Squid game is just so addictive. I was planning to only watch one episode but ended up binging the whole thing. The blood and organs parts was gross but the storyline was worth it.
But the glass bridge game kept me thinking about it because statistically speaking, the first few have near zero chances of surviving. For the very first player to cross the bridge, the chance is 2^18 = 0.004%. Feels bad for him because it is his first time being courageous.
Anyway, the survival rate in the show is very low at 18.75%. But then, we had 3 stupid deaths as well which had no contribution to the game in terms of revealing the safe piece.
Let’s look at the players stats first.
This is a luck game with 50% chance of successfully crossing one out of the eighteen tiles or falling to your death.
Given there is 16 players, 50% chance of choosing the right tile at every turn, chances are:
8 will plunge to their death on their first try (16*50%=8)
4 will survive the first tile, and fall in their second try (16*50%*50%=4)
2 will survive both their first and second try, fall on their third (16*50%*50%*50%=2)
1 will survive 3 tiles, and fall on the fourth (16*50%*50%*50%*50%=1)
Of course, if there’s someone who is very lucky, they have 3.125% chance of crossing 4 tiles before falling, 1.56% chances of crossing 5 tiles before falling etc, but if they’re really such lucky people, why the hell are they there?
So if we look at the probability above, given the best case scenario where the luckiest people goes first, to cross 18 tiles, we will need the first 7 to sacrifice (4+3+3+2+2+2+2=18).
In the event the unluckiest people goes first, we will need 12 people to sacrifice (8*1 + 4*2 = 18)
So basically, the last 4 had a very good chance to survive if they have enough time to cross, the first 7 had almost no chance of surviving, and 8-12 is a gamble.
In fact, if we look at the show’s results:
1st person fell on second try (tile 2)
2nd person fell on first try (tile 3)
3rd person (aka the math teacher who calculated his probability of crossing and gave up HAHAH) fell on his fourth try (tile 7)
4th person is an idiot and fell on tile 5
5th person, the sabotage woman, fell on her first try (tile 8)
6th person wasted time praying, 7th came to push him but got pushed off and revealed the safe tile for tile 9. 6th got pushed off by 8th and revealed the safe tile for tile 10.
8th fell on his second try (tile 12)
9th is the gangster who turns out to be quite a coward and refused to move. 10th came to push him but got thrown off without revealing any tile. 11th suicided with 9th and revealed the safe tile for tile 13.
12th fell on first try (tile 14)
At this point, there’s only 4 tiles left, and 4 players.
Luckily, 13th worked at a glass factory and safely crossed till tile 17. Until they switched the lights off. But at this point, 14th have a 50% chance of surviving if he made up his fucking mind, while the last 3 are guaranteed survival if they have time to cross.
If 13th didn’t have the advantage, it is likely that 13th and 14th would die before crossing the bridge. 13th had a 1/16 chance to passing (~6%), 14th will have 12.5% chance of surviving if 13th fell on his first try. But if everyone chose the wrong tile on their first try, that’s the end of the squid game because everyone died.
Their survival rate was lower that the expected (1-7 almost no chance, 8-12 maybe, 13-16 likely to live), but if the 4th person wasn’t dumb and helped in revealing one tile, 10th got thrown in front to reveal one tile, and 11th/9th revealed one more tile, that would put 12th at tile 16 instead of 13 when he started. If he was lucky, he could had survive by crossing 2 tiles successfully, or if he fell on his first, 13 would had survived because the VIP would not figure out he knew the trick to the glass. If any of the 3 dumb deaths crossed two tiles instead, 12th would had an even higher chance of surviving but yea, 3 dumb deaths at the front led to 2 more deaths towards the end, unfortunately.
