Average dice game

Consider the following game: you can roll a pair of regular dice up to \(4\) times, and after each roll you can either stop and get paid as many coins as the points you scored or roll again the two dice. After the last roll you're obliged to take whatever amount you scored last. Assuming that you're using the best strategy possible, what's your average win?

Details and assumptions

Assuming that your average win is the simple fraction \(\frac{a}{b}\), type the sum \(a+b\) as your answer.

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