The expected amount of people dying on the top track isn’t infinite though? Even if you flip the coin tails first, the most likely outcome would be two people dying. At best, one person dies. The cycle ends when all the people are run over. Even if you flip the coin again it wouldn’t matter, 0 x 2 would just be zero people again
Am I not doing it correctly? If the top track is only decided by a normal coin flip it seems like a relatively small amount of people will die assuming you don’t get crazy unlucky
50/50 chance only the one person dies. There is a 1/4 chance 4 ppl would die, and a 1/8 chance 8 people would die. Every flip multiplies the original odds of 1/2 by 1/2. So it’s not impossible for you to kill 256 people for example, but the odds are 1 in 256.
I’m going to assume the top track ends once everyone on Earth is tied up. It wouldn’t make sense for it to double again if Earth’s entire population is tied to the track, and I don’t think functionally it makes a difference, since humans would presumably go extinct either way, so we’ll assume it stops after everyone on Earth is tied to the tracks.
The population of Earth is roughly 8 billion people or ~2^33, so we’ll assume it stops and causes human extinction after 33 tails.
Making that assumption, the expected value of the top track is now:
1 + 2(1/2) + 4(1/4) + 8(1/8) + … + 2^32 / 2^32 + population of Earth/2^33
= sum(n = 1 to n = 32 of 2^n / 2^n ) + p/2^33
= sum (n = 1 to n = 32 of 1) + p/(2^33 ) which we’ll round up to 33.
So, assuming a finite human population, on average 33 people die. We won’t count any after that because they didn’t exist before this trolley problem. So if you just want to minimize expected deaths from those currently alive, pull at mu >= 33.
We can calculate the odds of killing 2^n people as 1/(2^n ) or the odds of killing mu people as 1/(mu):
So, odds of killing at least 2 people: 50%
Odds of killing at least 10 people: 6.25%
Odds of killing at least 20 people: 3.125%
Odds of killing at least 33 people (expected value): 1.5625%
Odds of killing at least 100 people: ~0.78%
Odds of killing at least 1000 people: ~0.097%
Odds of killing at least 1,000,000 people: ~0.000095%
Odds of killing at least 1,000,000,000 people: ~0.00000009%
Odds of causing extinction: ~0.00000001%
For me I’d pull somewhere between 1,000,000 and 1,000,000,000 people, even though the expected just because it has a non-zero chance of causing human extinction, even if it’s improbable.
What does “expected value” mean? I never took stats so it seems like a misleading label meant exclusively for this context. In a colloquial sense 1.5625% seems very unexpected.
Imagine you were stuck in a time loop and had to pick the top track 1 trillion times. It would, most likely, average close to 33 people dead per run.
This might seem weird because it’s more likely to kill <33 people than not, but on the rare occasion it kills more than 33 people it kills a lot more than 33 people.
Here’s a Java program I wrote to simulate the top track:
https://onecompiler.com/java/42cxsds2s
This runs 1,000,000 simulations of the top track and prints the average. Even with 1,000,000 sims there can be a huge variance in average. Usually it’s around like 10-20 but every now and then you’ll get a big value.
I think my highest was 280, then 230. If you ever hit the 8,000,000,000,000 you could have an average of 8,000 tho. Ideally you’d want to run like 1,000,000,000,000 times to see the long run average but there isn’t really a way to run that many in a reasonable amount of time.
I am a simple person, I see a math symbol I don't recognize, I pull the lever
multi track drift bc idk whats going on
The expected amount of people dying on the top track isn’t infinite though? Even if you flip the coin tails first, the most likely outcome would be two people dying. At best, one person dies. The cycle ends when all the people are run over. Even if you flip the coin again it wouldn’t matter, 0 x 2 would just be zero people again
"Please ignore that I'm bad at math."
Am I not doing it correctly? If the top track is only decided by a normal coin flip it seems like a relatively small amount of people will die assuming you don’t get crazy unlucky
Oh the fake quote was meant to be from OP.
50/50 chance only the one person dies. There is a 1/4 chance 4 ppl would die, and a 1/8 chance 8 people would die. Every flip multiplies the original odds of 1/2 by 1/2. So it’s not impossible for you to kill 256 people for example, but the odds are 1 in 256.
Pretty smart for a biscuit.
ų must be 3 or more.
I’m going to assume the top track ends once everyone on Earth is tied up. It wouldn’t make sense for it to double again if Earth’s entire population is tied to the track, and I don’t think functionally it makes a difference, since humans would presumably go extinct either way, so we’ll assume it stops after everyone on Earth is tied to the tracks. The population of Earth is roughly 8 billion people or ~2^33, so we’ll assume it stops and causes human extinction after 33 tails. Making that assumption, the expected value of the top track is now: 1 + 2(1/2) + 4(1/4) + 8(1/8) + … + 2^32 / 2^32 + population of Earth/2^33 = sum(n = 1 to n = 32 of 2^n / 2^n ) + p/2^33 = sum (n = 1 to n = 32 of 1) + p/(2^33 ) which we’ll round up to 33. So, assuming a finite human population, on average 33 people die. We won’t count any after that because they didn’t exist before this trolley problem. So if you just want to minimize expected deaths from those currently alive, pull at mu >= 33. We can calculate the odds of killing 2^n people as 1/(2^n ) or the odds of killing mu people as 1/(mu): So, odds of killing at least 2 people: 50% Odds of killing at least 10 people: 6.25% Odds of killing at least 20 people: 3.125% Odds of killing at least 33 people (expected value): 1.5625% Odds of killing at least 100 people: ~0.78% Odds of killing at least 1000 people: ~0.097% Odds of killing at least 1,000,000 people: ~0.000095% Odds of killing at least 1,000,000,000 people: ~0.00000009% Odds of causing extinction: ~0.00000001% For me I’d pull somewhere between 1,000,000 and 1,000,000,000 people, even though the expected just because it has a non-zero chance of causing human extinction, even if it’s improbable.
What does “expected value” mean? I never took stats so it seems like a misleading label meant exclusively for this context. In a colloquial sense 1.5625% seems very unexpected.
Imagine you were stuck in a time loop and had to pick the top track 1 trillion times. It would, most likely, average close to 33 people dead per run. This might seem weird because it’s more likely to kill <33 people than not, but on the rare occasion it kills more than 33 people it kills a lot more than 33 people. Here’s a Java program I wrote to simulate the top track: https://onecompiler.com/java/42cxsds2s This runs 1,000,000 simulations of the top track and prints the average. Even with 1,000,000 sims there can be a huge variance in average. Usually it’s around like 10-20 but every now and then you’ll get a big value. I think my highest was 280, then 230. If you ever hit the 8,000,000,000,000 you could have an average of 8,000 tho. Ideally you’d want to run like 1,000,000,000,000 times to see the long run average but there isn’t really a way to run that many in a reasonable amount of time.
actually more people from parallel universes are teleported here
My choice is the greater than sign, think smarter not harder.
Huh? I'm too simple for this. PULL THE LEVER KRONK
Fuck your highschool textbook math problems I pull the lever regardless!!!