Can you come up with a pseudorandom order for a deck of cards?

There are many ways to order a deck of 52 cards such that one would know the exact position of every card. The most obvious would be a standard new-deck-order, with Ace through King of every suit one after the other. However, I request of you, dear reader, to try to come up with such an algorithm that makes the deck "look" very random in the statistical sense, barring some 'loose' conditions:

1. The algorithm should truly be some sort of mathematical algorithm - it should require minimal rote-memorization.
2. One should be able to apply the algorithm to deduce the position of any card and the card given any position.
3. This algorithm should be simple enough that one can apply it one's own head and take, say, less than 10 seconds or so to compute.

The current best stack I've found is something known as the "Breakthrough Card System", however while algorithmic, (and very pretty), it unfortunately lacks an 'nth formula', so to speak. i.e., if you wanted to know what the 37th card was, you'd have to know the 36th, and so on.

I sincerely apologize for the lack of precision in my request. It is hard to be precise about statistical concepts of which I have no bearing. All I have seen are other 'stacks' of cards that either do not look random, or don't have a simple enough algorithm.

• Since 52 is twice 26, you could assign letters to each card, upper case for red, lower fit black, and now take any two sentences that use every letter exactly once.
– lulu
Commented Apr 24, 2023 at 19:04
• Exactly once is probably unreasonable... So use the standard phrases that use each letter at least once and have some rule to handle repeats.
– lulu
Commented Apr 24, 2023 at 19:07
• I like lulu's idea. So, as a starting point, googling "sentence with every letter" gives : "quick brown fox jumps over the lazy dog". Then, one way to complete the algorithm would be to identify-mentally-exclude repeated letters in the quoted sentence. Then, you would have to find a 2nd, similar sentence. Then, you would have to find some easy to remember rule that indicates which Capital Letters come from which of the two sentences. Then, you would have to learn/memorize which cards $~\longleftrightarrow~$ which capitalized/uncapitalized letters. Commented Apr 24, 2023 at 19:23
• A defect of my approach is that you also need to "randomize" the colors. Taken literally, mine would have all red first, then all black. Need a simple way to mix those up.
– lulu
Commented Apr 24, 2023 at 19:28
• To decide on which cards are red/black, I thought perhaps if the position of the card is a prime/square/cube/fifth power number, it's red, otherwise it's black. e.g. the 36th and 37th cards are red, but the 38th is black. Only issue with this is that the reds/blacks are split 25 to 27. Commented Apr 25, 2023 at 3:57