If John Skeet can't see the question, you've got something wrong.
I'm not a C# programmer, however, it looks like what you need, is a big fat:
At the bottom of your question, which basically says:
- I don't know how to calculate the permutionIndex
- I need an algorithm which computes one with minimal cost
- I need algorithm(s) which compute(s) the correct permutationIndex to indicate the current sequence of cards
(Essentially, That's just summing up what you've said in the question + some answers to people who wanted clarification)
You may also want to add in with more clarity why you want to do this with this method or some such.
EDIT: What I mean is, you need a summary at the end of your posts to outline the main points of the question. For example, If I posted concerning some algorithm or other, and it was a rather lengthy post, the question can get lost on the background information. What you need to do is just tell the viewers in short what you want to get done. People aren't getting the question, because the question is getting lost in all the information. If you can put a nice clear explanation of what you actually want to get done, it might go a long way.