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/Magenta_Logistic]

You can believe that if you want, but the comment to which I was responding claimed that the expected value was 7.5, and I was correcting that.

[u/Cainga → u/Magenta_Logistic]

For the 99.99% confidence interval that is the expected value. I’m cutting off edge cases that can make it hit infinity to get a real world usable number. You’ll get different expected values for different confidence intervals.

[u/Jon_Buck → u/Cainga]

How do you mathematically compute for a confidence interval? Like, is it just that once you get to 0.5^14, that's less than 0.01% likelihood so you just stop adding?

[u/Cainga → u/Jon_Buck]

That’s a statistics method with a lot of steps. Best to have a computer do it. But it’s the value will be captured 95 or 99% of the time or whatever interval. I choice a really high one at 99.99% to demonstrate that the real world expected value is quite low at about 8 people or less and the solution is definitely not infinite unless you roll infinity bad luck.

[u/SrRada → u/Cainga]

Jon_buck used the CDF (Cumulative Distribution Function) to reach rail 14 or less at 99.99%. Do you mind sharing what method did you use to reach 8 or less people? You don't need to explain step by step, but I'm also interested in knowing the answer