The criticisms began almost at once and most of them were about the cards rather than about the statistics. Early decks were printed on stock thin enough that the symbol could sometimes be made out from the back under good light, and the pressure of the printing could emboss the reverse. Warped or marked edges let a card be identified once seen. A subject facing an experimenter who knew the card could pick up unintended cues from face or voice. Shuffling by hand does not produce the randomness the arithmetic assumes. And a run that is stopped when the results look good, or reported only when they do, will show an effect whatever is happening.
Rhine and his colleagues answered a good part of this: opaque backs, screens between subject and experimenter, separate rooms, mechanical shuffling, predetermined run lengths, independent recording. The pattern that emerged is the one usually cited against the programme, which is that reported effect sizes tended to fall as the controls tightened, and that independent laboratories did not reproduce the striking early results.
Parapsychology largely moved on from card guessing to other designs in the decades that followed. The deck survived as a cultural object instead, familiar from films, television and games to a great many people who could not name the man who made it or say what the fifth symbol is.