Local play
A local move in the game of Hex is a move that is aimed at restoring the connections threatened by the opponent's last move. These types of moves are often made in response to an opponent's intrusion into a player's group or template. For example, if the opponent places a stone in a key empty cell that is necessary for a player's group to maintain its connection, the player's response would be a local move that restores that connection.
Playing local moves is referred to as local play and it is an important aspect of Hex strategy. By making local moves, a player is able to defend their position and maintain control of one area of the board. This type of play is often used to maintain a crucial connection.
On the other hand, the opposite of local play is to play elsewhere, also known as tenuki. Tenuki refers to a strategy where a player chooses to not respond to the opponent's last move and instead focus on other areas of the board. This type of play can be useful for creating new groups or chains, creating outposts that will be useful later, and for exploiting weaknesses in the opponent's position.
Overall, local play and tenuki are both important strategies in Hex and understanding when to use each can be crucial for success. Local play allows players to maintain control and defend their position, while tenuki allows players to create new opportunities and exploit their opponent's weaknesses.