Your odds of surviving the Squid Game glass bridge
- Article
- Statistics
Squid Game, the Korean drama that topped Netflix’s charts in late 2021, puts its characters through children’s games with lethal stakes. The fifth game caught the attention of Christian Koguchi, who wrote up a short analysis of it on Medium. If you ever found yourself in a teal jumpsuit picking a numbered vest, this is the math you would want.
The game
Sixteen players remain. They have to cross a bridge made of 18 pairs of glass tiles. In each pair, one tile is tempered glass that holds, and the other is ordinary glass that shatters and drops the player. The players cross in numbered order, and nothing distinguishes the two tiles by sight. Each step is a coin flip for whoever goes first. The catch is that every broken tile is information: everyone behind that player now knows which tile in that pair is safe.
The simulation
Koguchi used a Monte Carlo simulation, running the game 50,000 times with random tile layouts and tracking who survived in each run. Two quantities come out of that: the probability that a player with a given number makes it across, and the distribution of how many players survive in total. The simulation assumes each player remembers every safe step revealed so far and has enough time to cross.
Results
Player 16, the last to go, survived in 49,995 of the 50,000 runs, a survival rate of 99.99 percent. By the time the last player steps on, almost every pair has been resolved by someone ahead of them.
Survival climbs steeply with player number. The first five players essentially never survive (player 1 at zero, player 5 at about 1.5 percent). Player 8 makes it about 24 percent of the time, player 10 about 59 percent, player 12 about 88 percent, and players 13 through 16 all sit above 95 percent. Three characters from the show were called out in the post with their positions’ rates: 98.49 percent, 99.64 percent, and 99.99 percent.
The expected number of survivors is about seven. The histogram of survivor counts peaks at seven (with about 18.6 percent of runs) and is spread mostly between five and nine. Fewer than two survivors, or more than twelve, almost never happens.
The takeaway
Pick the highest number you can. Beyond that, the exercise is a small demonstration of what simulation is for. The exact probabilities here could be derived by hand, but the simulation gives the same answers in a few lines of code, and the same technique works when the rules get too complicated for a closed form. It also shows that the tools of data science apply just as well to a fictional game as to a real dataset.