How to implement a dealer class without storing a deck of cards?

Question

• Question

  Even only 52 cards, the permutationIndex where I describe in Explanations section, would be a huge number; it is

Answer 1

While I have a bit of a problem understanding what you are really trying to accomplish here, I suppose a coprime will generate a bunch of permutation numbers; that is: if you don't care too much about the distribution. You can use the Euclidian algorithm for that.

Algebra (set theory) states that you can simply use x = (x + coprime) % set.Length to get all elements in the set. I suppose each coprime is a permutation number as you describe it.

That said I'm not sure what distribution you get when using a generated coprime as 'random number generator'; I suppose certain distributions will occur more frequently than others and that a lot of distributions will be excluded from the generated numbers, for the simple reason that the generator will pick numbers in a ring. I'm being a bit creative here so perhaps it fits your needs, although it probably won't be the answer you're looking for.