It could be simply obscure like you say, but the absence of a network doesn't guarantee it's that easy to hack.
They could use a checksum and your trick would invalidate the card until you figured out the correct algorithm, which would require a new visit to the laundromat for every new attempt, so basically impractical.
That or the card is just simply encrypted, which would make it impossible to interpret. It would be easy to implement too because the shared secret is between machines that are all physically controlled by the laundromat.