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Epictetus comments on Stupid Questions May 2015 - Less Wrong Discussion
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A public transportation dilemma: to get to the nearest subway station, which is on the same boulevard as my apartment building a good few blocks away, I have to take a bus to there. A bus trip to the subway station is short, about 2 or 3 minutes, but buses come at irregular times. I might find one already there, with its doors open, when I arrive to the bus stop, or I might wait 15-20 minutes for one to come. If I were to walk to my destination, the trip would take about 10 to 15 minutes.
When I'm in a hurry, I usually head for the bus stop and hope a bus comes right away -- that would minimize the duration of my trip. The worst decision I could possibly make is wait 15 minutes for a bus to come, get annoyed, decide it's probably not my lucky day, and suck it up and walk to the subway station -- that's a full 25 minutes, up from the 2-3 minutes of a "lucky" trip. Very often I get to see several buses passing me by as I decide to walk. But if I were to take the opposite decision and decide to not even wait for a bus, instead just heading straight to the station, I'm still at a disadvantage of about 8 minutes, if the bus comes shortly after I pass by the bus stop.
After how much time is it rational to leave the bus stop and decide to walk, if the bus doesn't come? The probability of the bus to come after a given waiting time (the frequency with which it comes) is unknown, although it might get close to 1 after 30 minutes.
Just for the sake of completion, there are some bus services that offer real-time GPS tracking, so you'd know where the bus is and roughly how long until it arrives. Presumably no such service is available.
We go on to the age-old question: do you try to get the best average performance or the best worst-case performance? If it's the best average performance, go to the bus stop and wait. If you prefer to get the best worst-case performance, just walk every time.
If the bus arrival time is evenly distributed from 0 to 30 minutes, and takes 3 minutes, the average performance of the bus is 18, while walking is 15, so walking is also the best average performance.