Let's say there's a game where person A shuffles a number (D) of decks into a single large deck, and then draws a set number of cards (N) from that deck, face down onto a table.
Person B is then supposed to guess which cards are on the table. The order doesn't matter, but the same card may appear more than once when several decks are shuffled together.
Is there a formula to calculate the odds of person B guessing at least M cards correctly, that works for any number of decks and cards drawn?
Definitions:
- Deck - A normal 52 card deck, four suits of thirteen cards each.
- D - The number of decks combined and shuffled. At least one, no upper limit.
- N - Number of cards drawn from the combined decks. At least one, limited to total number of cards available in decks.
- M - Lowest number of correct guesses for a win. At least 1, at most N.
Example: Person A combines two decks for a total of 104 cards and shuffles them. He then draws 5 random cards: "A♠, 4♥, K♦, 8♣ and K♦".
What are the odds that person B guesses at least four of those cards correctly? If person B guesses "K♦" once that counts as one correct, she has to guess "K♦" twice in order to get them both.