If you haven't seen Squid Game yet, it's time to stop clicking on articles that promise to reveal spoilers in the title, because this article will be full of them.
Ok, if you're reading on we're going to assume that you've watched it all, and aren't going to get mad at us for plot points we're about to reveal. In episode seven of the hit Netflix series, the remaining 16 players are met with their most evil challenge yet, and that's saying something considering in episode one they were met with a giant robot doll that shoots half the players directly in the face. In episode seven, they must: choose a bib.
The bibs are numbered 1-16, which is eventually revealed to correspond to what order they do the next task in. This is unfortunate, as survival for the next task is (mostly) dictated by what position you have chosen for yourself.
The bridge's setup is fairly simple. It will take 18 steps to get to the other side. The problem is that to get there you will need to choose a pane of glass to stand on with each step. One is tempered glass, which will hold your weight and the weight of one other. The other is normal glass and will break if stepped on, sending you plummeting to your death. Another problem is that there is a time limit, meaning that being at the back isn't necessarily the best place to start, should people ahead of you take their time (understandably) deciding which pane of glass will save them from death.
If the contestants had sat down and ignored the fact that many of them were about to die (the first players are pretty much facing a death sentence) they would have surely remarked what an interesting math problem they were facing.
Player 1 is essentially facing a 50/50 chance every time he takes a step. That's (1 / 2)¹?, or a 0.0003815 percent chance of success. Our advice: probably best not to think about it.
Player 2 is not facing those odds, however, as player 1 has removed an unknown. In fact, if the players were to play the game rationally, each player has a 1/2 chance of removing not just one unknown, but two unknowns for the following player. The player in front of you even has a 1/4 chance of removing three unknowns, and so on.
I.e. on the first jump they have a 100 percent chance of removing an unknown, but only a 50 percent chance of surviving that in order to eliminate the next unknown.
So, what are the odds of you making it across the bridge? Actually, not too bad (look, you're in a reality show where there can only be one survivor, so "not too bad" is relative) if you are as near to the back as possible. This is basically because people in front of you are likely to remove more unknowns than you'd intuitively think. Say 1 in 4 people make it to their third jump (their survival on that jump is irrelevant here) then that means that 1 in 4 people is providing information about a whole three steps out of 18, and once those safe steps are known, they are known forever.
If you figure it out, which of course people have, you would expect each player to pass on information about two steps along the bridge, meaning that by the time you get to player 10 they are likely to survive. Over on Reddit, user SwissVictory even created a program in python to essentially play this scenario out 100,000 times, and tested it the hard way (well, not the really hard way, which involves tens of thousands of deaths).
His trials pretty much confirmed the math, with the average trial having "almost exactly 9 deaths" at 9.02. It appears that the players of the game in the show were unlucky, and, let's face it, were playing less than rationally.
Were they to play it completely emotionlessly, and with perfect memory, there would be around 75 percent chance of them making it through with 10 deaths or fewer, leaving six people to go on to the final challenge. The way they ended up, with just three survivors, was one of the least likely scenarios, at around 1.2 percent probability (according to SwissVictory's test, rather than the pure maths).
But what about the time aspect? Well, some suggested that this is a large consideration. And it sure would be, given the fear involved. Factoring that in, one Redditor believed that the best place to go would be position 10. However, if you can convince people to act rationally, there's no reason why you couldn't get players 1-9 to do their duty and die so that you can figure out which tiles to step on, leaving plenty of time to get across.
Plus, once the solution is figured out, it's merely a matter of stepping across, which wouldn't take too much time. The best bet would still be to go to the last position possible, so that more people ahead have given you information about the steps ahead of you, by dying horribly in your place. Happy squid gaming, everybody.