# A statistician figured out the perfect amount to put on a subway card so you'll never have leftover change

Every time you swipe your MTA card in New York City, you know you’re getting ripped off.

Inevitably, if you choose one of the MTA’s payment prompts (a \$US9.00 MetroCard with a \$US.45 bonus, a \$US19.00 card with a \$US.95 bonus, or a \$US39.00 card with a \$US1.95 bonus) you’ll end up with a card that has leftover change. That’s beacuse none of those cards are divisible by \$US2.50, the flat amount for every subway ride.

Most people will never be able to use that change, because they can never figure out the perfect fare. So all that money gets collected by the MTA.

Until now.

Statistician Ben Wellington wrote a mathematical proof to figure out how to defeat the turnstiles. His advice: Ignore all the machine’s prompts to get a card with a bonus. Instead, type in a custom amount: \$US19.05. That will get you a perfect eight rides, without a cent to spare.

Here’s his maths for all amounts under \$US40, taking into account the 5% bonus the MTA offers per bulk-paid card:

I Quant NY/TumblrMemorize these amounts: \$US11.90, \$US19.05 and \$US30.95.

Unfortunately, the MTA is about to hike up subway fares again. On March 22, the amount per ride will change from \$US2.50 per ride to \$US2.75. An 11% bonus will be tacked on.

So what will the new magic number be?

Wellington re-did his maths and came out with a new amount to memorize: \$US22.30.

Here’s his logic:

“The MTA might leave things as is, with \$US9, \$US19 and \$US39 preset buttons,” Wellington writes on his Tumblr, I Quant NY. “If they go that route, it’s time to start memorizing a new set of numbers again New York! And the magic number seems to be \$US22.30. Just use the “Other Amounts” button, type in \$US22.30 and you get \$US24.75 on your cardâ€¦ exactly nine trips.”

Here’s his updated chart, below.

I Quant NYThe new numbers to memorize after March 22 may be \$US22.30 or \$US27.25.

Note: you can’t get a perfect eight trips in like before. But you can get a perfect nine or eleven trips. Wellington also notes that the MTA might make the issue go away altogether and update the card and bonus amounts on its prompts. When he figured out the magic \$US19.05 last fall, the MTA responded, “We will certainly look at this as part of the process involved in rolling out the next scheduled fare increase slated for next year.”