Supermarket line karma is a myth. Yes, yes, I know, it happens to you all the time. Whatever line you get in at the supermarket (or airport, or concert, or fast food restaurant, or …) moves slower than the one beside it, and almost certainly slower than every other frickin’ line in the place.
I know I always feel like it happens to me. I usually warn people who get in line behind me at supermarkets or airports that they should pick another line. I have bad queuing karma — the line I’m in is always the worst.
But it’s almost certainly not true. Look at it this way: Assume there is a supermarket with four equal-length lines. Call them a, b, c, and d. For the sake of argument, let’s say that each line has an equal chance of being “fastest”, where fastest is defined as being the one where the person in position Nx (queue position N, line x), reaches the front first. Assuming the probabilities hold, it’s straightfowardly obvious that there is a seventy-five percent chance your line won’t be first. In other words, most of the time some other line will be fastest.
You protest, however, that there are plenty of times when your line starts out shorter than the other lines, and so I should finish first. Not so fast though. In general shorter lines should finish first, but keep in mind that the amount of time people spend at the front is a random variable, one with significant positive skewness. In other words, while the distribution of checkout times (unadjusted for scanner or bagger skill) is kinda normal, it has a significant right skew with a correspondingly fat right tail (i.e., those darn people with suitcase-sized purses who full-arm fish for a checkbook about three feet down). Further, there is a cumulative effect, where small delays cascade quickly, with a single tiny problem (“Can someone get me a price for organic, free ranch avocados?”) rapidly causing the queue to go out of kilter.
All of this is, of course, just Queueing Theory For Dummies, but I’m sitting in an airport lounge right now, having just spent the last twenty minutes in a line that went slower than all the ones around me. Hey, I needed some way to pacify myself.