You and a friend take turns picking numbers. The first player starts by choosing any integer from $1$ to $8$. After that, each player on their turn adds between $1$ and $8$ to the running total. Whoever is the player that makes the total hit exactly $200$ wins. Both players play optimally. You go f…

Counting Game to 200

Game Theory · Medium · Free problem

You and a friend take turns picking numbers. The first player starts by choosing any integer from

$ to $8$. After that, each player on their turn adds between

$ and $8$ to the running total. Whoever is the player that makes the total hit exactly

00$ wins. Both players play optimally. You go first. What number should you pick on your first turn to guarantee a win?