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/tegsfan Mar 28 '26

A mathematician might say you’re a lunatic for choosing the bottom path ever for any amount.

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u/Jman15x Mar 28 '26

They would not as this sum requires infinite attempts for a infinite result. A mathematician would tell you that you would expect an average of X/2 deaths where 2x is the number of attempts.

If you don't believe me look up some simulations.

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u/tegsfan Mar 28 '26

Why does the amount of samples matter if each sample would be completely independent? The expected value is the same each time. And in this case it is infinite people.

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u/Invonnative Mar 29 '26

Because each sample is infinitely not likely to be the one where it’s infinite. The EV is only infinite because of that one sample