Probability Basicshard
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Two players, Alice and Bob, take turns rolling a biased six-sided die. Alice rolls first. A player's turn consists of rolling the die. On any single roll: the player wins immediately with probability , the player retains their turn and rolls again with probability , and the player loses their turn (passing the die to the other player) with probability . The game continues until one player wins. What is the probability that Alice wins the game?
Two players, Alice and Bob, take turns rolling a biased six-sided die. Alice rolls first. A player's turn consists of rolling the die. On any single roll: the player wins immediately with probability , the player retains their turn and rolls again with probability , and the player loses their turn (passing the die to the other player) with probability . The game continues until one player wins. What is the probability that Alice wins the game?