Checkout line: how often does YOUR line finish first?
You join one of three checkout lines. All three are equally good: each has 5 shoppers ahead, every shopper takes a random amount of time from the same distribution, and the lines don’t affect each other.
Model used: 3 independent lines, 5 shoppers each, every checkout time drawn from the same exponential distribution. Ties are effectively impossible.
Bet first: the 100,000-trial run unlocks after you pick.
0trials ·
It’s you against two lines, not one.
With three equally good lines, each is equally likely to finish first — so yours wins only 1 time in 3.
That means some other line beats you 2 times in 3. That’s the feeling of “I always pick the slow line”, even though your choice was as good as any.
Any one particular other line beats you only half the time. This says nothing about whether switching helps — every line here is equally good.
Try it yourself: mathahadaily.kairoxbuild.com/lab