I've just listened to the part of the podcast about Zener cards again. I follow most of the way these can generate false positive results but I don't get the bit about "card counting", where the fact that there are (say) only five of each card means that the guesser would have a better chance of being right by knowing there are fewer of a particular card left.
Assuming that the guesser is not told whether they are right at each guess, surely they would not gain any advantage. For instance, if they had already guessed the circle 5 times, it's still 20% likely that a particular remaining card is a circle since the some or all of the 5 existing guesses could be wrong.
Can someone better at stats than I am explain whether this is a real issue (and why), or would it only be a problem if the guesser was told the correct card after each guess?