You gave a great description because just searching for "Supernatural 900 year old witch" immediately turned up results confirming that it was a character named Patrick. Then a quick glance at the show's wiki told me Patrick specifically appeared in Supernatural S05E07 entitled "The Curious Case of Dean Winchester." And although I've never actually watched Supernatural myself, I do happen to own an insanely large personal digital media library which includes the complete series... so it was easy enough to pull up that exact episode and skim through it looking for more clues. Below are some of the best screen shots I managed to grab.
The chips are clearly "Paranoid Inlaid" Crest & Seal chips. A quick search here on PCF confirms these were 39.6875mm chips mass produced by the United States Playing Card Company (USPCC) from 1907-1947 and then by Burt Co. for a time into the 1950s. And it was very common, especially in the years before WWII, for these chips to have generic religious and/or ethnic logos on them such as a cross, Star of David, 4-leaf clover, horseshoe, swastika, Fleur-de-Lis, or in your case a star & crescent. There's usually a good amount of chips like these available for sale on
eBay at any given time, although it might take a few purchases in order to build up a large playable set.
Unfortunately, I'm sorry to say that the chips were far easier to identify than those cards. I still do think the cards are paper stock rather than plastic, especially when you look at how warped and faded certain cards appeared to be in various scenes. Next I tried comparing a 39mm poker chip's width against the width of a
that was bridge sized and another poker sized (just like we see in the 3rd picture below). That comparison made me pretty confident that your cards are poker size with a standard index. So we can be fairly confident that they are poker sized paper cards with a standard index and a full-bleed back, but that's about as much as I can tell you. Even multiple Google Lens searches on the best screen grabs I could manage didn't yield any great matches. I think that "carbon fiber" type pattern on the back is just so common on products these days that Google has a hard time matching it to anything exact. Sorry I couldn't be of more help!
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