It’s also worth noting that, although that’s all correct as a mathematical matter, as a practical matter:
Playing card decks may not start out shuffled, but in a predetermined order.
Even if immediately shuffled by hand, they are humans, with similar biases, and, although some randomness will certainly come from that, a good deal of non-randomness that people THINK is randomness will also come from it: cutting the deck in half and interleaving a few times, for example.
So it’s quite probable that, for varying levels of shuffled, a shuffled deck may have been duplicated several times.
