4 friends make up a card drawing game on an evening filled with boredom. They make up random rules. Arun decides that if they all draw red cards, they will gain 1 star each, and if they all draw black cards, they will lose 1 star each. Dipak decides to complicate the game and says, if three of them draw red cards, then three of them lose one star each, while the person who gets the black card gains 3 points more complex by saying if they draw black and red cards in equal numbers, the ones who draw red cards lose 2 stars each, while those who draw black cards will gain 2 stars each. Charu also contributes to the rule book by saying, if they draw three black cards and one red card, then the player with the red card loses 3 stars, while the others gain one star each. After creating this massive rule book, they get to play several rounds. The game takes its own twists and turns.
1. At the end of three rounds, Arun has 6 stars, Dipak had scored 2 stars, Bankim and Charu both are in debt of -2 stars each.
2. At the end of six rounds, Arun had 7 stars, and everyone else is in debt. Bankim and Dipak have a debt of 1 star each, and Charu is now in debt of 5 stars.
3. Dipak’s star collection in the third round was less than his collections in the first round but was more than his collection in the second round.
4. In exactly two out of the six rounds, Arun was the only player who drew a black card.
In how many rounds did all four players make identical bids ?
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