Never draw a third side
A box with three sides drawn is a gift: your opponent closes it, scores, and moves again. Until the board runs out of safe lines, avoid any line that gives a box its third side.
Before each move, check both boxes the line touches. Border lines touch one box, inner lines touch two.
Count the safe moves
Sooner or later every remaining line gives something away. The player forced to draw the first of those lines is usually the one who loses the big chains.
So the real fight in the middle game is parity: count how many safe lines are left and try to leave an even number when it is your opponent’s turn, so they are the first to run out.
Learn to see chains and loops
A chain is a row of boxes, each with two sides drawn, joined end to end. Whoever opens a chain hands it to the opponent, who can take every box in it. A loop is a closed ring of such boxes and costs less to give away.
Short chains of one or two boxes are the cheapest to open. Long chains are worth fighting for.
Decline the last two boxes
When you are given a long chain, you do not have to take all of it. Take all but two boxes, then draw the line that leaves those two for your opponent. They take them, but they must then move again, and open the next chain for you.
You lose two boxes and keep control. On a long chain that is a bargain, so take everything only when the chain is the last one on the board.
Playing the computer
The Normal computer takes every box on offer and avoids giving away a third side while it can. It does not plan chain parity, so you can beat it by keeping control of the endgame: let it run out of safe lines first, then collect the long chains.