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.

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!

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A good system naturally covers all corner cases without further effort.

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

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.

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.

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A good system naturally covers all corner cases without further effort.

Of course. This is what superko and fixed ko rules are all about.



Please explain!



Sure. It means that it is a ko rule that does not only apply to basic ko captures and single stone suicides.



Of course not. A proof has worked for PSK and has been refuted for doubled fixed ko.

The similarities that you state do not remove that difference at all. In fact, nothing can remove the difference, as proven.



"purely" is an exaggeration, but philosophy is important here indeed. FYI, professionals would never like a rule with such a weak philosophy as the double fixed ko rule; they have great doubts even with good philosophy new inventions. (For theoretical study, double fixed ko or cycle removal rule is perfectly valid, of course.)

I think it is mostly just a matter of representation, and Double Fixed Ko (DFK) can be as consistent as Positional Super Ko (PSK).

We can represent a game of go as a graph (V, E), where each position is a Vertex (V), and each transition from one position to another is an Edge (E).

For the edges we can choose whether all edges must be unidirectional (→), or whether bidirectional edges (↔) are also allowed.

If only unidirectional edges are allowed, then two vertices A and B that can reach each other in a single move (i.e. basic ko) must have two edges between them (A→B and B→A). If bidirectional edges are allowed, we can represent this with a single edge (A↔B).

With PSK, when we make a play to move from A to B, we remove vertex A from the graph (and by extension all attached edges).

With normal Fixed Ko, we use unidirectional edges only, and we remove each edge as we use it.

With DFK, we allow bidirectional edges, and we remove each edge as we use it.

With this representation, DFK is consistent, nothing is removed that did not exist.

Note that to implement only basic ko, using bidirectional edges has the advantage that we can mark the last used edge as unavailable for the next move, no need to find the reverse direction edge.

Robert: all you complain about is that not all edges actually are bidirectional (in fact, only "basic ko" edges are---exactly those that are not covered under simple fixed ko). To appease your aesthetic sense, it should perhaps be worded such that not "all edges are seen as bidirectional" but "it applies to both uni- and bidirectional edges".

Two wording proposals:

"A move, which transforms one position to another, is prohibited if any previous move transformed one of those positions to the other."

"A move that transforms position A to position B is prohibited if any previous move transformed either A to B or B to A."

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A good system naturally covers all corner cases without further effort.

Herman, with your representation, DFK makes more aesthetical sense (but is hardly understood by non-mathematicians).

True, though much of the research texts behind all sorts of rules are not readily understood, of course.

It is certainly an advantage of superko that it is not hard to grasp, intuitively, for any player. I do doubt most of them will immediately grasp all the strategic implications, such as the one shown at http://senseis.xmp.net/?RulesBeast1

To make DFK more easily understood, you can also phrase it as a combination of basic ko and fixed ko, something like:

A player may not make a move that returns the position to that immediately prior to the opponent's previous move (i.e. basic ko).
If any other earlier position is reached, you may not make the same move as you made the last time in that position.

But of course that is no longer as elegant as Harleqin's phrasing.