Do You Want to Build a Snowman

On a snowy afternoon, your friend Ajay came to your house with a large pile of snowballs. You both were bored and it was freezing outside. So, you two decided to play a game. Suppose, initially there are $n$ snowballs in the pile. You get the first turn and take at least one snowball from the pile if it is possible by rules. Then Ajay has his turn to also take some snowballs. However, there are so