Which Alice?

Tweedledum or Tweedledee?
"Not necessarily" was the reply. "Each time we go into the house,
the game begins afresh, and we are at liberty to change our cards or
not."
"I understand," said Alice.
ROUND TWO The brothers then went into the house, and,
shortly after, one emerged with a card in his pocket and said, "If I
am Tweedledum, then I am not carrying a red card."
Alice found this considerably more difficult than the first puzzle,
but she finally managed to solve it. What is the solution?
RO UND THREE In this round, a brother came out and
said, "Either I am Tweedledum, or I am carrying a black card."
Who was he?
ROUND FOUR In this round, a brother came out and said,
"Either I am Tweedledum carrying a black card, or I am
Tweedledee carrying a red card." Who was he?
ROUND FIVE This time, the brother who emerged said,
"Tweedledum is now carrying a black card."
Who was he?
"Very good!" he said to Alice. "You solved that one very nicely!
Now, the last round of this game is more complicated: I go into the
house, and my brother and I go into a huddle, and then both of us
emerge, each with a red or a black card in his pocket. Our cards
"might be of the same color, or of different colors. Then we both
77