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Part of 2010 Ukraine Team Selection Test

Problems(1)

game with 2010 red and 2010 white cards

Source: Ukraine TST 2010 p1

5/4/2020
There are 20102010 red cards and 20102010 white cards. All of these 40204020 cards are shuffled and dealt in two randomly to each of the 20102010 round table players. The game consists of several rounds, each of which players simultaneously hand over cards to each other according to the following rules. If a player holds at least one red card, he passes one red card to the player sitting to his left, otherwise he transfers one white card to the left. The game ends after the round when each player has one red card and one white card. Determine as many rounds as possible.
combinatorics