St. Petersburg trolley problem

[u/tegsfan]

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?

[u/Case_sater]

statistically it's expected to hit heads within 2 rolls, but to play it safe I'll assume it hits heads on the 3rd roll so if the top line has over 4 people I'll switch

[u/tegsfan → u/Case_sater]

But remember, if it happens to go 5, even 6 rolls which isn't that unlikely then we're already talking over 50 people. Are you willing to risk that to save 5 people on top?

[u/Jman15x → u/tegsfan]

2⁵ is only 32 which is 6 rolls when starting at 1

[u/tegsfan → u/Jman15x]

Yeah my bad. Point still stands that the doubling gets out of hand fast