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In the game of Go (Wei Qi/Badouk), hoshi is the Japanese word for the points on the goban (board) marked with a small, round dot. These points are sometimes known as star points in English (since hoshi is, literally, "star" in [Japanese[), but the Japanese word is used equally, if not more frequently.

There are nine hoshi on a standard 19x19 goban - one at the 4-4 point in each corner, one in the middle of each side (10-4 point), and one in the center (known as tengen, or the 10-10 point). On the board below (as on the board for all my recent and future Go writeups, although I think I may have used a comma instead in some of the early ones), the hoshi are marked by plus signs.

   a b c d e f g h j k l m n o p q r s t 
19 . . . . . . . . . . . . . . . . . . . 19
18 . . . . . . . . . . . . . . . . . . . 18
17 . . . . . . . . . . . . . . . . . . . 17
16 . . . + . . . . . + . . . . . + . . . 16
15 . . . . . . . . . . . . . . . . . . . 15
14 . . . . . . . . . . . . . . . . . . . 14
13 . . . . . . . . . . . . . . . . . . . 13
12 . . . . . . . . . . . . . . . . . . . 12
11 . . . . . . . . . . . . . . . . . . . 11
10 . . . + . . . . . + . . . . . + . . . 10
09 . . . . . . . . . . . . . . . . . . . 09
08 . . . . . . . . . . . . . . . . . . . 08
07 . . . . . . . . . . . . . . . . . . . 07
06 . . . . . . . . . . . . . . . . . . . 06
05 . . . . . . . . . . . . . . . . . . . 05
04 . . . + . . . . . + . . . . . + . . . 04
03 . . . . . . . . . . . . . . . . . . . 03
02 . . . . . . . . . . . . . . . . . . . 02
01 . . . . . . . . . . . . . . . . . . . 01
   a b c d e f g h j k l m n o p q r s t 

The main purpose of hoshi is for reference, to make it easy to determine where stones are on the board. 19x19 is a fairly big grid, and if there were no hoshi, it would be difficult to tell at a glance where a stone was on, say, the 9-6 point and the 9-7 point. They also serve as the points on which handicap stones are placed, in a game between players of different skill levels.

During the first few moves of the game (fuseki), however, hoshi has a slightly different meaning, referring solely to the corner 4-4 points and, more specifically, to a stone played there as a first move in a given corner.

There are essentially only five commonly played opening moves (six, if you count tengen, but that's rare). The board is symmetric and initially empty, so there are actually 24 such points, eight in each corner (one san-san, one hoshi, and two each of komoku, takamoku and mokuzuhashi), but from the point of view of the first move, all corners are equivalent and the pairs of off-diagonal plays in a given corner are equivalent as well. The standard etiquette for Black on his first move is to play in the far right corner, from his point of view. If playing an off-diagonal move, it should be on the right side of the diagonal. In the diagram below, the Black stone (X) marks hoshi, the move being discussed, while the points marked "o" are other more-or-less common first moves.

   a b c d e f g h j k l m n o p q r s t 
19 . . . . . . . . . . . . . . . . . . . 19
18 . . . . . . . . . . . . . . . . . . . 18
17 . . . . . . . . . . . . . . . . o . . 17
16 . . . + . . . . . + . . . . . X o . . 16
15 . . . . . . . . . . . . . . . o o . . 15
14 . . . . . . . . . . . . . . . . . . . 14
13 . . . . . . . . . . . . . . . . . . . 13
12 . . . . . . . . . . . . . . . . . . . 12
11 . . . . . . . . . . . . . . . . . . . 11
10 . . . + . . . . . + . . . . . + . . . 10
09 . . . . . . . . . . . . . . . . . . . 09
08 . . . . . . . . . . . . . . . . . . . 08
07 . . . . . . . . . . . . . . . . . . . 07
06 . . . . . . . . . . . . . . . . . . . 06
05 . . . . . . . . . . . . . . . . . . . 05
04 . . . + . . . . . + . . . . . + . . . 04
03 . . . . . . . . . . . . . . . . . . . 03
02 . . . . . . . . . . . . . . . . . . . 02
01 . . . . . . . . . . . . . . . . . . . 01
   a b c d e f g h j k l m n o p q r s t 

Hoshi is the most balanced of the possible opening moves, slightly favoring influence over territory (san-san and komoku are more territorial), but not as much so as takamoku, while also lacking the directionality of mokuzuhashi. As such, it is also the most commonly played opening move, suitable for almost any strategy or style.

A common misconception by beginners is that hoshi takes corner territory. In fact, it does not guarantee any direct territory at all. If Black plays a hoshi stone, White can easily invade at san-san and take all the corner territory, as shown in this diagram (now showing only a quarter board):

k l m n o p q r s t 
. . . . . . . . . . 19
. . . . . 9 8 a . . 18
. . . . b . 1 O . . 17
+ . . . . . X 2 . . 16
. . . . . . . 3 4 . 15
. . . . . . . 5 6 . 14
. . . . . . . 7 . . 13
. . . . . . . . . . 12
. . . . . . . . . . 11
+ . . . . . + . . . 10

This is the most common joseki (standard corner pattern) for a san-san invasion of an unsupported hoshi. White invades under the black hoshi (X) at san-san (O). Black blocks at 1 (notice that the position until now is symmetric so Black could also block at 2 and the diagonally mirrored image of this would result - this is an important choice, to be based on analysis of the rest of the board). White pushes at 2, Black plays hane at 3, White keeps pushing at 4, more pushing ensues at 5,6 and 7. White plays hane at the other end at 8, Black blocks at 9, White connects at a and Black protects his cutting point at b. Final position:

k l m n o p q r s t 
. . . . . . . . . . 19
. . . . . X O O . . 18
. . . . X . X O . . 17
+ . . . . . X O . . 16
. . . . . . . X O . 15
. . . . . . . X O . 14
. . . . . . . X . . 13
. . . . . . . . . . 12
. . . . . . . . . . 11
+ . . . . . + . . . 10

As can be seen, White has all the territory (totalling maybe 10 points) and Black has none. A beginner, once learning that the san-san invasion can't be stopped (without local support), might begin to think hoshi is bad for this reason, and stop playing it. However, an experienced player realizes that this sequence is not, in fact, good for White. Black does not take any territory, but gets a very strong wall on the outside, whose influence is worth considerably more than the territory White takes in the corner.

If immediate san-san invasion is generally not good for White, though, how should White deal with a hoshi stone? And what should Black's ideas for development be?

First of all, it is important to realize that because it lies on the line of symmetry, until the board develops further, play on one side or the other of the stone can be considered more or less the same. Thus, it is not particularly urgent for either player to play here early in the game - approach moves (kakari) and enclosures (shimari) will usually (not always) be played in corners containing komoku, takamoku or mokuzuhashi stones before either player does anything about san-san or hoshi stones.

For Black, it's most common to let White make the first move against a hoshi stone, playing moves towards the center of the sides adjoining the hoshi instead, but if Black has nothing better to do, the usual idea to build an enclosure using a hoshi stone is a keima or ogeima (small or large knight's move) to one of the points shown by asterisks here:

k l m n o p q r s t 
. . . . . . . . . . 19
. . . . . . . . . . 18
. . . * * . . . . . 17
+ . . . . . X . . . 16
. . . . . . . . . . 15
. . . . . . . * . . 14
. . . . . . . * . . 13
. . . . . . . . . . 12
. . . . . . . . . . 11
+ . . . . . + . . . 10

As for White, when approaching the hoshi stone, the most common move by far is the small knight's approach shown by the white stone (O) below. It is approximately ten times more common than, say, the high approach at the point "c."

k l m n o p q r s t 
. . . . . . . . . . 19
. . . . . . . . . . 18
. . . b B . . . . . 17
+ . . . b . X . . . 16
. . . . . . . d . . 15
. . . . . . c O . . 14
. . . . . . . . . . 13
. . . . . . a A . . 12
. . . . . . a a . . 11
+ . . . . . a a . . 10

The usual idea for Black is to pincer at one of the points marked "a" below (capital "A" being the most common), trying to prompt White into invading san-san and letting Black build a wall facing to the left (where Black should be aiming at building a moyo (territorial framework). If this isn't good for Black (because he can't put strength facing to the left to effective use, or because White is strong near the lower center of the right side, and can jump out and counterattack the pincer stone instead of invading san-san), Black can make an extension to one of the points marked "b" (capital "B" being the most common), which will generally result in a safe group and a small amount of secure territory for both players. The contact move at "c" is sometimes seen (giving White territory and security on the right, and territory in the corner and influence along the top for Black). The diagonal contact move at "d" is playable if Black already has a stone at one of the points marked "a" (for instance, if Black pincers and White plays elsewhere instead of answering), but is a mistake if no such Black stone is present.

As mentioned above, hoshi is a very balanced move and the most popular first move for both Black and White. Many of the common fuseki (e.g. san-ren-sei, Chinese fuseki and orthodox fuseki) involve a hoshi stone. If I had to state one single "purpose" for a hoshi play, it's to try to force the opponent to invade san-san and use the resulting wall to build a moyo. However, it's mostly just a general-purpose play that can be later incorporated into whatever sort of strategy the player tries to put into action, depending on how the game develops.

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