We begin with $2n+1$ cards, each with a distinct number from $-n$ to $+n$ on it, face up in between the two players of the game. The players take turns selecting a card and keeping it. The first player to collect three cards that sum to zero wins the game. If the cards are exhausted and neither player has won, a draw is declared.

Tic-tac-toe, or noughts and crosses, is of course the special case $n=4$.

Has the case of general $n$ been studied?

We begin with $2n+1$ cards, each with a distinct number from $-n$ to $+n$ on it, face up in between the two players of the game. The players take turns selecting a card and keeping it. The first player to collect three cards that sum to zero wins the game. If the cards are exhausted and neither player has won, a draw is declared.

Tic-tac-toe, or noughts and crosses, is of course the special case $n=4$, by using the essentially unique $3\times3$ magic square:

$$\begin{matrix} 3 & -4 & 1 \\\ -2 & 0 & 2 \\\ -1 & 4& -3\end{matrix}$$

Has the case of general $n$ been studied?

We begin with $2n+1$ cards, each with a distinct number from $-n$ to $+n$ on it, face up in between the two players of the game. The players take turns selecting a card and keeping it. The first player to collect three cards that sum to zero wins the game. If the cards are exhausted and neither player has won, a draw is declared.

Tic-tac-toe, or noughts and crosses, is of course the special case $n=7$.

Has the case of general $n$ been studied?

We begin with $2n+1$ cards, each with a distinct number from $-n$ to $+n$ on it, face up in between the two players of the game. The players take turns selecting a card and keeping it. The first player to collect three cards that sum to zero wins the game. If the cards are exhausted and neither player has won, a draw is declared.

Tic-tac-toe, or noughts and crosses, is of course the special case $n=4$.

Has the case of general $n$ been studied?