I was reading this paper that analyses some strategies of the game dots and boxes. To understand this concept I tried to apply some of the techniques used in the paper to other games such as noughts and crosses.
For example: in the game dots and boxes you may represent a board by the notation of $G$ (game) = $H$ (the moves played previously) $+ 3 + 4$ where $3$ and $4$ are "chains" that is to say rows of unfilled boxes on the grid. Extending this you can prove that certain moves are optimal in certain circumstances by looking at the value $v(G)$ of certain moves.
How could you use these principles to show for example that an optimal move on a noughts and crosses game is to start by playing in one of the corners.