What is the largest key size that could be carried by a shuffled deck of playing cards?
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.