2006-04-28 newest contents, 2009-01-17 last update, 2006-04-28 first day online, Robert Jasiek
version 3; 2006-04-14 day of the original

Model for the World Amateur Go Championship Rules

In principle, the World Amateur Go Championship 1979 Rules (WAGC79) can be modelled in a design similar to the Japanese 2003 Rules (J2003). However, modelling WAGC79 is significantly more difficult than modelling the Japanese 1989 Rules (J1989). Therefore a formal model for WAGC79 has not been found yet. Here the remaining key problems are described: "alive" and "partially perfect pass".

Alive

The problem to define "alive" for a model of WAGC79 is already solved:

Step 1

WAGC79 tries firstly to define concepts of "eye shapes" and secondly to derive the concept "two eye formation". This approach fails because there are arbitrarily many different "eye shapes" but only one kind of "two eye formation". The inverse order would work: firstly define "two eye formation" and secondly derive all "eye shapes". However, it turns out that concepts of "eye shapes" are entirely superfluous for defining "alive". Therefore a model for WAGC79 should omit all concepts of "eye shapes".

Step 2

The concept "two eye formation" works for so called independent life - but what about so called coexisting life (seki)? J2003 has already provided suitable concepts: uncapturable, capturable-1, and capturable-2.

Step 3

In a position, a two-eye-formation is a set of one or several strings of the same player and exactly two empty intersections so that each of the strings is adjacent to each of the two intersections, none of the strings is adjacent to another empty intersection, and each of the two intersections is adjacent only to the strings.
In a position, a string of a player is two-eye-alive if the opponent cannot force no intersection of the string with a two-eye-formation on.
J2003-alive is defined like in J2003 as either uncapturable, capturable-1, or capturable-2.
In a position, a string is WAGC-alive-in-seki if it is J2003-alive and not two-eye-alive.
In a position, a string is WAGC-alive if it is either two-eye-alive or WAGC-alive-in-seki.
In a position, a string is WAGC-dead unless it is WAGC-alive.

Step 4

Chris Dams has proven:

WAGC-alive equals J2003-alive.

Hence also the terms two-eye-formation and two-eye-alive are superfluous for a model of WAGC79. It suffices to use J2003-alive only. In other words, also for WAGC79 the terms uncapturable, capturable-1, and capturable-2 are the best choice to describe alive.

Partially Perfect Pass

WAGC79 does not simply allow passes but restricts them by restrictions for direct kos, dame, teire, etc. For the researcher, the problem of modelling all this is a nightmare. It is as difficult as finding and defining "capturable-2" in J2003. Even worse, several restrictions have to be considered. The following is a draft for them.

Restrictions

J2003-like direct kos.
Prohibiting possibility of direct kos other than J2003-like direct kos and if local-score-improvement is possible.
Prohibiting possibility of both such a direct ko and its colour-inverse direct ko on the board. Define a local environment to separate both.
Filling of all dame in between independently alive strings.
Filling of all 1-sided or 2-sided dame in sekis.
Removal of prisoners from sekis while maintaining their seki status.
Answer removal of prisoners from sekis while maintaining their seki status.
Prohibiting possibility of surviving invasion in territory.
Prohibiting possibility of surviving invasion under two-eye-alive stones.
Prohibiting the opponent's possibility of score-improvement for the opponent over all the scoring-points in all the player's strict-two-eye-regions considered together. Consider also the prisoners made there during possible continuations. Possibly require at least one new permanent stone of the opponent during a possible continuation and inside at least one of the opponent's (?) strict-two-eye-regions?
Prohibiting the opponent's possibility of score-improvement for the opponent over one particular strict-two-eye-region of the player. Presumably the player might have to defend with more plays than the opponent uses to invade. The opponent's invasion stones, as far as they are in the particular strict-two-eye-region of the player, all have to be removed as prisoners. Globally the score-effect is neutral (otherwise the previous defense case applies).
WAGC rules speak of defense inside territory. If all independent-dame are filled and there is some teire, then this teire is not surrounded by two-eye-alive stones, so WAGC rules have the mistake of not also requiring to obtain territory per then (immediately or a little later) existing local strict-territory-string. Such a defense to obtain territory is necessary.

Terms

Besides, many related terms like score-improvement, score-maintenance, independent-dame, strict-two-eye-region, etc. have to be defined so that those terms can be used by rules for the restrictions.

Force

Because WAGC79 sets life and death requirements for both the alternation and the analysis, defining one type of "force", as it is done in J2003, might not be enough. This does not make research easier. At least, all kinds of "force" are related. Whichever definitions will be necessary here, they can be derived from that in J2003. While it could make a model for WAGC79 much longer, it is a comparatively easy remaining problem for the researcher.

Comparison

A good model for WAGC79 will be like J2003 with additional rules and terms to achieve a partially perfect pass. Concluding, necessarily application of WAGC79 is more difficult than application of J2003, which models J1989.