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.
And would have to use fancy ones as cheap ones have no security
...well unless you run official tournament and want people to stop using fakes there but that's more a thing Games Workshop would do for miniatures.
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.