You might argue that it is not fair that black won the instruction game because he had the advantage of moving first. You are right about that. That's why the white player receives compensation for the fact that he moves second. This compensation is called komi (Japanese). Remarkably enough, the komi hardly depends on the boardsize. According to Japanese professional Go players the komi should be 5½ points for the boardsizes 9x9, 13x13 and 19x19. In the instruction game we played on a 7x7 board. Let's assume that the komi would still be 5½ points, then white would have won the above game with ½ point, the smallest margin possible.

Note 1: The amount of komi can differ between countries. It can even differ between tournaments. Basically, it is up to the organiser to decide with exactly how much komi the game is played.

Note 2: The fact that the komi includes half a point (5½) ensures that the game can't end in a draw.