You can get plastic NFC cards. I bet there are companies that will print and program them.
It must be possible to have flexible paper-like cards because my city has one-time tickets with NFC. Game would be nicer with card stock and not rigid plastic.
Altered attempted something similar. QR codes that add a digital copy to your digital collection. The physical card is just a proxy of the digital one. To enter tournaments or trade a card you have to own/trade the digital one. There was an official print service to order physical copies of the digital cards.
Fakes don't actually hurt the game. Just print out whatever cards you want and play with them, nobody is hurt and you don't pay usury prices to a company literaly printing money.
The idea is more for collecters, get something hard to clone that supports public key crypto like the more recent NXT miifare cards. Program them with a unique number and key each and you could do remote verification that someone holds the card in question. Registries of card location etc. hell if you are clever you could invent a little database and state machine to load on the card to store it's values and logic in electronic access form.
It must be possible to have flexible paper-like cards because my city has one-time tickets with NFC. Game would be nicer with card stock and not rigid plastic.