Tromp-Taylor Rules

    Keywords: Question, Rules

Tromp-Taylor rules, named for their creators John Tromp and Bill Taylor are also known as [ext] the logical rules of go.

Table of contents Table of diagrams
White to play
Ing example (cont.)
W to play
W wins
W wins
Ing example (cont.)

Formulation of the rules

  1. Go is played on a 19x19 square grid of points, by two players called Black and White.
  2. Each point on the grid may be colored black, white or empty.
  3. A point P, not colored C, is said to reach C, if there is a path of (vertically or horizontally) adjacent points of P’s color from P to a point of color C.
  4. Clearing a color is the process of emptying all points of that color that don’t reach empty.
  5. Starting with an empty grid, the players alternate turns, starting with Black.
  6. A turn is either a pass; or a move that doesn’t repeat an earlier grid coloring.[1]
  7. A move consists of coloring an empty point one’s own color; then clearing the opponent color, and then clearing one’s own color.
  8. The game ends after two consecutive passes.
  9. A player’s score is the number of points of her color, plus the number of empty points that reach only her color.
  10. The player with the higher score at the end of the game is the winner. Equal scores result in a tie.

Objectives

As their pseudonym implies, these rules aim to optimize

  • simplicity of rules
  • conclusiveness and therefore unambiguity

while at the same time trying to retain the ‘spirit’ of the game by satisfying the following boundary condition

  • keeping things close to how Go is played by humans.

Bill Taylor:

“These are essentially the New Zealand rules, re-worded to be as simple and elegant as possible. The NZ rules are in turn the simplest version of Chinese-style rules around.”
(quoted from [ext] http://tromp.github.io/go.html)

Comparison with New Zealand rules

Significant differences between Tromp-Taylor and New Zealand rules include:

Differences
Topic Tromp-Taylor New Zealand
Preventing indefinite play Positional superko Situational superko
End of game Two successive passes An “agreement phase” starts when the players concur that competitive play is over

Notes and references

[1] “Grid coloring” refers to a coloring of the entire grid, not just one point.


Discussion

Ko rule

Actually, New Zealand rules use the situational superko rule, not the positional one. At least, they do on 6 Feb 2007. As Tromp and Taylor intentionally made their rules equivalent to the New Zealand rules ([ext] http://tromp.github.io/go.html), I guess that the New Zealand rules must have changed since. The history page evidences how the rules have changed a few times since their beginning. —anonymous

Since, I think 1996, Tromp-Taylor uses positional superko. This decision was made independently of New Zealand rules. —RobertJasiek

P.J.Traill: John Tromp’s page comments on rule 6:

This is the positional superko (PSK) rule, while the situational superko (SSK) rule forbids repeating the same grid coloring with the same player to move. Only in exceedingly rare cases does the difference matter, sufficient reason for the simpler PSK rule to be prefered.

Flower: Let us change the main article then so that it does not insinuate that NZ rules use PSK :). I noticed that TT rules end the game after only two successive passes. Would that not cause trouble in certain KO situations? —Flower, 2007-02-20

Robert Jasiek: The "trouble" might exist in your perception. It does not exist in my perception. I do not mind if rules do have strategic consequences, even if they differ from such tradition that existed during some times in some parts of the world.

Herman Hiddema: Trouble with ko situations seems extremely unlikely. Under area scoring, not defending a ko does not increase your score, but suppose you get into a situation where you have no ko threats but want your opponent to fill or otherwise defend the ko (Can anyone construct an example where this would be desirable?). Playing in your own territory or in you opponents territory does not change the score, so you can simply play in your own (or your opponents) territory as a ko threat, and if your opponent does not defend the ko you can retake it.
Note that the above rules do not include a removal phase. The only rule on scoring is rule 9, therefore both players should capture all dead stones before passing. On John Tromp’s page, there is a comment regarding removal of dead stones (Comment 8) which includes a 4 pass game end.


5x5 Test case 1: Comparison with Ing rules

Bill: Here is an example from the Ing rules, slightly altered.

[Diagram]
White to play  



[Diagram]
Ing example (cont.)  

B6 = pass, W7 = pass

White wins by 4 under Tromp-Taylor rules. Black wins by 25 under Ing rules. (Tromp-Taylor: white 11+1=12 points _vs_ black 8 points)

ihope?: Well, that’s if Black passes on B6. What happens if the game is played out the rest of the way, as Tromp-Taylor scoring is meant to handle (as I see it, at least)?

Bill: Pass is best for Black under Tromp-Taylor rules. The game is played out, in the sense that Tromp and Taylor intend. See Rules Beast 1 for another anomalous position and John Tromp’s comments.

ihope?: It seems to me that it would be best for Black to play right below B4 on B6, as this would capture White’s group. Could White recapture Black afterward? It seems unlikely.

Karl Knechtel: That play does not capture the White stones, because they have a liberty at the point where White has just captured (with W5). Therefore it is instead a suicide in the corner (the Black stones are cleared).

John Tromp: Black 6 pass is a mistake. Instead Black should suicide! Then, after white adjacent to 1, black recaptures in the upper left, and proceeds to kill White. But White 3 is also a mistake. After White 3 at 5, both sides should pass, for W+2.


5x5 Test case 2

Here’s another example I was thinking about, admittedly contrived. —emeraldemon

[Diagram]
W to play  
[Diagram]
W wins  

Under Japanese rules (and I think other rulesets too) after W1 black passes, White passes, and the white stones are declared dead and removed. But in Tromp-Taylor, Black must actually try to remove them, but the only legal move is self-atari, so Black must still pass. White passes, the stones are alive, and in fact that ko point is white territory. I doubt such a position would ever occur in a game, but it is worth noting. —emeraldemon

Black would just play suicide in the top right instead of passing, then White can’t do anything useful. —Dave

emeraldemon: True, I forgot suicide is legal in TT rules. So the problem only occurs when Black has no play that doesn’t lose, like so:

[Diagram]
W wins  

That looks good. I was thinking even single-stone suicide was legal, so that it would be harder to fix, but on second thought a single-stone suicide would violate positional superko, so that example would work. — Dave


Replay after capture

When I read these rules I get the impression that playing in an area where captured stones once were is illegal, am I right? Here Black plays 1, White Captures at A. I read the rules as saying Black has no legal move now. (rule 6)

[Diagram]
Ing example (cont.)  
Chris: No, that is not true. "grid coloring" refers to the coloring of the entire board. The final words of Rule 6 just imply Positional superko. Note that from the first rule it is clear what "grid" means if that were not clear enough just from the word "grid".
Ah I see, thanks.
Added a footnote to rule 6 to clarify this. P.J.Traill 2018-12-10

Tromp-Taylor Rules last edited by PJTraill on December 10, 2018 - 12:49
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