Where are the points?

I have recently been talking to my students about where the points are on a Go board. At first, this might appear as either blindingly obvious, or possibly even nonsensical. But, if you have not considered this question before, please stick with me, as the answers might surprise you.

Figure 1. First of all, let’s consider a 9×9 board. The one we all most likely started with as beginners. This board contains 81 intersections, or points that are available to the players. In a typical 9×9 game we would expect each player to place somewhere between 25-30 stones. Ignoring captures for the moment, that leaves something in the region of 20-25 points of territory to be shared between the contestants. We call this the rough rule of thirds.

But where are those points?

Figure 2. If we add some green and yellow dots, we can easily see that 56 of the 81 points sit within the first two lines, at the edges and corners of the board. In percentage terms, this means that 69% of the available territory is also there.

On a 9×9 board, 69% of the territory sits
on the first two lines.

Figure 3. And we can see how those numbers play out in a simple 9×9 game. In this match, the total number of moves was sixty-two. Each player captured eight of the enemy’s stones. Black ended up with 19 points of territory, and white with 18 points. So, with a Komi of 5.5, white won by 4.5 points. Notice how all the territory is at the sides or in the corners, and the whole of the centre is largely filled with stones. Black has a few points around E3/G4 and G3, as that is where a white group died.

Let’s now continue our analysis and move onto the 13×13 board. As I am sure we are all aware, as we move onto the larger grid, some of the deeper dynamics of the game start to come into play – corner enclosures, joseki moves, side extensions and so on.

Figure 4. Here we have our 13×13 board, and this time, we have 169 points available to our players.

Figure 5. Again, by adding coloured dots to our board, we can again see that 88 of these points or 52% sit on the first two lines. In addition, 120 points, or fully 71% of the board is positioned in the corners or on the first three lines.

So, on a 13×13 board, 52% of the territory sits on the first two lines. Or 71% on the first three lines.

Again, our rough rule of thirds applies. With 169 points available, I would expect each contestant to play somewhere in the region of 55-60 stones. That leaves around 60 points of territory to be divided and shared between the players.

And that indeed is what we see in most 13×13 games.

Figure 6. Finally, let’s take a look at a full-sized 19×19 Goban.

Here we have 361 points available to the players, and the full mind-blowing brilliance of the game comes into play. This board is characterised by its interconnected battles, bloody sieges, encirclements and escapes, and of course, sudden deaths and bitter defeats.

But once again, we have to ask ourselves, where are the points?

Figure 7. This time, we are going to take into account the first three lines and not just the first two. This is because centuries of historical Go theory – joseki and fuseki – has developed around the principles of building corner enclosures, and then extending out along the sides. Even more recent AI Go theory, despite some of its surprises and innovations, has not fundamentally challenged this bedrock strategic principle of Go. And the reason is quite clear. A full 192 of the 361 available points on a 19×19 board, reside again in the corners and along the sides. That translates to 53% of the board.

On a 19×19 board, 53% of the territory sits in the corners or on the first three lines.

And still our rule of thirds holds roughly true. I recently played the game in Figure 8. There were two hundred and seventy-six moves. Black captured five white stones, and white captured six of blacks. The Komi was 6.5 points and the total territory at the end of the game was 94 points. Black won by 2.5.

Again, please note that of those 94 points of territory, 24 of them were in the centre, the rest were held in the corners and along the sides.

So, there we have it. Next time you are in the fuseki, playing your opening moves and unsure as to where to play your next stone. Just remember where the points are; and bring to mind the old Go proverb:

“The corners are golden, the sides are silver, but the belly is straw!”

I hope you have enjoyed the ideas in this article. Have fun and see you across a Goban soon

Robin

Ten Minutes to Go