God plays dice

Service on Bay Area Rapid Transit (BART) runs every fifteen minutes on each route; every twenty minutes on evenings and Sundays. Here’s a map of the system. (The lines in red and green don’t run all the time, but that’s not relevant for what I’m about to say.)

The San Francisco city segment (Daly City to Embarcadero) is served by four of the five routes, and so has service by sixteen trains an hour when all those lines are running, between about 6 AM and 7 PM. Here’s a schedule. If you’re standing at, say, 16th Street (which I was a couple hours ago), northbound (Embarcadero-bound) trains depart at

6:11 am (red, i. e. Richmond-bound)

6:17 am (blue, i. e. Dublin-bound)

6:19 am (yellow, i. e. Pittsburg-bound)

6:24 am (green, i. e. Fremont-bound)

and then that pattern repeats every fifteen minutes through 4:11 pm. (Things get complicated slightly…

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