What is the largest key size that could be carried by a shuffled deck of playing cards? If you are carrying a standard 52 card pack of cards (no jokers) what is the largest key size, or the amount of data the cards can hold?
Without the cards being marked or distinguishable from an identical pack, but some cards may be placed in the deck upside down.
Any set of $N$ distinguishable objects can be permuted in $N!$ different ways, thus giving you the ability to represent $N!$ different keys, resulting in a representable keylength of $\log_2(N!)$ bits. For $52$ distinguishable playing cards, this would be $\approx 225$ bits.

However with the additional property, that each object can have two distinguishable states -- a card can be face up or face down in the deck -- we can encode one additional bit of Information per card, since for each permutation there are $2^N$ different configurations. For your $52$ playing cards with the two states "face up" and "face down" you can thus represent $52!\cdot 2^{52}$ many keys, or a key length of $277$ bits.