Alert: I have taken care to not include player names, but one of the games that features in the reality show will be discussed from a probability standpoint. So, if you don't want any spoilers whatsoever, please stop reading.
I was super intrigued by the idea of the reality show and there was a lot of thought put into making it as close to the drama as possible, without harming the participants. This included wearing devices which would burst into black ink when a participant was eliminated, to signify someone "shooting" them.
The season final just dropped and it had a game which made me wonder what is the best spot to pick based on highest probability of success.
The Game Mechanics
Here's how the game worked:
Three contestants have to approach a station which has three buttons, in an order that they have to decide between themselves.
Each contestant can press only one button which may turn into any of three colors: green, grey or red.
If you get green, you automatically advance and can pick another person to advance with you. The remaining person is eliminated.
If you get red, you are automatically eliminated and the remaining two advance.
If you get grey, no consequence and you wait your turn to see what the other two get.
Any pressed button stays in the same color and the next contestant has to choose from the remaining (unpressed) buttons.
Also, if someone gets green or red, the game is over and no more buttons need to be pressed. If you get green you make a choice of who you want to advance with you and if you get red, the other two players advance.
I made a quick tree diagram:
The probabilities are shown on the buttons and each branch traces a distinct and unique possibility.
Remember, this is not an independent probability question as your chances of going to the next round depends on the color the person before you got. Unless, of course, you go first.
Optimizing the decision
There was a great debate on who goes in which order. So naturally, we want to see which position has the greatest probability of winning.
Let's say person A goes first and person B goes second and the hapless third will be named C. (Big Surprise!)
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Probability that A will advance
These are the scenarios in which A will advance:
Total probability for A = 1/3+1/6+1/12 = 7/12
Probability that B will advance
These are the scenarios in which B will advance:
Total probability for B = 1/3+1/6+1/6 = 4/6
Probability that C will advance
These are the scenarios in which C will advance
Total probability for C = 1/6+1/6+1/3+1/12 = 9/12
So what spot should you pick?
Obviously because C has the highest probability, you would want to go last to maximize the chance of going to the next round, or in other words, let other's decide your fate.
SPOILER: But what really happened on the show?
SPOILER ALERT: Person A knew that if B or C got a green ball they would pick each other. So they wanted to take control of the game and decided to go first, which was the lowest probability spot. They went first and got Grey. Then person B and C debated much and B decided to go next.
However, when B pressed the button, it turned RED and B was booted!
So probability on paper is one thing but it could be anyone's day.
Conclusion
It's good to have probability to back your decisions, but don't feel too bad if you don't get the branch you are hoping for and things turn south on you. All you can do is decide based on the data you have and then work towards making that projection come true. But there could be things outside your control which may affect the outcome.
Disclaimer: I am in no way an expert. So experts, please check my work and tell me if I am thinking about this the right way.
Credits: Karisma Wagh , my partner in crime, for helping me analyze this.
Thanks to Ken Yoshimi for catching an error I made in adding up fractions for total probability of C.
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1yYour math is wrong. The expected outcome of players passing should be 2. Your expected outcome = 7/12 + 4/6 + 7/12 = 22/12 = 1.8 players. Never forget to make some quick checks.