Let's create a card game with any number of red and black cards.
First I'm creating any number of decks containing chosen number of red or black cards. I shuffle them.
Then I want to draw N cards from the decks I've created. I can draw multiple cards from one deck, but I cannot peek the cards I'm taking, nor look inside those decks while drawing. However after every draw I can add any number of red or black cards to a deck (and shuffle) and/or remove any number of cards from that deck (at random, without peeking).
The goal is following: for given N cards make sure, that the probability of drawing exactly X red cards is the same for every $X: X \in <0, N>$
For N = 4, I'm drawing 4 cards and I want to be sure that I have 20% chance to get zero red cards, 20% chance to get one red card, 20% chance to get two red cards ... and 20% chance to get four red cards.
What is the proper strategy to create decks and modify them while drawing to achieve this goal?