Connect Four

IQ Test Game

Go is a game of territorial capture - the primary objective is to encircle as much territory as possible. In doing so, opposing stones may be captured and the winner is the player at the end with the greatest amount of territory and captured stones.

Basic Definitions and Play
The most essential terms to understand are "group" and "liberty".

A group of stones is any set of stones of the same colour that are connected orthogonally. So three stones in a row along a line forms a group because every stone sits orthogonally next to at least one other stone. However 2 stones next to each other diagonally are not connected in any way and so simply form two groups of one stone each. If a third stone were to be added to the two diagonal stones so that it sat next to both of them, however, a group of three stones would be formed. Groups can get quite large and convoluted but the principle remains the same - if a stone lies orthogonally next to another stone then both stones are part of the same group.

Any empty point orthogonally adjacent to a group of stones is said to be a liberty of that group. A single stone by itself in the middle of the board therefore has 4 liberties, 1 in each of the 4 directions. A group of 3 stones by itself in a line on the edge of the board has 5 liberties - 1 at either end and 3 towards the middle of the board. And a group of 8 stones set in a square by itself has 13 liberties - 12 around the outside and 1 in the middle. But each stone laid by the opponent next to a group reduces the number of liberties by 1. So a single stone with opposing stones North, South and East of it has only 1 liberty.

Go is not only pleasing to the eye, the game itself is also beautifully aesthetic in its simplicity. In fact, in essence there are really only 3 rules to the game:

Starting with black, each player places stones on the board in turn.
When a stone is played so that it causes a group of opposing stones to have no liberties, that group is captured.
A player cannot play a stone to a location if such a play would cause a previous position to be repeated.
So a single stone is captured if the opponent places four stones on the four orthogonal points surrounding it. And a group of 2 stones on the edge of the board is captured by 4 enemy stones.

Eyes - the key to Go
An important point to realise is that a group of 8 stones set in a square is difficult to capture because if the opponent places a stone in the middle of the group, under most circumstances, that stone is immediately captured by the surrounding group. Consequently, no player would ever normally make such a play. The unoccupied point in the middle of the group is an example of an "eye". An eye is any empty point that is surrounded orthogonally by pieces of the same colour - always difficult for an opponent to capture. However, eyes are not impossible to take - the group of 8 stones can be captured by an opponent who first occupies the 12 surrounding points. After this, the group of 8 stones is vulnerable - if the player who owns it plays to the middle of the group, the group of 9 stones would be immediately captured having no remaining liberties. And this is the only situation where it is legitimate for the opponent to play a stone to the middle since in doing so, the last remaining liberty of the group is eliminated and the group is captured. The stone just played would be left surrounded by 4 liberties.

Derived from this is the key factor in Go defence - any group containing two eyes is safe and can never be captured. This should be easy to understand after a moments thought - in order to capture the group all liberties must be eliminated and so both eyes would need to be occupied. But since a stone played to either eye would immediately be captured, it is impossible for both eyes to be occupied. QED.

In conclusion, eyes are useful and a group with 2 eyes is invulnerable.

Other terms
"Ko" is a local situation in which a position can be repeated indefinitely. For an example, lay a white stone on the edge of the board and a black stone three points away from it also on the edge. Lay another white stone diagonally next to the first white stone in the direction of the black stone. Finish the pattern symmetrically by laying a second black stone diagonally next to the first black stone. Now play a white stone on the edge next to both black stones. This situation is Ko. A black stone played to the remaining point in the middle captures the white stone but the white player can then play another white stone back to the same spot capturing the black stone in the same way and putting the position back to how it started. And so on. Of course, due to the third rule above, the black player would not be allowed to do this immediately after the capture of the black stone - at least one stone must be played elsewhere before black could play otherwise the a previous position would be repeated.

"Seki" is another local situation. This term applies to an area into which neither player dare play because to do so would cause the opponent to capture territory or stones.

To have "Sente" is to be in a position to make a move that will force the opponent to take a counter-action. If a player with sente makes the play in question and the opponent, instead of responding in the predicted way, makes a different play with an even greater threat, the opponent is said to have "assumed Sente".

Any group of stones that is under threat of imminent capture i.e. having only one liberty left is said to be in "Atari".

A "dame" point is an empty point between territories. When there is a dame point there is no benefit to either player. Dame points are left alone until the end of the game and then ignored in scoring.

Starting
Go employs a simple and effective handicapping scheme. The weaker player always plays black but also places an amount of stones onto the board before the start of the game according to the amount of the handicap. The board has nine highlighted intersections in a square shape marked on the board called "star" points. The requisite number of stones are placed the star points in the following way:

1 stone handicap - on a corner star point
2 stone handicap - on opposite corner star points
3 and 4 stone handicap - on 3 or 4 corner star points
5 stone handicap - 4 corner + 1 side star point
6 stone handicap - 4 corner + 2 opposing side star points
7 and 8 stone handicap - 4 corners + 3 or 4 side star points
9 stone handicap - all 9 star points.
Beginning the game in Go is both critical and very difficult to do well. Players try to play stones far enough apart so that they form the beginnings of territory encirclements but close enough so that they can be linked up into groups should they come under attack. Initial stones tend to be played near the corners - corners are the easiest places to capture territory because they only have to be surrounded on two sides. Good players will begin by positioning stones seemingly at random across the board but in reality they are staking their claims to particular areas. After this initial period, local skirmishes and larger battles will form in areas of contention. Players need to be able to comprehend and deal with all the smaller conflicts while never becoming distracted from the overall picture of the war.

Finishing
Eventually, the players agree that no more stones can be played since all territory is claimed and all local battles have been played to their conclusion. Play continues until both players agree to this. At this point the winner and the margin of victory is determined. Essentially, each player scores the number of points of territory plus the number of prisoners captured. The totals are unimportant - it is the difference between them that is measured and it is customary to calculate this in a special way.

Firstly, the stones on the board are moved around to form neater patterns, easier for counting. Players do this by sliding stones from one place to another taking care not to change the amounts of territory owned. Some of the black stones will be moved to a different point within black's territory so that the stone's new position reduces the territory by one but the point freed up increases it by one to compensate. White stones similarly. Once this repositioning has been done, all the captured prisoners taken are laid down into enemy territory, again in a neat way to make counting easy. This is done on the basis that losing a point for a prisoner is equivalent to reducing by one the number of points of territory held by the opponent.

Once the board and prisoners have been consolidated in this fashion, the winner and the margin of victory can be quickly determined by a count of the simplified territories.

Since it is generally recognised that black has an advantage by going first, non-handicapped games are often decided as the best of two games with players taking turns to play black. The margins of victory are summed after both games have been completed to determine the winner.