Rules Beast 1

    Keywords: Ko, Rules

Rules Beast 1 is a 6×6 position described by John Tromp in which most superko variants[1] surprisingly let what seemed to be a seki become a ko fight. A more realistic scenario would have the lower left corner be an unremovable ko threat for Black.

Table of contents Table of diagrams
Strange … (W to play)
Standard superko – W1 = pass
Standard superko – W9 = pass, W11 at WC forbidden
Kee – Initial board position
Kee – Black sending two (again)
Kee – W4 triggers a cycle
What about 1-1? 1,2
What about 1-1? 3,4
Alternative position

Starting position: John Tromp’s introduction

John Tromp: On small boards the superko rule has peculiar consequences as exemplified in this 6×6 game:

[Diagram]
Strange … (W to play)  

Here, White to move had better connect in the lower left, else Black can exploit[2] the superko rule to capture a white group.
    – Hint: Black aims to make it illegal for White to capture in the top-right a second time.
    – (Play below.)



I don’t see these strange consequences as an indication that there’s something wrong with the superko rule. In fact it seems to fit right in with the other simply-stated Go rules that yield a game so rich in strategy and subtleties.


Comments on John’s introduction

Charles Matthews I think the final paragraph is a partisan statement, by the way. If various organisations of standing in the go world have been persuaded to adopt superko, was it really to introduce more 'subtleties', or because it was represented as suppressing others?

Bill: I created this page using John’s example in Superko. As one author of an elegant rule set, John has an informed opinion. I felt that it was fair to retain it here.

I am pretty much in agreement with you, Charles. The behavior of this board under most rules sets with a superko rule seems to me to be an unintended consequence.

[1] Robert Pauli: Be it situational, positional, or natural situational (and maybe even supernatural ;-)

[2] Robert Pauli: For the cause of this flaw in the superko rules and how to cure it, see Cycle Completion or Sound Superko.

Patrick Traill: I do not read John’s comment as saying that the intention of the rules is to introduce subtleties, but that one should appreciate them when they arise. Personally, I see small-board beasts as curios which can be fun but have little to tell us about which rules are most satisfying in a larger board; perhaps a case of “[ext] hard cases make bad law”.


Most superko rules: Black captures if White passes

With any of the following superko rules, White is forced to connect at B4 (below), since Black can capture if she passes (listed from most to least restrictive):

Positional superko forbids the recreation of any board position that has previously occurred in the game.
Situational superko forbids the recreation of a board position previously faced by one’s opponent (a previous ‘situation’).
Natural Situational superko forbids a board play recreating a position one has previously created with a board play.
as used by:
AGA, Lasker-Maas, New Zealand: situational or natural situational (not clear in all cases)
Tromp-Taylor: positional

Black uses the cyclesending two, returning one” in the top right corner to prevent White recapturing:

[Diagram]
Standard superko – W1 = pass  

Black forces with B2 to ensure that White has made the last move in the “sending two, returning one”.
He then forces with B4

[Diagram]
Standard superko – W9 = pass, W11 at white+circle forbidden  

… and B6 so that White will need to pass after B8.
This lets him start another “sending two, returning one” cycle with B8 and B10.

What was ABCD (legal cycle completion with D = pass under [N]SSK and PSK' [4]), now has become CDAB (illegal completion with B = take two).

White now needs to play W11 at white+circle to take B8 and B10 and avoid capture, but that would repeat the situation after W7.

Since W7 and W11 are both board plays by White, this W11 is forbidden by natural situational superko and hence a fortiori also by situational and positional superko.

Thus White loses everything as a consequence of her initial pass.



This line of play shows that W1 should not have been a pass, but a connection at B4. After that, if Black tries the same trick, a White capture is the last legal move in the “sending two, returning one”, and Black has no other sensible move.

RP: What trick? S2R1 isn't the trick, the trick is shifiting the cycle start, but since Black now has no threat, he can't. Just playing the S2R1 under, say, area scoring and [N]SSK won't hurt him, and her last legal move in this cycle (believe me, I can't hear that word any more ;-) would be her pass . . . no wait, she first has to capture the loner in the seki! Then he can again play S2R1. Now she completes the cycle with a pass (legal) and he can't send two again since that would complete a cycle with a non-pass (illegal), so he passes too.


Spight rules

Spight rules forbid repetition of a position without an intervening pass (they do not care whose turn it is).

This allows W11 to take the stones, since White’s pass (W9) lifted any ko or superko ban. Black may recapture (for the same reason) and the game ends with White’s second pass in the same position.


Kee rules

Kee Rules cover games with any number of players; when restricted to normal two-player games they:

  • allow a player, when passing because of forbidden repetition, to appeal for the previous move to be rescinded
    • (and specify the consequences of that appeal);
  • forbid repetition of a position unless:
    • the player has passed without appealing since it last appeared; and
    • their opponent has only made stone play(s) since its first appearance.

With these rules:

[Diagram]
Kee – Initial board position  
[Diagram]
Kee – Black sending two (again)  

Black captures the white stone by B1. W2 is a normal pass play and Black sends two again by B3.

[Diagram]
Kee – W4 triggers a cycle  

W4 triggers a cycle, but Black is prohibited from playing in the remainder of the game because White has a normal pass play within the cycle but Black has not. White wins by playing the remainder of the game by himself alone.


Robert Pauli’s ‘Logical Japanese Rules’

Robert Pauli: Let’s see how LJRG perform.

Cycles, besides ko, are not prohibited by LJRG. Instead, one may (if passing wouldn’t end) remove the cycle.

If White passes and Black disturbs, the situation after W11 is similar to the one after W7 (with no history, trees growing out of them are identical). LJRG now allows Black to

  • clear the cycle arena (top three intersections of the right-most column) – thereby earning one white captive and prohibiting any further play in it – and
  • do a move.

Since there is nothing worth continuing, Black will skip the second part, White will pass, and Black will pass too, ending the game (ultimately): W+5 (no part of the board is controled, and there are two white and seven black captives).

Since the whole mess doesn’t pay, Black will rather pass after White did initially: tie (neither any control nor any captives).

Thus, White should have captured the black loner in the seki instead to pass initially: W+1.


Comment and discussion

What about 1-1?

[Diagram]
What about 1-1? 1,2  

Osh?: maybe White is better to bring everything to Seki? If there is komi...

Robert Pauli: Osh, BassJohn already explained that White should have made seki, but of course not at 1-1: she, quote, connects. Guess where . . .

By W1 it is seki in left below side. If B2 eats...

[Diagram]
What about 1-1? 3,4  

White cuts then black captures this white stone, but after that White takes three black stones and...

Bass: It seems unlikely that Black would play B4 when the four white stones are in atari.


Remaining diagrams removed in view of Bass’s refutation; see [ext] https://senseis.xmp.net/?RulesBeast1:v42 for details

Alternative initial position

Anonymous contribution [ext] version 52, 2019-01-16 by 90.193.184.180
[Diagram]
Alternative position  

A slightly different setup which avoids the white pass at the start. The colours are switched because this way there is 1 more black stone than there are white stones. This makes sense when we assume there are no prisoners, no previous passes, and that it is white's move.



See also

  • Rules beast — for other strange positions that challenge the rules

Notes

[4] Robert Pauli: How to bring PSK closer to the rest is explained in Cycle Completion. Instead to lose immediately, a further pass lets the opponent win.


Rules Beast 1 last edited by PJTraill on February 11, 2019 - 18:30
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