Conquest using zero walls. Black owns 2 spaces.

Conquest using one wall. Black owns 3 spaces.

Conquest using two walls. Black owns 12 spaces.

The connection points aren't in the same or adjacent quadrants. Black doesn't own anything. Black would need to play at one of the to own the upper-left region.

If Black plays at either , then all of the stones within the region are removed (white and black), and the region is permanently conquered by Black. Note that, since Black has two spaces where he can play, White cannot prevent this from happening.

Odd-Board Conquest

On an odd-numbered board, each of the four "T-bone" intersections—those that are against a wall and in two quadrants at once—may be used as a connection point in either of the quadrants—but not both!

Since the upper-left region is smaller than the upper-right region, the counts for only the upper-left quadrant. Therefore, Black owns only the 9 spaces on the upper left.

If Black plays at the , then Black will gain the remaining 15 spaces in the upper-right region. Then the will be removed, because it is now completely inside the upper-left region. So Black would then own 10 spaces in the upper-left region.

Black may play at the , but doing so will not remove the . The reason is that if the is removed, then Black's only connection points enclosing the upper-left region would no longer be in the same or adjacent quadrants. That would mean Black would lose his entire territory, which is prohibited by the rules.

Bridging

A region is not conquered if you've used three walls as edges of your border. Black doesn't own anything.

Now Black owns 14 spaces, and is not allowed to remove either , because without them, Black wouldn't own anything.

Trying to make an expansion by placing around either is illegal and pointless. It's illegal because you cannot play inside your own territory. It's pointless because Black already owns all of the spaces up there, so there's nothing left to gain.

Expansion

Conquest using your own stones. The is removed, and then Black will own 1 space.

Black may expand his territory by playing at the . Doing so will cause the to be removed, because it will be completely inside the region. Black will go from owning 1 space to owning 2 spaces. Practically, Black could simply slide the down to the .

Re-conquest

White can capture by playing at the . However, if Black first plays at the , then the will become part of Black's territory, and therefore be off-limits for either player.

Even if Black conquers a region, White can re-conquer it by surrounding Black's border. If White plays at the , then all the black stones are removed. Note that the three inner spaces are still off-limits to either player, but they are now owned by White instead of Black.

Salients

If Black plays at the , it doesn't earn him any more points, but it prevents White from playing there. Such a stone is called a Salient. If White plays at the , then white removes the two , thus gaining two points.

Terms

Territory is empty spaces that are conquered by a player.

No-Man's Land is empty spaces that are not conquered by anyone.

Fronts are stones that touch empty spaces, and that are directly helping to enclose (or could eventually help to enclose) regions.

Links are stones that do not help to enclose regions, but rather connect multiple enclosures to each other.

Salients are stones that neither help to enclose nor link, but simply jut out and prevent enemy expansion.

Fortresses are territories that can never be re-captured, because of their intrinsic position and size (not because of linkage). A fortress includes its front.

Bridges are stones that touch only a player's own stones and his own territories. They ensure that a player's territories are legally owned, by keeping the number of walls used below three, or by making sure that the two connection points of each territory are in the same or adjacent quadrants.

Large Conquests

The largest possible "convex" territory can be achieved by enclosing half of the board, but making an "elbow" so that only two walls are used as edges of the border.

The largest possible "concave" territory can be achieved by taking the previous territory and expanding it to the left.

I think that the fullest conquest of the board be achieved by making an incomplete diamond as shown in the image. Black has conquered 51 spaces here. If someone can conquer even more, please replace this image with yours!

Example Endgame

White wins 144-113. There are no more legal moves. Things to note:

• White cannot remove its Bridges at either D19 or T11, as either removal would cause White to no longer own the large region in the top right corner.
• White encloses the entire lower left territory by connecting at A18 and R1, and only two walls are used as edges of the white border. However, the two connection points are not in the same or adjacent quadrants, and therefore White does not conquer the entire lower left region.
• Some of Black's stones (e.g. L15) aren't helping to conquer territory, but are preventing White from expanding her boundary any further. Such stones are called Salients.
• Some of Black's stones (e.g. K9) aren't helping to conquer territory, but are protecting Black's inner territories by linking them to outer territories. Such stones are called Links.
• If White's stone at T11 were on T10, then White would no longer own the upper-right corner, because the stone at T10 would only count as being in the lower-right quadrant.
• If Black's stone at A9 were on B9, then Black would no longer own the bottom left territory, because its only two connections (A17 and Q1) wouldn't be in the same or adjacent quadrants.

Pure Conquest

This is an alternative way to score territories. At the end of the game:

1. Remove all Salients.
2. Remove all Bridges.
3. Players expand their territories to fill the resulting No-Man's Land. If certain regions can be filled by both players, then they must divide it as evenly as possible, with preference given to whomever has less points so far.

• Pure Conquest scoring can be significantly different than regular Conquest scoring, so its usage should be agreed upon prior to the beginning of the game. In the above game, it increased White's lead from 31 to 42.
• For example, Black's stone at K9 was not directly enclosing a region, but it was protecting Black's inner regions from being conquered, by linking them to Black's lower region. Therefore, Black's stone at K9 was not removed.

Game Features

• The game ends with a very distilled and polished appearance. Every single stone is critical; none can be removed or added. The borders are as thin as possible. This aesthetic is enhanced with Pure Conquest scoring, making the territories look closer to real-world country borders.
• The game is shorter because more intersections become "off-limits" more quickly.
• It is much easier to enclose using walls, and using two walls is easier than using one.
• Any regions that remain unconnected to a wall will eventually be captured.
• There is an emphasis on making long, unbroken lines.
• It seems more effective to block from a distance than to block directly. This is reminiscent of Hex.
• However, unlike Hex, you can break someone's line if you force them to go diagonal, and then capture one of their stones in the diagonal line.
• There are "races" where players rush to connect to the wall.
• Players might tend to aim for the largest possible territories, since anything smaller can eventually be surrounded.
• Because of the previous point, most of the game will probably be large-scale strategies and attacks, with all the major conquests happening towards the end of the game.
• There don't seem to be any sort of final seki or dame possible, apart from premature passing or resignation.