There are Black and White.

There are stones.

There are lines.

Definitions 1

A player is one of Black and White.

A black-stone / white-stone is a stone of Black / White.

The grid consists of 19 horizontal and 19 vertical lines.

An intersection is a place of the grid where a horizontal line meets a vertical line.

Two intersections are adjacent if there is a line but no third intersection between them.

A position is the distribution of black-stones and white-stones on the grid's specific intersections.

A black-string / white-string is an intersection with a black-stone / white-stone on and, recursively, any adjacent intersection with a black-stone / white-stone on.

A string is either a black-string or a white-string.

A liberty of a string is an empty intersection adjacent to at least one of the string's intersections.

Move

A play

• puts one stone of a player on an empty intersection,
• {capture} then removes the stone(s) of any opposing string(s) without liberty, and
• {no suicide} thereby creates a position in that each string has a liberty.

A move is either a play or a pass.

Alternating-sequence

The alternating-sequence is a sequence of moves that

• starts by Black from the empty grid,
• lets the players alternate moves,
• ends with the pass that succeeds a pass,
• {basic-ko} does not include a play that recreates the position just before the last opposing move,
• {long-cycle-tie / long-cycle-win} exceptionally and immediately after a play lets the game end with the result tie / win of Black / win of White if the position just after the play is the same as a position just before an earlier move and if the number of white-stones minus the number of black-stones that have been removed during plays since the first occurrence of that position is equal to / greater than / smaller than zero, and
• {direct-ko} does not include a pass that succeeds a pass if then a final-string were capturable-3.

The final-position is the position just after the alternating-sequence's ending pass.

A final-string is a string in the final-position.

A ko consists of two adjacent intersections so that a play on one of them succeeded by a play on the other one would recreate the position.

A ko-stone is a string on one intersection of a ko.

A ko-capture is a play that is in a ko and removes exactly one stone.

A ko-pass by a player is announced as "ko-pass" if a ko-capture by the player in some ko is currently available but prohibited.

A hypothetical-move is either a play, a ko-pass, or a pass.

Hypothetical-sequence and Hypothetical-strategy

For a given player, a hypothetical-sequence is an imagined sequence of hypothetical-moves that

• starts from the final-position with the given player,
• lets the players alternate hypothetical-moves,
• either has a finite number of hypothetical-moves and ends with the pass succeeding a pass or has an infinite number of hypothetical-moves and does not have a pass succeeding a pass, and
• {hypothetical-ko:} between a player's ko-capture on one intersection of a ko and the next ko-pass by him or his opponent does not include an opponent's ko-capture on the other intersection.

A player's hypothetical-strategy is a set of one or more than one left-parts of hypothetical-sequences so that

• each left-part starts with a hypothetical-move of his,
• each left-part ends with a hypothetical-move of his,
• there are not two left-parts so that they without their last hypothetical-move are equal, and
• the above is not true for the set together with any left-part not in the set.

A player can force something if there is at least one hypothetical-strategy of his so that each compatible hypothetical-sequence fulfils that something.

Life and Death

A player's final-string is uncapturable if the opponent cannot force capture of its stones.

A permanent-stone is a stone that is played during a hypothetical-sequence and then not removed during the rest of the hypothetical-sequence.

For a final-string, local-1 is all the string's intersections.

A player's final-string is capturable-1 if

• it is not uncapturable and
• the opponent cannot - with the same hypothetical-strategy - force both capture of the string's stones and no local-1 permanent-stone of the player.

A player's final-string is capturable-2 if

• it is neither uncapturable nor capturable-1 and
• the opponent cannot - with the same hypothetical-strategy - force both capture of the string's stones and no local-2 permanent-stone of the player.

A final-string is capturable-3 if

• it is a capturable-2 ko-stone and
• its local-2 and local-3 are unequal.

• uncapturable,
• capturable-1, or
• capturable-2.

Hypothetical-analysis

The hypothetical-analysis assigns either alive or dead to each final-string.

Definitions 3

In the final-position, a black-eye-string / white-eye-string is an intersection that is empty and, recursively, any adjacent intersection that is empty or occupied by a stone of a dead white-string / black-string.

In the final-position, an intersection of a black-eye-string / white-eye-string is a black-eye-point / white-eye-point if the black-eye-string / white-eye-string is adjacent and only adjacent to intersections with stones of one or more than one alive black-strings / white-strings.

In the final-position, an eye-point is either a black-eye-point or a white-eye-point.

In the final-position, a dame is an empty intersection that is not an eye-point.

In the final-position, a black-region / white-region is an intersection with a stone of an alive black-string / white-string and, recursively, any adjacent intersection that has a stone of an alive black-string / white-string or is a black-eye-point / white-eye-point.

In the final-position, a black-region / white-region is in-seki if at least one of its intersections is adjacent to a dame.

In the final-position, an intersection is black-territory / white-territory if it is a black-eye-point / white-eye-point that is not part of an in-seki black-region / white-region.

The prisoner-difference is the number of white-stones minus the number of black-stones that are removed during the alternating-sequence.

In the final-position, the score is

• the number of empty intersections that are black-territory
• plus twice the number of not empty intersections that are black-territory
• minus the number of empty intersections that are white-territory
• minus twice the number of not empty intersections that are white-territory
• plus the prisoner-difference.

The result is

• a tie / win of Black / win of White if the alternating-sequence ends and the score is equal to / greater than / smaller than zero or
• given due to the rules about long-cycle-tie / long-cycle-win.

The game consists of the following in the given order:

• 1. the alternating-sequence
• 2. the hypothetical-analysis
• 3. the result

Copyright

• The rules text is under copyright according to international and national law. The author Robert Jasiek is the copyright owner.
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• The author is grateful for suggestions of improvement whereever practical application of the rules should behave unexpectedly.
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