# Dice Trouble

Discrete Mathematics Level pending

Two players $$A$$ and $$B$$ alternately throw two fair six-sided dice. Player $$A$$ wins if he scores 6 points before $$B$$ scores 7 points. Otherwise, player $$B$$ wins. Calculate the probability that $$A$$ wins, knowing that this player starts the game.

If the value of this probability can be written as $$\displaystyle{\frac{m}{n}}$$, where $$m$$ and $$n$$ are relatively prime integers, find $$m+n$$.

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