I'm trying to get more into stats and I had a problem that I couldn't wrap my head around.
It's a solitaire card game in which you play 4 hands. Each hand consists of putting 4 cards on the table. There are four unique decks to choose your cards from. The decks are Jack (J), Queen (Q), King (K), and Aces (A), one of each suit.
With each hand, you start by taking a card from the top of one of the decks and place it on the table. Next, you take another card from the top of the deck and place it to the left or the right of the first card. Again, the third card comes off the top of one of the decks, and goes to the left of the other two cards, in the middle of them, or to the right of them. The same thing happens with the fourth card.
You are able to choose the same pile twice in a hand if you like. Here is a sample turn,
Choose from Aces
Table - |A|
Choose from Queens, place to the left of the Ace
Table - |QA|
Choose from Kings, place in the middle
Table - |QKA|
Choose from Queens, place to the right of the King
Table - |QKKA|
So I'm trying to find the number of possible ways to play a game. I know that when playing, you can choose from 4 piles, then place the card in 1, then 2, then 3, then 4 places. That's pretty easy to calculate. But my problem is how to take into consideration the limited size of each deck. If I choose to play all four Aces in the first hand, then I will only have 3 decks to choose from in the next hand.
Any insight would be greatly appreciated.
Sidenote - This is an abstraction of the game "Miracle Merchant" on mobile devices if anyone was wondering what it was based on.