Unlimited, or Pay-Per-Ride? That’s the question posed by the New York Times City Room blog this morning, as New Yorkers confront the great algebraic unknown of August: are unlimited subway passes still a good value even if you’re going out of town on vacation?

Perhaps the author, reporter Clyde Haberman, has been reading too much of his paper’s misguided screeds against mathematics education (nicely rebutted by my colleague Evelyn Lamb), but the column, titled “Doing the Metrocard Math,” never does the math.

This is a shame, because the math is not all that difficult to do (despite the Metropolitan Transit Authority’s bizarre decision two years ago to change the base bonus from a nice, even 20 percent to an ungainly 7 percent). The base fare for a subway or bus ride is \$2.25. Any Metrocard purchase of at least \$10 qualifies for the 7 percent bonus, lowering the net base fare to \$2.10.*

Beyond that, you have two choices: An unlimited 7-day card for \$29 or an unlimited 30-day card for \$104. Cost per ride is simply this cost divided by the number of rides. Here I plugged a few numbers into a spreadsheet. For simplicity I based the calculations on the number of rides a passenger expects to take per week.

Rides per weekCost per ride
7-day card30-day card
8\$3.63\$3.03
9\$3.22\$2.70
10\$2.90\$2.43
11\$2.64\$2.21
12\$2.42\$2.02
13\$2.23\$1.87
14\$2.07\$1.73
15\$1.93\$1.62
16\$1.81\$1.52
17\$1.71\$1.43
18\$1.61\$1.35
19\$1.53\$1.28
20\$1.45\$1.21

As we can see, a 7-day unlimited pass only makes sense if you’re planning to take 14 or more rides a week—twice a day, weekends included. A 30-day unlimited pass works out after 12 rides a week, just in case you prefer to spend Sundays at home. To my surprise, a standard 10-ride-a-week commuter should always pay by ride. (Indeed, Haberman quotes Gene Russianoff, the staff attorney for the Straphangers Campaign, a riders’ advocacy group, as saying that a quarter of all 30-day unlimited buyers “don’t use them often enough to get their discount value.”)

But back to our original question: Should the summer jet-setter still buy a 30-day pass? Depends, obviously, on the jet-setter. But unless they’re a three- or four-trip-a-day rider, they may want to consider going à la carte even after August comes to an end.

*: Update 7/31/12 5:46pm: To my shame, I mistakenly said the MTA provides a 7 percent discount on Metrocards over \$10. They give a 7 percent bonus. (So \$10 in the machine nets you a \$10.70 card.) This changes the net base fare from \$2.09 to \$2.10. The rest of the calculations (and the conclusions) remain unchanged.

Update 8/6/12 6:52pm: Here's a link to a Google Doc of the spreadsheet I made for the calculations, for anyone who's interested (or would like to play with the values for their home transit system).

Photo by cfarivar on Flickr