On card guessing with two types of cards

We consider a card guessing strategy for a stack of cards with two different types of cards, say m(1) cards of type red (heart or diamond) and m(2) cards of type black (clubs or spades). Given a deck of M = m(1) + m(2) cards, we propose a refined counting of the number of correct colour guesses, when the guesser is provided with complete information, in other words, when the numbers m(1) and m(2) and the colour of each drawn card are known. We decompose the correct guessed cards into three different types by taking into account the probability of making a correct guess, and provide joint distributional results for the underlying random variables as well as joint limit laws.