Randomized strategies for the plurality problem Original Research Article

We consider a game played by two players, Paul and Carol. At the beginning of the game, Carol fixes a coloring of image balls. At each turn, Paul chooses a pair of the balls and asks Carol whether the balls have the same color. Carol truthfully answers his question. Paul’s goal is to determine the most frequent (plurality) color in the coloring by asking as few questions as possible. The game is studied in the probabilistic setting when Paul is allowed to choose his next question randomly.