Calling out integers

Two players \(A\) and \(B\) are playing a game. They take turns and call out an integer during their turn. The first player to call out \(50\) wins. They must follow these rules :

  • The first player \(A\) must call out an integer in \([1,10]\).

  • A new integer called out must exceed the most recent integer called, by at least 1 and by no more than 10.

Which player always has a winning strategy ?

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