Could you possibly make a wallet using a deck of cards? There are an insane amount of combinations possible, and you could at least just make a brainwallet by putting in the cards in order. Then you can just keep the deck in that order to save it.
52 different cards, thoroughly shuffled, and I mean thoroughly, would get you 225 bits of entropy. More than you really need for a secure key.
Let's say you chose twenty cards randomly from a full deck of 52, and throw away the leftover cards. Now you have twenty objects chosen randomly from a set of 52.
Adopting the strategy in your post, we preserve the order of the cards -- so we can treat this as an ordered set. There are 52 possibilities for the first card, 51 possibilities for the second card, and so on. So the number of possible twenty-card ordered decks is 52 factorial divided by 32 factorial. (Assuming complete randomness in the selection.) If you have a thoroughly shuffled 52 card deck, you can just take the top twenty cards, in order, and go with that.
Type "52!/32!" (without the quotes) in the Google search box and it tells you the answer is 3.065 x 10^32. This is the entropy, but you want it expressed as a power of two, so
2^x=3.065x10^32 solving x = 107.9 bits of entropy
That's generally accepted as enough passphrase strength for today's computers and some decades into the future. If you want a stronger password use more cards and recalculate. If you add just one more card, it will garner you exactly 5 bits more entropy, because it is chosen from exactly 32 leftover cards, and 2^5=32.
Thus 21 cards gives 112.9 bits of entropy. Each card you add after that will add entropy, but not as much.
Okay, that covers the math, the next question is how do you convert a deck of cards into a passphrase. You could convert the ordered cards into a base58 string by assigning a letter or number to each card in any way that seems logical to you, using 52 symbols out of the base 58 set. You convert that string into a key by treating it as your passphrase.
Of course you have to record the numbering scheme you used and store that somewhere, if you ever want to regenerate the passphrase. So you have to keep the deck and a list of the letters and numbers you assigned to the cards. Also, you have to know which end of the deck you're counting from. It would be less work just to write down the passphrase.
So what advantage would you get from using a deck of cards? Keep the cards in one location and the symbols list in another location, I suppose...
Mostly, the utility comes from the ability to get a random string by shuffling cards. The actual storing of the passphrase is another issue that might be solved more effectively by some other method than holding a deck of cards.
