How to outsmart the MTA – and save cash – when buying MetroCards

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NEW YORK (PIX11) -- Refilling your MTA card is a pretty standard procedure for anyone traveling underground in New York City.

But for those who pay attention to the details, you probably noticed that annoying leftover balance that’s either a nickel or dime, or just a few cents shy of a ride. In other words, it’s useless.

According to Ben Wellington, a data guru and assistant professor at the Pratt Institute, that odd number is no accident.

“I’d be surprised if the MTA didn’t notice the remaining tens of millions of dollars [that’s] showing up,” he told PIX11 News. “To say that they haven’t noticed anything would be surprising.”

Wellington, who took to his Tumblr “I Quant NY” broke it all down using some “old school” math.

The culprit in all this, Wellington says, are the amounts the MTA so graciously suggest to customers when buying a MetroCard.

“What they do is give you a 5% bonus when you buy a MetroCard, so when you use the pre-set buttons that are present on the machine,” Wellington explains, “you automatically end up with unusable remainder balance.”

Regardless of how you do the math, the odd balance is inevitable. So what’s the easy fix? For starters, ignore the MTA’s suggested amounts and ride to the beat of your own drum, or amount.

Instead, Wellington advises to select the "other amounts" tab and plug in the magic numbers of $9.55, $19.05 and $38.10.

Selecting these amounts will use up the card’s entire balance every time.

PIX11 reached out to the MTA to see if there was a simple fix. According to a spokesperson, it’s not so simple.

“These machines do not hold an infinite amount of change and the denominations are suggested to insure there is ample change to accommodate customers who pay with cash,” a spokesperson said in a statement.

“That being said, we will certainly look at this as part of the process involved in rolling out the next scheduled fare increase slated for next year.”

In the meantime, memorizing these so-called magic numbers will surely pay dividends.



  • Jun Yan

    Simple, just calculate S = 2.5*R/1.05 , where S = amount you need to pay, R = the number of rides you want. For example, if you want 5 rides, S = $11.90 is the amount you would pay. If you want 10 rides, S = $23.81. Etc.

  • A S Berlin

    Professor Ben Wellington is partially correct.
    When you add the 5% bonus to $9.55 you get $10.02 so $9.55 isn’t a magic number. You can buy pre-valued/packaged MetroCards for $9.52 which will get 4 rides ($10.00) at authorized stores.
    The $11.90 (which will give you $12.50) for 4 rides as cited by Jun Yan and $19.05 and $38.10 as cited by Professor Wellington are correct.

    It should be stated that the MetroCard Vending Machines will only accept transactions in multiples of 5 cents so $23.81 for 10 rides (value of $25.00) will not be accepted.

    You can, however do the “odd” amount transaction at a subway booth. Subway booths are cash only.

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  • Diego

    the MTA puts the “useless” amounts before they started charging 1$ for the metrocard itself as an insentive for people not to throw out the metrocards since they have a couple cents they would refill them. once they started charging the 1$ fee they just never removed it.

  • mike

    To keep it simple, in my case i had a remaining balance on my MetroCard of 50 cents, so i added 4.50 to have a total balance of 5.00. After 2 trips on the bus, my balance was zero. Bottom line, always save your metrocards, and also bottom line, saving money helps in the long run.

  • ben c

    i tried posting the following response to I Quant NY’s post on Gizmodo, but the author seems to be unwilling to approve it. while i’m a fan of fun math trivia like that pointed out here, the implication that the remainders left on metrocards that are too small to use add up to some major financial benefit for the MTA and that therefore the MTA intentionally designs it’s vending machines to encourage small remainder amounts doesn’t actually make sense when your analysis goes beyond simple mathematics and takes into account the actual financial and economic aspects. after writing the below post i dug up a bit of research that states that the MTA, on its books – which is for accounting and reporting purposes, and does not alter the facts of where funds go or how they are used – keeps track of unused metrocard balances as ‘liabilities’ until they expire. this is a technicality only, because metrocard balances cannot be returned for cash, so the MTA will never have to pay out the face value recorded as liabilities, and the operating costs for operating the public transit system have only a very tangential relationship with individual ridership, which is the only other way the economic impact of those liabilities would be felt. if everyone with outstanding metrocard balances consolidated them tomorrow, and decided to use up the combined balances immediately it would result in a huge mess, but wouldn’t make any sort of fundamental long-term financial or operational impact for the MTA, for reasons pointed out in my original comment:

    game theory: the MTA undoubtedly starts “floating” and earning investment income as soon as people hand over their real $ (aka non-redeemable interest-free loans/advances to the MTA) in exchange for future services not yet rendered (rides) redeemable a present-$-value fare prices, with prices increasing as a function of time, drawn against the quasi-currency balance credited 1:1 nominal $ paid at time purchase. it’s almost like an FX into an imaginary currency you can’t get out of, and they throw in a 5% exchange rate as an up-front incentive. the more $ you give them up front, the more $ they make by investing it and the more relative value you lose as fare rates marginally increase over time. so the MTA has a powerful incentive to encourage people to put more and more $ “onto” their metrocards. however, once the initial purchase is made, despite all appearances, there is no cash value sitting on your metrocard waiting to be spent at the turnstile. the MTA already has that money, which is already booked as revenue and circulating in their treasury. whether or not thousands upon thousands of stub metrocards are sitting in shoeboxes with balances never being redeemed. there is no direct relationship between individual ridership on a case by case basis and operating cost for the MTA – those trains are still going to run. and the anecdotal cases of people having low balances and having to reload or get a new card would do nothing to benefit the MTA or increase their revenues, since the revenue element is driven by the frequency of reloading of the cards – which wouldn’t change significantly whether there was $1.47 rattling around on the card or $0.01. in fact it IS economically beneficial for the MTA to reduce situations where someone has to back out of a turnstile and hold up the flow of commuters – and since they already spent that $1.47 you think you have remaining on your card, the salary paid to the person at the ticket booth you then have to talk to and have manually combine the balances of all the old metrocards in your shoebox significantly outweighs any possible benefit to the MTA of $X of unclaimed metrocard credit left to expire and be forgotten. as a commuter, who wants to minimize the amount of money you spend on fares, your best strategy is to loan the MTA the least amount of your cash as possible (maintain a small metrocard balance) while still benefiting from the up-front purchase incentives, tuned to the amount of fares you will actually use relatively soon — and at the same time, you benefit by fares not going up, so the more other people load up their metrocards and help the MTA increase revenues by floating that capital the less your own fare rates fractionally increase over time. in this sense, you as an individual rider have an aligned economic interest in the MTA convincing people to put bigger balances on their metrocards — with bigger being the only significant variable. big, easy to press, high $ round number amounts. the MTA doesn’t bother you with long division not to trick you into having credit left on your card, but because the less you think about the math the easier it is for them to engineer the experience to marginally increase the $ they are receiving up front, which, realistically, on an aggregate basis all MTA riders benefit from, by offsetting fare rate increases that would be necessary to add up to the total net income generated from investing all those microloans so kindly provided by MTA riders.

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