# A problem by Sreejato Bhattacharya

Calvin and Lino play a modified game of Nim. First, they randomly choose a positive integer \(n\) between \(10\) and \(100\) (inclusive). They then take a pile of stones having \(n\) stones. The players take turns alternatively removing a certain number of stones from the pile. The rules are:

At the first move, the first player removes a positive integer number of stones, but he cannot remove \(10\) stones or more.

At the consequent moves, each player has to remove a positive integer number of stones that is at most \(10\) times the number of stones removed by the other player in the last turn.

The player who removes the last stone wins.

Calvin goes first. Assuming each player plays optimally, the probability that Lino wins the game can be expressed as \(\dfrac{a}{b}\), where \(a, b\) are positive coprime integers. Find \(a+b\).

**Details and assumptions**

At each move, a player has to remove a **positive** number of stones. Removing nothing from the pile isn't considered as a valid move.