I'm a professional card counter, i developed a software that let me count cards in Blackjack very easily, and now i'm trying to implement an algorithm that lets me see all the probabilities of one card to show up from the deck, let me be more clear, having a text file like this that contains all the cards that left the deck in succession:
244QJX966AK37A... and so on
i should be able to see all the odds of drawing a certain card.
The problem is that i don't know the mathematical approach to this problem. Thanks in advance to all those who want to contribute. I also posted a question on Stack Overflow where i will post the code after knowing all i need.
The simple formula is that if you have a particular card $c$ in mind, then the probability that the next card dealt will be a $c$ card is
$$\frac{\text{number of $c$ cards remaining in the shoe}}{\text{total number of cards remaining in the shoe}}.$$
If there are any face-down cards on the table (or in the discard tray) that nobody has looked at, then those cards need to be treated as though they were still in the shoe.
If the dealer has peeked at his hole card in order to check for a blackjack, then things get a little more complicated. I don't have the formula off-hand.
Does this answer your question?