TMark wrote:After over 130 posts, and the several years that Robert has spent (seems more like millenia to observers), I would have expected greater progress. Or is it beyond your capabilities?
Best wishes.
If one takes into acoount the amount of time, Robert has spent for "rules", and the level of maturity of his texts, it would be impudent to expect more than small steps from the level he has reached.
What Robert refers to as "Basic Rules" does not provide any serious problem.
Basic Rules
- The usual fundamental rules apply.
- The game consists of the phases 1. Competition, 2. Analysis, 3. Scoring.
- The Competition is a sequence of alternating moves.
- A move is either a play or a pass.
- Two successive passes end each sequence of moves.
- Removed stones become prisoners.
- Suicide is prohibited.
- The basic ko rule prohibits a player to make a play just after which the position just before the preceding opposing play would be recreated.The second sentence is a kind of meta-statement; the following ones refer to "Competition" in the first instance.
"Competition" is named "Play" by me in my "Cassandra's rules" thread.
"Scoring" is named "Score" by me.
"Analysis" is named "Evaluation" by me. Robert likes to have "identification of stones that can be removed from the primary position and their removal" and "identification of territory" as part of "Analysis"; my preference is to have these steps in "Score".
All these aspects are nothing more than a matter of personal taste.
Within territory oriented rules you have to identify strings, which can border territory, and strings, which cannot. In one of the phases after Competition / Play, strings of the second type, which are complety surrounded by opponent's strings of the first type, will be removed without play and become prisoners.Robert's identifying concept relies on "Independently Alive", following his J2003.
Independently Alive
- The only considered type of life is being independently alive.
- The concept independently alive relies in two other concepts: force and two-eye-formation.
- "force" is a technical term used in the Japanese 2003 Rules. It can be understood also intuitively though: That a player forces something means that he can and does choose his moves well enough to always achieve it - regardless of how the opponent replies.
- A "two-eye-formation" consists of one or several strings of the same player and exactly two empty intersections so that these properties are fulfilled: 1) Each of the strings is adjacent to each of the two intersections. 2) None of the strings is adjacent to another empty intersection. 3) Each of the two intersections is adjacent only to the strings.
- A string is "independently alive" if its player moving second can force to get a two-eye-formation on at least one of its intesections.The difference to my proposal can be found in the last sentence: "at least one".
This will come to life only, when evaluating strings, which are part of
not outplayed positions, named "Seki" colloquially in the world of J1989.
Usually one of two neighboured strings of different colours will become "independently alive", the other one will become "not independently alive". The latter would become prisoners after Competition / Play.
In my proposal, both strings would become "not two-eyed", so none would become prisoners after Play.
Robert's version is disadvantageous for the player, who owns the "not independently alive" string; my version is disadvantageous for this player, too, but to a smaller extent. In both versions this player would be better, had he played out the position during Competition / Play.
As Robert stated correctly, positions of this type will not be "common" after endgame. Despite this fact, it is important that the rule set gives a
consistent solution for this type of position.
Robert's Analysis has the same effect on identifying strings, which can border territory, and strings, which cannot, as my proposal.
Analysis
- The Analysis consists of these steps: 1. Determination of the independently alive strings. 2. Removal. 3. Determination of territory.
- Each string is analysed separately. It is determined whether or not it is independently alive.
- For analysis of each string, imagined move-sequences starting by the attacker are considered. The defender shall try to prove "independently alive" while the attacker shall try to prove "not independently alive". Until the truth has been revealed, yet more sequences must be considered.The content of the following sentences can be found in my proposal within "Score":
- During the step Removal, one considers the connected regions that are adjacent only to one player's independently alive strings and that consist of intersections being empty or having opposing not independently alive strings on, which are removed.
- During the step Determination of territory, a player's territory consists of the intersections of connected empty regions adjacent only to his independently alive strings.
Scoring
- Territory Scoring applies according to the territory determined in the Analysis.
- The score is visualized by means of Japanese Fill-in Counting.The final result of "Long Cycle Repetition" will be the same, too.
Long Cycle Repetition
- During Competition, a cycle ends the game exceptionally and immediately. It is, however, tolerated that the players notice occurrence of a cycle delayed.
- During Competition, a cycle with an equal number of new prisoners lets the game result be a tie. For traditional reasons, this is also called "No Result" or "Neither Victory Nor Defeat" and the players are perceived to agree on the fact that such a cycle has occurred.
- During Competition, a cycle with an unequal number of new prisoners lets the game result be a win for the player with the smaller number. For traditional reasons, it is tolerated though that the players perform the cycle up to ca., say, a thousand times because the player having collected enough prisoners can at some time depart, let the opponent control the entire board but still win by Scoring.
- During Analysis, every sequence of moves leading to a cycle is treated as if ending upon completion of its first cycle. No stone played during such a cycle is "independently alive" though. This is equivalent to the original rules' implicit assumption of infite recurrence of that cycle.None of the strings, which will become part of a long cycle repetion (including the strings, which are "neighboured" to a long cycle and cannot become independently alive / two-eyed due to the cycle), will become independently alive / two-eyed.
Within "Ignored Rules and Rules Aspects", you will find the aspect that makes the difference to J1989 (and between Robert's text and mine):
Ignored Rules and Rules Aspects
...
- The hypothetical ko rule is ignored. Instead the basic ko rule applies also during the Analysis. A "triple ko with one eye and one external ko" becomes a precedent: The strings of the player having the "eye" are independently alive while the opposing strings are not independently alive. The combination of a "double ko death" and a "basic ko fight about whether to dissolve it like a teire" elsewhere on the board becomes a precedent: In the double ko death, the strings of the player having the "eye" are independently alive while the opposing strings are not independently alive. The ko stone in the basic ko is not independently alive.The type of Ko rule during Analysis / Evaluation is part of the "forcing procedure".
The J1989 results for Life&Death-examples 16, 17, and 18, cannot be derived by the J1989 procedure.
Robert's J2003 hypothetical Ko rule is a genious idea to get the J1989-wished results be using a consistent procedure.
If he uses the basic Ko rule borrowed from Competition (what I do also in my proposal), there arises the need to have some precedents to keep the application of the rule set as "user-friendly" as possible, if you want the rule set to provide a wished result for some special positions.
If the number of precedents is limited, there will be some very "exotic" positions (like J1989 Life&Death-examples 16, 17, and 18), which results will differ from those of J1989.
Referring to the discussion of Chris' proof, primary developed in another context, it is very important in the course of the comparison of different rule sets and has a side effect on / from Robert's "user-friendly" rule set.
What Chris has proven in the second part of his proof, is that every string, which is a "two-eye-formation", is either one of Robert's J2003 "uncapturable", "capturable-1", or "capturable-2" strings. Under the precondition that the "forcing procedure" used is the same.
Perhaps this precondition has been underestimated by Robert so far. The "forcing procedure" is immanent part of "two-eye-formation", so one has to pay attention to this dependency. This finding may be one of the small steps I mentioned in the very beginning of this posting.
