Make the cards out of gold/silver/platinum and then use something like vapor deposition to give them a nice coating of diamond. This way they are strong, non-stick and scratch resistant.
[T]he growth of diamond directly on a substrate allows the addition of many of diamond's important qualities to other materials .... Diamond films are being grown on valve rings, cutting tools, and other objects that benefit from diamond's hardness and exceedingly low wear rate .... Diamond's very high scratch resistance and thermal conductivity, combined with a lower coefficient of thermal expansion than Pyrex glass, a coefficient of friction close to that of Teflon (polytetrafluoroethylene or PTFE) and strong lipophilicity would make it a nearly ideal non-stick coating for cookware if large substrate areas could be coated economically.
By regulating the processing parameters—especially the gases introduced, but also including the pressure the system is operated under, the temperature of the diamond, and the method of generating plasma—many different materials that can be considered diamond can be made. Single crystal diamond can be made containing various dopants. Polycrystalline diamond consisting of grain sizes from several nanometers to several micrometers can be grown. Some polycrystalline diamond grains are surrounded by thin, non-diamond carbon, while others are not. These different factors affect the diamond's hardness, smoothness, conductivity, optical properties and more.
However, this may make them very hard to shuffle as they are rigid, but you only said they had to be stack-able, not bendable. In any case you could invent a special machine to shuffle them. This machine could polish up any finger prints, remove any dirt or marker ink, and even check the cards for defects. You may want to give them a matte finish instead of a high gloss one, that way they could hide fingerprints, or some other kind of coating that evaporates fingerprints, otherwise someone could just leave an oily print on a card to mark it. Of course this depends on the nature of the game and if cards are cycled between players without being reshuffled/cleaned.
I envision a shimmering card of transparent diamond, with a intricate pattern of precious metals on the back. Maybe even do different colored diamond layers for the colors.
Something like this this (just for examples sake, I just added the link for the sake of citing the image source)
Basically someone would describe them as mesmerizing and distracting to look at. Make them over the top opulent and extravagant. And who doesn't like cards of precious metal coated/plated with diamond. You could even throw in some holographic properties as well, so something like "foil cards" from some of those collectable card games like MTG or Pokemon (you know the ones).
I just wanted to go for the ridiculously fabulous and expensive answer :-p If it's a high profile high stakes game, part of the fun would be the exotic nature of the cards. So may them something special and flashy.
Preventing counterfeiting is pretty easy. It could be something as routine as the difficulty in making them and their intricate detail. Or you could make the cards worth more then the actual winnings of the game. This way it wouldn't be worth faking them ... ha ha.
slim - Vapor deposition can be on the order of a few atoms thick, if you have the tech for it. The thickness would depend on how strong the underlying "backer" is. You could start with something like titanium, plate that with gold, silver, copper, platinum for the designs. Then cover it with the diamond. Like a lamination.
stackable - check. Although they are not bendable.
marks - they are basically diamond so with the high gloss any scratches would show easy. They are hard, so you would need something harder then diamond to even do the scratching. I'm not sure how hard it is to write on diamond, but if you added enough layers to give it depth, it would look like any marks float above the background, because you would have a under layer of background and several layers of "clear". Similar if you made them somewhat holographic, any marks would stand out like a sore thumb.
card types - is a given and sort of out of the scope of the construction of the card, and more a matter of the specifics of the game.
identical backing - see above.