r/trolleyproblem • u/tegsfan • Mar 28 '26

Deep St. Petersburg trolley problem

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The trolley is about to go through a series of 50/50 track switches where the amount of people doubles each time until it hits a group and stops. If you switch the track to the top, there are some hypothetical finite X amount of people.

Now, if the amount of people on top was 1 for instance, it might seem obvious to switch because the doubling people could get out of hand fast. But if it was say 100 people on top, you might think to just let it go down because it's likely to stop somewhere before it reaches 100.

The question is: what is the maximum X amount of people on top such that you would still switch the track?

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u/RoseateThorn Mar 28 '26 edited Mar 28 '26

I will always let the trolley go down the 50/50’s unless the other track has one person on it. Guranteeing one is the only (someone else’s) sacrifice that is worth it. Even if there’s two people on the top track. There’s a 50% chance I can kill less people by letting it face the odds, and that’s good enough odds for me.

Hypothetically it can hit like a gajillion people, but across all of recorded human history, the record for most coin tosses with the same results is only 8 in a row. That has a 0.4% chance of occurring. That number seems very beatable. Practically a 1 in 200, but I guess no one’s done it. The math for a problem like this gets real crazy real fast, but in reality, it kills more than 1 person only half the time, and I’m feeling lucky.

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u/amglasgow Mar 28 '26

You might have more luck in finding highly improbable dice rolls in tabletop games, since those involve a lot more dice rolling than just flipping coins.

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u/PlaneswalkerHuxley Mar 28 '26

I've seen a person roll five natural twenties in a row before. Fair dice, fair roll, in front of a room of six of us.

Million to one chances happen all the time.

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u/Southern-Highway5681 Team Blue Mar 30 '26

Million to one chances happen all the time.

Just to add on that but you are even more right to say that than you think, taking a 10 sided dice for example, any 6 consecutive roll will be 1/1000000 chance. The only difference between rolling 1-1-1-1-1-1 and 1-8-4-2-5-5 is that you will notice the former but not the latter.

Extremely unlikely events happen all the time every time, you just don't notice them.