Fixed Ko Rule: Continued Discussion

[nagano]

Apologies, I missed this thread at first. The main question is what is the simplest solution for an all-encompassing ko rule while still allowing kos to be contested and decided by the players' skill and the strength of their positions. Situational superko seems the best solution presently, but it has flaws in some positions. I will continue this discussion later but need to go presently.

[RobertJasiek]

Harleqin, quite like cycle stone removals, doubled fixed ko rule is an artificial construction: It even prohibits something that cannot be executed as a play. Therefore the rule should not be used in human play.

[RobertJasiek]

what is the simplest solution for an all-encompassing ko rule while still allowing kos to be contested and decided by the players' skill and the strength of their positions. Situational superko seems the best solution

Positional superko is simpler, so, by your standard of wishing the simplest solution, situational superko does not qualify.

[nagano]

Positional superko is simpler, so, by your standard of wishing the simplest solution, situational superko does not qualify.

Perhaps I should rephrase my goal as "simplest without compromising the potential for variation". This was part of the reason I objected to the fixed ko rule. I object to the positional ko rule as well because of situations like this one. So see it does meet my standards, at least in that regard.

[RobertJasiek]

my goal as "simplest without compromising the potential for variation". This was part of the reason I objected to the fixed ko rule.

Your goal is still too imprecise. Which variation do you mean? If you mean number of legal move-sequences, then the fixed ko rule used alone beats superko very easily. Therefore you must mean a different kind of variation but which? Maybe something related to strategic choice complexity? Such is extraordinarily hard to assess though! E.g., PSK has shapes (like Molasses Ko) that are strategically much more demanding than under SSK or NSK. So you will have a very hard time arguing that PSK would be compromising in strategic choice complexity. Rather it is easier to argue that among those ko rulesets with in practice comparable strategic choice complexity PSK is the simplest.

Why at all do you object to a particular ko rule on the grounds of a particular shape's slightly surprising behaviour?

Which (subjective) objection do you have with respect to your linked example? Why do you expect Black to play 2?

[Harleqin]

Harleqin, quite like cycle stone removals, doubled fixed ko rule is an artificial construction: It even prohibits something that cannot be executed as a play. Therefore the rule should not be used in human play.

I think that you have not understood what I have written (that might be my fault). I see no base for your claim; it is not any more artificial than superko. What prohibition do you mean?

If you see the game as a graph of edges (moves) and vertices (positions), superko prohibits revisit of a vertex, while double fixed ko prohibits revisit of an edge (edges are treated as being undirected for this). Both have the same result as basic ko in the basic case, but they differ in the long case (I think that double fixed ko roughly treats each long cycle as something like a "disturbing ko").

[willemien]

If you see the game as a graph of edges (moves) and vertices (positions), superko prohibits revisit of a vertex, while double fixed ko prohibits revisit of an edge (edges are treated as being undirected for this). Both have the same result as basic ko in the basic case, but they differ in the long case (I think that double fixed ko roughly treats each long cycle as something like a "disturbing ko").

Thanks for the explaination i lost the meaning of the "double fixed ko rule".

It has some strange concequences

if white has played position A -> White move -> position B
then Black may not play position B -> Black move -> position A

Is that really what you want?

[HermanHiddema]

If you see the game as a graph of edges (moves) and vertices (positions), superko prohibits revisit of a vertex, while double fixed ko prohibits revisit of an edge (edges are treated as being undirected for this). Both have the same result as basic ko in the basic case, but they differ in the long case (I think that double fixed ko roughly treats each long cycle as something like a "disturbing ko").

Thanks for the explaination i lost the meaning of the "double fixed ko rule".

It has some strange concequences

if white has played position A -> White move -> position B
then Black may not play position B -> Black move -> position A

Is that really what you want?

You realize that the sequence (A -> B -> A) you describe is exactly equivalent to basic ko?

[nagano]

After being puzzled by your last post, I looked at the definition again. I noticed in the notes that it refers to the whole board position, not local as I had read it. I therefore withdraw my objection.

[RobertJasiek]

Harleqin, double fixed ko rule: Suppose a play by Black captures at least 2 stones, transforming position A to position B. Afterwards neither player, in particular White, may make a play that transforms B to A. However, such a move does not even exist! This is where the rule is artificial.

Superko or the fixed ko rule do not have such artificial aspects of prohibiting plays that cannot even exist in theory.

[Bigstrongpolarbear]

This may be a simple question but I don't understand this. Why does it matter if a rule doesn't allow a move that can't be played anyway? What difference does it make? Why isn't it what the rules do to moves that are possible that's important? Sorry for being 20 kyu at rules.

[Harleqin]

Harleqin, double fixed ko rule: Suppose a play by Black captures at least 2 stones, transforming position A to position B. Afterwards neither player, in particular White, may make a play that transforms B to A. However, such a move does not even exist! This is where the rule is artificial.

Superko or the fixed ko rule do not have such artificial aspects of prohibiting plays that cannot even exist in theory.

Positional superko: Suppose a play by Black captures at least 2 stones, transforming position A to position B. Afterwards neither player, in particular White, may make a play that recreates A. However, such a move does not even exist!

[RobertJasiek]

Why does it matter if a rule doesn't allow a move that can't be played anyway? What difference does it make?

Rules and their intention should be readily understood. With artificial behaviour beyond all reality, many players will not.

[RobertJasiek]

Positional superko: Suppose a play by Black captures at least 2 stones, transforming position A to position B. Afterwards neither player, in particular White, may make a play that recreates A. However, such a move does not even exist!

You are wrong.

Proposition: Such a white play always exists!

Proof:

Case 1: Black's play did not commit suicide:
A has at least one white stone because, according to your assumptions, in A Black could capture at least two, namely white, stones. Therefore there is a position Z that is like A but with one white stone less on the board. In Z, the white play on that A stone's intersection would (if allowed) create A.

Case 2: Black committed suicide: The subcase of Black's whole board suicide cannot occur because, by PSK, such a Black play would be illegal. Therefore only the other case of at least one white stone in A (else Black suicide would be impossible) remains to be proven, see case 1.

QED.

Corollary: Either (no) suicide rule together with your assumptions is possible.

[Harleqin]

Robert: So you wanted to mean "afterwards" as "any time afterwards". Even in that case, you artificially selected a specific subset of moves that might trigger the respective restriction.

The more general description could be like this:

Positional superko: A play transforms position 'A' to position 'B'. Any time afterwards, recreation of 'A' is prohibited. This holds even if from the current position there is no play available to do so.

Double fixed ko: A play transforms position 'A' to position 'B'. Any time afterwards, another move that either transforms 'A' to 'B' or 'B' to 'A' is prohibited. This holds even if the current position is one of 'A' or 'B', but no play is available to create the other one.

Your distinction is just bogus. Under both rules, there are some situations in which a theoretically available play is prohibited, and some situations where there is no theoretically available play that could be prohibited.

Whether a prohibition is in place when no prohibited play is theoretically available is a purely philosophical question. This question applies to either rule anyway.