16,640 electrum, to be exact. (65 x 256)
I had done a lot of T50 farming lately, and some people make relic farms. I kept them all because there have been rumors that there will be a use for them eventually, and I couldn't justify selling them - the electrum yield wasn't high enough.
I assume it rolls over at 1 byte, or 255 -> 0. I definitely had well over 100, didn't think I had over 200 but I guess I hadn't checked in a while. Zanz would have had no reason to make card counts 2-byte... the max reasonable cards for a deck is 59 (if you're insane), and that's just for pillars. For the rest it's 6, or 12 if you're stockpiling stuff to upgrade later. Relics are the one exception, and they don't have a use... yet.