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Omni-MATH / Tim and Allen are playing a match of tenus. In a match of tenus, the two players…

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problem

Tim and Allen are playing a match of tenus. In a match of tenus, the two players play a series of games, each of which is won by one of the two players. The match ends when one player has won exactly two more games than the other player, at which point the player who has won more games wins the match. In odd-numbered games, Tim wins with probability 3/43 / 4, and in the even-numbered games, Allen wins with probability 3/43 / 4. What is the expected number of games in a match?
Plain-text mathematical notation (without MathML)
Tim and Allen are playing a match of tenus. In a match of tenus, the two players play a series of games, each of which is won by one of the two players. The match ends when one player has won exactly two more games than the other player, at which point the player who has won more games wins the match. In odd-numbered games, Tim wins with probability 3/4, and in the even-numbered games, Allen wins with probability 3/4. What is the expected number of games in a match?
Original LaTeX notation
Tim and Allen are playing a match of tenus. In a match of tenus, the two players play a series of games, each of which is won by one of the two players. The match ends when one player has won exactly two more games than the other player, at which point the player who has won more games wins the match. In odd-numbered games, Tim wins with probability $3 / 4$, and in the even-numbered games, Allen wins with probability $3 / 4$. What is the expected number of games in a match?

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task_id
3a424fb3-2119-5645-81d8-b2bb1ea3bf23
task_key
test--3a424fb3-2119-5645-81d8-b2bb1ea3bf23
task_revision_id
1
config / split
/ test

Official source

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