# A 50 sided die

Alex plays a game in which you have to roll a fair 50 sided die.

Alex's first throw is to determine his game number $$G$$.

If on the second roll he gets his $$G$$ number he wins, if he gets either 1 less than $$G$$ or one more than $$G$$ he loses and if he rolls neither $$G, G-1$$ nor $$G+1$$ he rolls again until he gets one of these 3 numbers.

The game ends when Alex either wins or loses.

What is the probability that Alex will win?

If the probability can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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