In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?
Forty.
The number of decks is irrelevant; the answer is the same if one or one-hundred decks are used.
Any card drawn will be a A,2,3,4,5,6,7,8,9,10,J,Q, or K, so there are 13 possibilities each time a card is drawn.
The fastest way to draw a four of a kind is if the first four cards all have the same 'value.' The slowest way, which provides the solution, is to first draw 13 three of a kinds, and then one more card.
Since 13 x 3 + 1 = 40, if 40 cards are drawn it is guaranteed that those forty cards contain at least one four of a kind.
