The checkout at a supermarket has the same phenomenon. Let's say with 50% probability you choose a line that takes 10 minutes and with 50% probability you choose a line that takes 20 minutes. On average now 67% of the time the other line will move faster.
https://news.ycombinator.com/item?id=7622626
Counterintuitively, in stop-and-go traffic everybody spends more time
watching others pass them than passing others.
Let's say you have to drive 100 km. Half of the distance your lane
moves at 100 km/h, and the other half your lane creeps along at
10 km/h. So you'll spend 50 / 100 + 50 / 10 = 5.5 hours in the
car, at an average speed of 18.18 km/h.
For every one minute you spend passing other cars, you'll spend
10 minutes watching other cars whiz by you!
Even though the fast and slow distances are evenly distributed,
all drivers perceive that they're in the wrong lane.So, out of a total wait time of 5200+2600= (7,800) minutes you spent 2/3 of it in the slow lane and 1/3 of it in the fast lane.
>On average now 67% of the time the other line will move faster.
This should be: "On average, you spend 67%~ of your time in the slower lane."
On average the other lane is still only faster 50% of the time assuming the odds are truly 50/50 - but you spend 67% more time in the slower lane.
Thinking of total time for grocery store lines may feel unnatural, but it's certainly the perspective that makes sense on a road. I wouldn't start a 200 mile trip by saying "I'm going to spend this trip in the right lane," I'd do some of my driving in each.
And if I drive 100 miles in the fast lane and 100 miles in the slow lane, I'll have spent >50% of my time in the slow lane, even if my odds of picking the right one are 50/50 at any given moment.