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Omni-MATH / Allen and Brian are playing a game in which they roll a 6-sided die until one of…

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problem

Allen and Brian are playing a game in which they roll a 6-sided die until one of them wins. Allen wins if two consecutive rolls are equal and at most 3. Brian wins if two consecutive rolls add up to 7 and the latter is at most 3. What is the probability that Allen wins?

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