My suggestion was going to be for Bicarbonate Soda, but I see 214 red had the same idea.
It's cheap, you can get it from your local supermarket in the baking aisle. If it was my problem and I was going to try the bicarb, I'd be spreading the cards as best I could on a tray of some sort and sprinkling the bicarb all over them, and every now and then I'd muss them about to ensure that all cards were covered at some point. I'd leave them like this for a day or two, take them out, dust them off, shuffle them up and take a whiff to see whether or not their condition had improved.
If the smell wasn't totally gone but an improvement was detected by your nose-ometer, then I'd repeat the process as necessary till it was all gone.
Worth a try at least I reckon and shouldn't cost you more than a couple of bucks in the attempt. Weigh that up against the cost of replacing smelly decks and it seems worthwhile to me.