[jvandonsel]

They seem to be ignoring another useful aspect of a deck of cards. Each card could be placed face-up or face-down in the deck.

[rerdavies]

And another 51 bits of info for whether the picture of the puppy on the back of the card is right-side-up or upside-down! (Or, absent puppies, any other asymmetrical pattern or image that you chose for the message deck).

Because your recipient has to be able to determine the reference orientation of the deck, you get 51 bits of extra information from puppy orientation, and another 50 bits of extra information from face-up/face-down orientation.

To place the deck in correct orientation, in preparation for decoding, ensure that the top and bottom card are face up, and that the puppy on the back of the top card isn't upside-down.

An extra 101 bits of information is significant!

[bombcar]

There’s additional because at least some faces can be rotated - 3 of spades has to have two spades ♠ up and one down or versa-vice.

And some face cards are not mirror images, but that depends on the deck.

[rerdavies]

In an asymmetrical design, the orientation of face carries no extra information, since orientation information is already carried by the orientation of the design on the back.

For decks with a symmetrical back design, the following cards have asymmetrical faces:

- The seven of diamonds.

- The ace, three, five, seven and nine of hearts, clubs and spades.

In my deck (a standard design), none of the face cards are asymmetrical.

So there are sixteen cards that carry orientation information, one of which must be used to define the reference orientation of the deck, yielding 15 additional bits of information.