I have finished a human-readable draft of the rules that KataGo's next training run should support.

Some test runs indicate that Japanese rules self-play learning "works" using these rules as written. The bot does learn all the basics and seems to be doing very reasonable things, and nothing appears to be overtly broken or buggy. However, not surprisingly, corner cases appear to be hard to learn - things like one-sided dame, and no-points-in-seki are nontrivial for the bot to understand properly in some sekis. And I have absolutely no confidence that the neural net will see three-points-without-capturing-like positions often enough to know how to count them. But, that's not necessarily any different than any other rare blind spot or misjudgment the bot may make.

Anyways take a look here!
https://lightvector.github.io/KataGo/rules.html

This is still a draft - if bugs, weird cases, or bad behaviors are found in these rules, I'm of course open to fixing them.

Congratulations.



Yes, indeed. Seki proved so difficult to formalize that the Japanese 1989 (J89) rules came up with the new concept of the anti-seki. Unfortunately, they did not provide a clear definition of it. My attempt at something like the J89 rules ( https://senseis.xmp.net/?SpightJapaneseStyleRules ) did not quite get seki right, either.



Neither did the J89 rules writers. (The traditional ruling was correct, and Berlekamp and Wolfe show. )




Indeed.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I skimmed your rules. One thing I had thought of mentioning was that for his territory rules Berlekamp needed two encores (cleanup phases) to avoid the group tax. I just took another look and it seems like you also have a version of a once-only rule for whole board repetition in an encore.

As for evaluating kos that remain on the board after the main play or arise in an encore, I am considering a variant of Berlekamp's komaster rule. By that rule if the komaster takes a ko (or plays in a superko) she must immediately resolve the ko or superko. My variant is to allow the opponent to reply instead of having the komaster make more than one move at her turn.

Consider Moonshine Life. One player uses a double ko or other ko threat to take the Moonshine Life, but leaves the ko mouth open. Berlekamp's rule forces the player to fill the ko, thus allowing the opponent to capture.

Consider double ko seki. Berlekamp's original rule would allow one player to take one of the kos and then take the opponent's group on the same turn. My modification allows the opponent to take the other ko. Then the komaster must fill the ko she just took and it is she who loses a group. Under this rule neither player will attempt to be komaster for the double ko seki, and so neither will take the ko.

Consider an approach ko. One player can claim to be komaster and resolve the ko, the other player cannot do so under the modified rule because the opponent will be able to capture her stones in the ko.

Consider a ten thousand year ko. One player will be able to resolve the ko safely, the other player will not. Only the first player can be komaster and will be allowed to resolve the ko.

Consider the J89 anti-seki. Each player is able to resolve the ko as komaster, so it should be resolved before any encore.

There is no pass for ko rule. Instead you allow one player or other to attempt to be komaster. The komaster does not need to make any ko threat and the koloser cannot do so. Play is hypothetical. Since the koloser is allowed to reply when the komaster takes a ko, any gain that the koloser makes is not counted if the komaster is able to resolve the ko safely.

Consider bent four in the corner. At some point in the play a ko arises. Only the player who takes the new ko is allowed to be komaster.

I haven't checked everything out, but I think this approach works pretty well.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

First random selection of comments on the draft on 2019-11-28 9:40 UCT:


"Point(s)" is a bad word because it invites ambiguity for intersection and scoring unit. Write "intersection(s)". If you need to use a graph theory term, write "vertice(s)" or "node(s)".

Instead of "adjacent/bordering" and then using both adjectives / verbs, only use "adjacent" and always write the adjective, never the verb.

Instead of ambiguous "any points" aka "any intersections", consider unequivocal uses with "at least one intersection".

"A set of points borders a color if it borders any points of that color." I read this as "at least one" so it does not describe "surrounded by" aka "adjacent and only adjacent to" that colour. If you want to express the latter, you need to reformulate.

"Maximal": Maybe "Maximum" is correct English style, but I am not sure.

"any point that empty point that": an "of" seems to be missing.

"captures": I am not happy with this word. It is suggestive but creates confusion. When stones have been removed, we can give them a clear term: "prisoners". The process of filling the last liberty and taking away stones is called "removal" but this word is probably superfluous here. The more important question is why and whether you need the word "captures" at all. Certainly not for hiding the possibly ambiguous concept of "dead".

"adds to the total number of captures": no, they are called prisoners.

"Resolving captures": see. You are being ambiguous. Here, you refer to captures as something still on the board. This meaning differs from the meaning of prisoners, which you also refer to as captures.

"grid coloring": strictly, you have not defined this:)

"An empty region that borders both black and white is a dame region.": You can define whatever you want, but... "independent-life area if it does NOT contain any dame regions" your definition contains a fundamental problem: Before removals, most would-be independent-life areas are dame regions...! I have bitten myself through such vicious circles in several of my rulesets, see there.

"Area": This is bad to use both "area" and "region" for the same purpose. Only use region!


End for now.

Nice work! It's great to see something that captures the spirit of Japanese rules but is relatively short, readable and precise.


It could work either way. I prefer the use of "point" because it's shorter than "intersection" and more familiar to go players than "node", so it makes the text more readable. Notice that the sections on scoring use the phrase "A player's score is the sum of...", which does not contain the word "point", so there is no ambiguity here. The score is just a number (a dimensionless quantity, without units).

(I've spent a lot of time reading mathematical works by John Conway, who is able to be informal, even chatty, with his language while still being clear and precise. Paul Halmos has the same talent to a lesser degree, No need to use a long or formal word if a short and familiar word can do the job adequately.)


I don't see this as ambiguous.


No, "maximal" is correct (although it may be unfamiliar to native speakers if they haven't studied mathematics much beyond high school). "Maximum" usually refers to numbers, whereas "maximal" carries the connotation of not being properly contained in a superset; a region can be maximal even if it is not of maximum size when compared with regions elsewhere on the board.


This is actually one of my favourite aspects of this rule set! It does not contain the word "stone" at all (except in paragraphs that are intended as commentary, i.e. not part of the rules proper). Rather than referring to physical stones, it refers to points being coloured or empty. Nothing is placed on or removed from the board; rather, the points change status during the game. (It's truly a rule set for computers!) Therefore it does not make sense to talk of "prisoners" here.

For what it's worth, I agree with Robert's other comments.

Even if point is unambiguous within the text and not used as scoring unit, discussion about the rules will create ambiguity with point as a scoring unit because of very frequent usage in this meaning.

If it is not about physical stones, not only prisoners is superfluous but also captures is a superfluous term. If it is all about colouring, then it should be described as change of colour.

Thanks!

I'm sticking with "point" for now, since within the formal parts of the document the usage is unambiguous. I'm not sure ambiguity in casual outside discussions or commentary is an issue, as I'm not easily imagining where such confusion may actually arise in practice. I may consider changing it still.



I thought the same, until I reread it several times and realized there there is some outside chance that someone might parse "any" as "all", i.e. "X borders any points of Y" might be misinterpreted as "any point of Y is bordered by X". So I went ahead and just made the wording more precise. Also added a disjointness condition to fix a possible hole in the definition.



Thanks, xela. Leaving this the same for now since "capture" is defined in just one way in this ruleset - to describe the process of changing a grid point from black or white to empty, and the "number of captures" refers to the cumulative total number of times this process has occurred for a color. I note also that the word "capture" itself also somewhat suggests a physical thing being captured - although less strongly than the word "prisoner" does - which is arguably incongruent with the formulation in this rules as purely a change of gridpoint color status, but I think there's also readability value in using the common Go word for it.


Yes, most of space on the board will be "dame" and cause very few of the groups to be "independent-life" until the very end by this definition. But I think this is okay - since this is designed for computer play, the expectation is that purely due to self-interest, the players will generally clean up all dead stones, finish borders, etc. During the second cleanup phase it will become generally cost-free for them to do so (and empirically, this is what happens during self-play training). This is quite similar to how Tromp-Taylor rules contain no provisions for agreeing upon alive or dead stones - the expectation is that players will manually capture all "dead" stones out of self-interest, at least, if doing so is necessary to win. And until they do, the region will not be scored as their territory.


Fixed! Along with other minor typo fixes, some of which you pointed out. Thanks!



How does one computer-implementably define "komaster"?

Also, how does one computer-implementably define "resolve"? It cannot be "fill the ko" because sometimes a player needs to capture a surrounding group rather than filling. And I think "resolving" might also sometimes even involve a non-capture move that leaves the ko mouth to still exist on the board longer. For example, here white should be able to kill everything no matter what, but if black is the first to play and plays "a", then white will need to capture at "b" or "c" to generate a liberty before playing at "d". White must not be forced to fill "b" or "c" thereafter, and neither should we prevent white from being allowed to later capture into "b" or "c" a second time after finishing capturing the black group on the upper side.

Click Here To Show Diagram Code

[go]$$c
$$ ---------------------------------------
$$ | . X c X O O X . X d O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | b X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O a X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

It seems to me also if the opponent's "reply" is an arbitrary move elsewhere on the board that is threatening in some way, and the opponent keeps playing such moves, one must allow a potentially arbitrary number of responses by the komaster to those moves before "resolving" the ko - is there a way to handle this?

The rules quoted are not the formal rules used by KataGo, but are informal paraphrases for human consumption. Humans are very good at disambiguation. We can walk and chew gum at the same time, as they say. Some of us can talk and chew gum at the same time, but that is not such a good trait.



Well, -ent in Latin <-> -ing in English, so they are both verb forms.



In English any carries existential import; i.e., it implies at least one. The an in any is derived from one.



I suppose that you are referring to this phrase:
"A liberty of a black or white region is any point that empty point that borders it." I would correct the typos this way:
"A liberty of a black or white region is an empty point that borders it."



Is this what you are referring to?
"Resolving captures of a color consists of emptying all points of regions of that color with no liberties."

Captures in that sentence refers to the act of capturing. It might be better style to replace it with "the capture".

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I have not gotten that far. But first, you have to have identified a ko or superko. In Berlekamp's original formulation, the komaster is the player who is permitted to break the ban for that ko but then must continue, at the same turn, to make one or more plays to win the ko. It may not be obvious, but that is a cost to the komaster.

In the case of end of game resolution of kos, "winning" the ko may actually not be desirable. And giving the komaster two or more moves in a row may be a benefit to the komaster. So we give the koloser the option of responding to the komaster. But the komaster still has to resolve the ko.

So for these cases we allow either player to claim the right to be komaster, i.e., to resolve the ko by playing first. The koloser has no right to break the ko ban. If and only if neither player claims the right to be komaster for a ko does that ko remain unresolved.

Since we are talking about hypothetical play, the komaster of a ko is the player who, for that period of play, has the right to resolve that ko.




A ko is resolved when it no longer exists.



An interesting position, which I will discuss below.



The komaster does not have to answer any arbitrary play. Her job is to resolve the ko. As long as she can do so safely, all hypothetical plays by the koloser are ignored. Details may need to be worked out.

Click Here To Show Diagram Code

[go]$$c Ambiguous temperature
$$ ---------------------------------------
$$ | . X c X O O X . X d O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | b X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O a X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

While this is a scorable corner, it has an ambiguous temperature.

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ ---------------------------------------
$$ | . X . X O O X . X . O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | 2 X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O 1 X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

raises the temperature quite high, as it threatens to recolor many White intersections.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ ---------------------------------------
$$ | . X . X O O X . X . O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | 1 X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O 2 X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

After the local temperature is 0, as either player can play at 2. What these two sequences show is that we can regard the local temperature as lying between 0 and -1, inclusive. At or below temperature zero, either player can make a play, but neither player has to make a play.

For scoring purposes what we want is a position unambiguously with temperature -1. Such as the following position.

Click Here To Show Diagram Code

[go]$$Wc Temperature -1
$$ ---------------------------------------
$$ | . X . X O O X . X . O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | O X O O O O X O O O . . . . . . . . . |
$$ | . O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Assuming that White wishes to show that Black is dead, we presumably will reach this position via the White first diagram above. By human rules White may have to reopen play in order to do so.

Now, in this position neither player will claim to be komaster for either of the double kos.

Click Here To Show Diagram Code

[go]$$Wc White claims to be komaster for ko
$$ ---------------------------------------
$$ | . X 1 B O O X . X . O . . . . . . . . |
$$ | X X X O 4 O X X X O O . . . . . . . . |
$$ | O X O O O O X O O O . . . . . . . . . |
$$ | 2 O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

at

After White is forced to resolve the ko by filling at , losing a large group. OC, it does no good for Black to claim komaster status, either.

So in the encore White will recolor the Black points on the right before tackling the very corner. In fact, White could start off that way, as in the following diagram.

Click Here To Show Diagram Code

[go]$$Wc Variation
$$ ---------------------------------------
$$ | . X . X O O X 3 X 1 O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | . X O O O O X O O O . . . . . . . . . |
$$ | B O O X X X O O . . . . . . . , . . . |
$$ | O O 2 X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Now let White claim komaster status for the ko. Black could do so, as well, and fill the ko safely — for the moment, anyway. But why bother?

Click Here To Show Diagram Code

[go]$$Wcm5 Variation, continued
$$ ---------------------------------------
$$ | 7 X 5 X O O . O . O O . . . . . . . . |
$$ | X X X O . O . . . O O . . . . . . . . |
$$ | 1 X O O O O . O O O . . . . . . . . . |
$$ | B O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

at

As komaster White takes the ko and, without objection, resolves it by filling it. Then White claims komaster status for the remaining corner ko and takes and resolves it. OC, Black could claim komaster status for the last ko, as well, but to no avail. She would just have to fill it and let White capture.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I need much more time to study the rules and understand whether pass-fights can occur. The main threat is pass-fights like in AGA rules without the White passes last rule.

So as not to hijack this topic, I have started a new one here. https://lifein19x19.com/viewtopic.php?f=45&t=17091

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Click Here To Show Diagram Code

[go]$$c
$$ ----------------------
$$ | . X O . O O X . . .
$$ | X O . O O X X . . .
$$ | b X O O X X . . . .
$$ | X O O X X . . . . .
$$ | O O a X . . . . . .
$$ | X X X X . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$[/go]

During regular play black is dead in the corner. However, in the encore after the dame at a has been filled

Click Here To Show Diagram Code

[go]$$B
$$ ----------------------
$$ | . X O 3 O O X . . .
$$ | X W 1 O O X X . . .
$$ | 2 X O O X X . . . .
$$ | B O O X X . . . . .
$$ | O O X X . . . . . .
$$ | X X X X . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$[/go]

the ko at is blocked. If white uses his turn to unblock the ko black captures at

I am not sure what you are saying. Do you mean that after Black captures this ko with . . .

Click Here To Show Diagram Code

[go]$$c
$$ ----------------------
$$ | . X O . O O X . . .
$$ | X W 1 O O X X . . .
$$ | . X O O X X . . . .
$$ | X O O X X . . . . .
$$ | O O X X . . . . . .
$$ | X X X X . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

White is prohibited from capturing this ko?

Click Here To Show Diagram Code

[go]$$c
$$ ----------------------
$$ | . X . X O O X . . .
$$ | X 4 X O O X X . . .
$$ | O B O O X X . . . .
$$ | . O O X X . . . . .
$$ | O O X X . . . . . .
$$ | X X X X . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Yes, point is ko-blocked for white.

Thanks.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Thanks, that's a clever example!

What about the following change:

Changing to:


That would seem to allow white's recapture of W4 because the block would be removed after W2.

Such a change would result in a different behavior in the case where two groups have three shared ko mouths and no other liberties. But I'm not sad about having that case become a no-result during cleanup too rather than only during normal play - if anything, that's more consistent. It might also result in different behavior in cases with throw-in or sending-two-returning-one-like shapes that are connected with a ko mouth. I need to play with those cases a bit more. Are there any major oddities you can think of that result from making such a change? (Or, more cases like this one but that would not be solved with such a change?)

Would this change mean, that in a multistage ko after unblocking the first ko, one may recapture them all in succession?

Yes. In fact, in common multistage kos, this would be true already even without such a change.

For example, in this position, where black is dead...

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | O . O X . X O . . O
$$ | . O X X X X O . . O
$$ | O O O O O O X X . O
$$ | . . . . . . O O O .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

If during cleanup we had this sequence:

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | O 1 O X . X O . . O
$$ | 3 O X X X X O 2 . O
$$ | O O O O O O X X . O
$$ | . . . . . . O O O .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

Then results in C19 being unblocked even without the proposed change. After black plays the move, C19 is no longer a ko-move for white, as it's not even a pseudo-legal move for white. Therefore, when black unblocks non-ko-moves for the oppponent at the end of playing , it becomes unblocked for white.

So if spends a turn to unblock A19, then and can capture successively (assuming black doesn't connect or interpose any other moves) without having to also spend a turn unblocking C19.

Did you have any tricky cases in mind involving either this, or the proposed change to unblock all moves for either player that aren't ko-moves, rather than just those of the opponent?

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X O X . X . X O O . .
$$ | O . O X O X O X O . .
$$ | . O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Black seems to be dead.

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X O X 2 X 4 X O O . .
$$ | O 1 O X O X O X O . .
$$ | 3 O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X . X O X O X O O . .
$$ | b X O a O . O X O . .
$$ | X O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

unblock at a, unblock at b

Click Here To Show Diagram Code

[go]$$cB
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X 4 X O X O X O O . .
$$ | 2 X O 1 O c O X O . .
$$ | X O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

unblock at c

Is this what we want?

This seems to be used when Chinese-like rules are selected as well, but doesn't it make sending-two-returning-one play out differently? I think Chinese superko (which forbids 3-play cycles) should be included as well.