Traditionally, the game of Rock, Paper, Scissors is played with two people. Each of the two people, on the count of 3, reveals their hand in the shape of a rock, a piece of paper, or a pair of scissors as best they can (usually with a closed fist, a flat hand, or their index and middle fingers outstretched to form the V of an open pair of scissors). As the rules go, rock smashes scissors, paper covers rock, and scissors cuts paper. The game can be extended to an arbitrarily large number of, say, nn people, where nn is greater than or equal to 2. If when all nn people reveal their play and only 1 or all 3 options appear, that round is deemed indecisive and they just play again. If when all nn people reveal their play precisely two of the three options appear, that round is decisive, and those with the winning play continue while those with the losing play are eliminated. Play continues until only one person remains. Assuming threethree initial players, determine the expected number of rounds needed until a winner is declared. Express your answer to two decimal places.
Traditionally, the game of Rock, Paper, Scissors is played with two people. Each of the two people, on the count of 3, reveals their hand in the shape of a rock, a piece of paper, or a pair of scissors as best they can (usually with a closed fist, a flat hand, or their index and middle fingers outstretched to form the V of an open pair of scissors). As the rules go, rock smashes scissors, paper covers rock, and scissors cuts paper.
The game can be extended to an arbitrarily large number of, say, nn people, where nn is greater than or equal to 2. If when all nn people reveal their play and only 1 or all 3 options appear, that round is deemed indecisive and they just play again. If when all nn people reveal their play precisely two of the three options appear, that round is decisive, and those with the winning play continue while those with the losing play are eliminated. Play continues until only one person remains.
Assuming threethree initial players, determine the expected number of rounds needed until a winner is declared. Express your answer to two decimal places.
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