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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