Life In 19x19

What axioms, assumptions and principles are there for go rules design derived from a) evaluation or b) not from evaluation?

RobertJasiek wrote:What axioms, assumptions and principles are there for go rules design derived from a) evaluation or b) not from evaluation?

We have had any number of discussions about this over the years, since I even took this approach on rec.games.go before 1998 with positions without multiple kos. The first principle, which is similar to Ing's is that evaluation is determined by play. The second principle is that a score remains the same by play, no matter who plays first, or is worse for the first player. That is, some positions have a score at which play can cease, because neither player can gain from continuing play. There is a condition, not a principle, that play is finite, so that play eventually reaches a position with a score. Ko and superko rules are intended to make play finite. A simple ko rule means that a triple ko can lead to infinite play, and in that case the result may be hung or declared a tie. Infinite play is not an anomaly, but a result of the ko rules.

Edit: When I talk about evaluation here, I mean go style evaluation. There is another style of game evaluation in which the evaluation is derived from the score, by backing up the game tree from the end. For instance, consider the empty 5x5 board. Black to play, with perfect play, ends up with 24 pts. of territory. Backing up from the result, we would say that the empty board is worth 24 pts. to Black, because Black plays first. But go evaluation does not depend upon who plays first, so by symmetry we say that the average value of the empty board is 0. OC, this value is not a score, since it is not a scorable position. Whoever plays first gains points.

Edit2: We already know how to evaluate No Pass Baduk with no kos or superkos. That is why I can claim that the No Pass Capture Game and No Pass Misere Capture Game have no anomalies.

If we want to keep a rule understandable by novices and programmable, I think that area scoring is necessary.

In area scoring, the winner is the one who has more intersections on the grid : stones plus empty intersections surrounded by one's stones.

In territory scoring, things are way more complicated. All books for beginners say that the winner is the player with the most territory (empty intersections surrounded by one's stones). This is wrong.
A correction is usually given after 100 pages of various teachings : the winner is the player with the most territory (empty intersections surrounded by one's stones), plus the number of stones that he captured during the game. This is a bit more complicated (wait, what ? the goal of the game is to maximize the value of a mathematical function ?)... but this is also wrong !
In reality, under territory scoring, the winner is the player with the most territory (empty intersections surrounded by one's stones after dead stones have been removed without capturing them !) plus the number of stones that he captured during the game, plus the number of opponent's dead stones that were removed without capturing them.

This operation is always overlooked, but it is at the heart of territory scoring : dead stones must be removed without capturing them.
In area scoring, this is just an optional convention for practical purposes. In territory scoring, this is a mandatory rule.

Bill Spight wrote:Well, as the guy who introduced the idea of pass stones in the AGA journal in the 1970s, I know what I'm doing. (BTW, I was probably not the first person to come up with the idea of pass stones; I was not the only one, OC.) This method requires AGA territory scoring, not area scoring, which requires a token or other adjustment. But, IIUC, most players use territory scoring anyway, and the idea of requiring White to pass last has met with confusion and opposition.

Button go is a hybrid between area and territory rules. This is accomplished by requiring an equal number of pass stones or other stones played after the button instead of an equal number of stones on the board for scoring.

Sorry, I still don't understand.
Can I read the text of the button go rule, and of the AGA button go rule somewhere ? It will certainly help me.

Pio2001 wrote:Can I read the text of the button go rule, and of the AGA button go rule somewhere ? It will certainly help me.

Here are alterations for AGA rules to play Button Go.

I. Button go rule using area counting:

2) Play: The players alternate in moving, with Black playing first. In handicap games, White moves first after Black has placed his or her handicap stones. A move consists in playing a stone of one's color on an empty intersection (including edges and corners), or in passing, or in taking a token called the button. The button is worth ½ point.

3) Compensation: In an even (non-handicap) game, Black gives White a komi (compensation) of 7 points for the advantage of the first move. This komi is added to White's score at the end of the game. In handicap games, Black gives White no compensation. The ½ point button avoids draws.

6) Repeated Board Position (Ko): It is illegal to play in such a way as to exactly recreate a previous full board position from the game, with the same player to move, except that after the button has been taken, it is only illegal to recreate a previous full board position with the same player to move if that position arose after the button was taken or by taking the button.

7) Passing: On his or her turn, a player may pass rather than playing a stone on the board or taking the button.


11) The Last Move: {deleted}

12) Counting:

Area: All live stones of a player's color left on the board together with any points of territory surrounded by [those stones] plus ½ point if the player took the button constitute that player's area.

----

II. AGA button ko rule using territory counting:

2) Play: The players alternate in moving, with Black playing first. In handicap games, White moves first after Black has placed his or her handicap stones. A move consists in playing a stone of one's color on an empty intersection (including edges and corners), or in passing, or in a special move called "taking the button," which occurs only once per game. To take the button the player hands a stone over to his or her opponent as a prisoner.

3) Compensation: In an even (non-handicap) game, Black gives White a komi (compensation) of 6½ points for the advantage of the first move. This komi is added to White's score at the end of the game. In handicap games, White gives Black ½ point compensation. This avoids draws.

6) Repeated Board Position (Ko): It is illegal to play in such a way as to exactly recreate a previous full board position from the game, with the same player to move, except that after the button has been taken, it is only illegal to recreate a previous full board position with the same player to move if that position arose after the button was taken or by taking the button.

7) Passing: On his or her turn, a player may pass, rather than playing a stone on the board. When passing the player hands the opponent a stone, called a pass stone, except as provided in rules 9) and 10).


9) Ending the Game: Two consecutive passes normally signal the end of the game. The player to make the second pass does not hand over a stone if he or she also took the button.

10) 10) Disputes: If the players disagree about the status of a group of stones left on the board after both have passed, play is resumed, with the opponent of the last player to pass having the move. The game is over when the players agree on the status of all groups on the board,in which case, if it is the turn of the last player to pass before resumption, that player passes and hands over a pass stone, or, failing such agreement, if both players pass twice in succession, in which case the second player to pass does not hand over a pass stone if that player played first in the resumption. In this case any stones remaining on the board are deemed alive.

11) The Last Move: {deleted}

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Maybe that's too much, but I tried to be thorough. I hope that's clear, now.

Thank you. This is exactly what I needed.

I am going to study this.

Pio2001 wrote:Thank you. This is exactly what I needed.

I am going to study this.

I think it would be clearer, in the territory counting version, when first introducing "taking the button", to say that on average taking the button loses ½ point.

A bit more on basing end of game aspects of baduk rules on evaluaion. In a way it seems like common sense. After all, we have to score games, and that means evaluating them. But many rules disputes have been about more specific questions. Are these stones alive or dead? Does this ko have to be filled? And so on. In addition, we have only been able to evaluate general baduk positions rigorously for a little over 20 years.

Combinatorial game theory provides the basis for evaluating no pass baduk positions with no kos or superkos. Evaluation is done via play. A score of 0 is defined as the value of a position in which neither player has a move. Other positions may also have a score of 0.

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

How do we evaluate this position by play? Let each player play first.

Click Here To Show Diagram Code

[go]$$ Capture game, Black first
$$ ----------
$$ | . O X X 3 |
$$ | 4 O O X . |
$$ | 2 O X X 1 |
$$ | 6 O O X 5 |
$$ | . O X X . |
$$ -----------[/go]

At this point Black must fill an eye and put herself into atari, Then White will capture the Black group and win the game. The result for Black is the same as if Black had no play; Black to play loses. Similarly, White to play would also lose. This position (after ) has a score of 0.

Now let's back up one play.

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X X |
$$ | O O O X . |
$$ | O O X X X |
$$ | 1 O O X . |
$$ | 2 O X X X |
$$ -----------[/go]

Let's focus on the different sides of the board. We already know that White has no play on the right side, and if Black plays there she loses; so the score on the right side is 0. We know that White can play on the left side to a position worth 0. If Black plays on the left side White can capture the Black stone and win, so Black has no play there. We count the left side as 1 pt. for White. By convention we write values from Black's point of view, so we score the left side as -1. Adding the scores together gives us a score for the whole board of -1. That means that White wins, even if White plays first. (At this point each play costs 1 pt.)

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

Continuing in this vein, we can score the right side as +3 and the left side as -3, for a total score of 0. The players can score the game without bothering to play it out by counting the territories.

At this point I can sense eyes glazing over. Like, who cares, right?

Indeed. Not many people, I dare say. After all, we don't count territory by play, do we? No, we don't, as a rule. However, when there is any question, we do appeal to play, either actual or hypothetical.

Let me mention a couple of points, however. This form of the Capture Game has a group tax. That is almost always the case with any form of No Pass Baduk. We do not use a group tax today, but throughout most of its known history, baduk has been played with a group tax. It is not just a feature of stone scoring.

Also, playing inside your own territory, if it is not disastrous, costs 1 point. That is true for this capture game and also for regular baduk with territory scoring. If it does not cost anything to play on an intersection, it is not territory. (I'll address area scoring later.)

Also, where did this territory come from? Nothing in the rules of the No Pass Capture Game says anything about territory and scoring. Actually, both the idea of territory and the ability to score by counting territory arise from the no pass rule (and finite play). That means that, for any form of baduk, not allowing passes will enable us to score the game without any rule about scoring.

Bill Spight wrote:At this point I can sense eyes glazing over. Like, who cares, right?

You're being too pessimistic
I care. But I don't understand yet all this.

I know the french, british and the AGA rule (to the point that I was shocked to see "All live stones of a player's color left on the board" in the definition of area scoring...), and the japanese rule.

But I don't understand button go yet. I know group tax, but I don't know no-pass baduk.

I must take some time to read this carefully.

A bit late to respond to this...

Pio2001 wrote:a wish of my own : there should be only one ruleset in the world, so that we don't have to worry under which rules we are playing.

This doesn't seem likely. The duality of the Chinese and Japanese/Korean approaches is not just a coincidence, not a random consequence of traditions, it is deeply rooted in the game. The whole problem with writing complete rules is like a snowball, one thing follows the other.

The strong point of Japanese is that (with a small, easy-to-accept addition of forbidding suicide) you can have a ruleset with only simple basic rules that already allows play - up to the first stop. Most importantly, the normal ko rule works. The price of this is that you need extra rules AFTER the stop, i.e. about L&D.

The Chinese approach eliminates L&D, so you don't need extra rules after the stop. But at the same time, normal ko (forbidding immediate recapture, i.e. a time-wise restriction) doesn't work anymore. You inevitably need some ko rules trickery, even in the main game. And the moment you start to fiddle with the ko rule to fix a known problem, you usually end up with introducing a new problem elsewhere.

But IMO the two approaches are not equal in value. Since disputes are rare and most games end naturally at the first two passes, trading problems after it for earlier problems and rule complexities sounds like a bad idea, a net loss.

About anomalies: I don't think the extent of their rarities (like 1 in 10000 or 1 in 1000000) matters. All anomalies are rare, and you either have flawless rules with no anomalies (like chess) or rules that only approximate the real game.

moha wrote:A bit late to respond to this...

Pio2001 wrote:a wish of my own : there should be only one ruleset in the world, so that we don't have to worry under which rules we are playing.

This doesn't seem likely. The duality of the Chinese and Japanese/Korean approaches is not just a coincidence, not a random consequence of traditions, it is deeply rooted in the game.

I am more hopeful. For one thing, the results of games under the two approaches are the same about half the time and differ by only one point about the other half. The main difference in scoring and strategy has to do with counting territory in seki, not with anomalies, which usually have the same result under the different rules. Pros and amateurs who play by one set of rules can switch to another set with little difficulty, although mistakes are sometimes made. The Ing ko rules are a challenge, however.

As for the different traditions, the oldest known description of weiqi sounds like stone scoring, which lasted into the 20th century in China. It used what is called a group tax, under which points of territory needed for life are not counted. OTOH, the oldest known scored game records indicate that they used territory scoring with a group tax. Until fairly recently it was not understood why territory scoring would have a group tax, since the game naturally ends long before most groups come down to just the eyes necessary to live. So most people thought that territory scoring with a group tax derived from stone scoring. Thanks mainly to Professor Berlekamp, we now know that territory scoring and a group tax can go together with no reference to stone scoring. In fact, with his rules he had to go to some trouble to eliminate the group tax (Mathematical Go). Each of these forms of ancient weiqi could have derived from the other one, or could have derived from a common ancestor, on could have arisen independently. John Fairbairn has expressed the opinion that they probably coexisted for centuries in China.

The strong point of Japanese is that (with a small, easy-to-accept addition of forbidding suicide) you can have a ruleset with only simple basic rules that already allows play - up to the first stop. Most importantly, the normal ko rule works. The price of this is that you need extra rules AFTER the stop, i.e. about L&D.

The Chinese approach eliminates L&D, so you don't need extra rules after the stop.

This is why Button Go basically uses Japanese/Korean rules until the point where play would normally stop, at which point the button is taken, after which the game is played by Chinese rules. Adding the button is a simple way to marry the different approaches. Like the modern Chinese rules, territory is counted in seki, however. Aside from that, the basic strategy is for territory scoring.

But at the same time, normal ko (forbidding immediate recapture, i.e. a time-wise restriction) doesn't work anymore. You inevitably need some ko rules trickery, even in the main game.

Well, both types of the game were played without written rules until the mid-twentieth century. I think ko rules trickery is of recent vintage.

But IMO the two approaches are not equal in value. Since disputes are rare and most games end naturally at the first two passes, trading problems after it for earlier problems and rule complexities sounds like a bad idea, a net loss.

I agree. Complicating every game in order to handle rare occurences seems like a poor tradeoff. But the Japanese 1989 rules not only complicated the game with difficult to understand rules, it changed the nature of the game. That is why I regard them as an abomination.

moha wrote:The strong point of Japanese is that [...] you can have a ruleset with only simple basic rules that already allows play - up to the first stop.

This is a strong point not only of Japanese rules or only territory scoring rules but of all rules.

Most importantly, the normal ko rule works.

1) If you mean that the effect of the basic ko rule applies, this is so for all rules.

2) If you mean that the basic ko rule would cover all kos, you are wrong.

The price of this is that you need extra rules AFTER the stop, i.e. about L&D.

The price of not having (1)? Since (1) applies for all rules, there is no price.

The price of not having (2)? Since (2) is wrong also for Japanese rules or territory scoring, your point is void.

The Chinese approach eliminates L&D,

It should. Well designed area scoring rules eliminate L+D. The Chinese Rules do not.

normal ko (forbidding immediate recapture, i.e. a time-wise restriction) doesn't work anymore.

See above.

You inevitably need some ko rules trickery, even in the main game.

It depends on what you call trickery. If you call the practical application of superko trickery, you must call that of any ko ruleset trickery because any requires detection whether repetition occurs / has occurred / is about to occur.

Area scoring does NOT require superko. There are alternative ko rulsets, such as the Basic-Fixed-Ko-Rules.

And the moment you start to fiddle with the ko rule

See above. Each ko ruleset needs detection whether repetition occurs.

to fix a known problem,

What problem?

you usually end up with introducing a new problem elsewhere.

Bad rules design is not mandatory.

Since disputes are rare

You make the assumption that one should not talk about the problems of applying territory scoring rules in each game. Their correct application creates disputes in each game. Only the informal, implicit agreement NOT TO APPLY THE RULES STRICTLY avoids disputes in each game.

moha wrote:The strong point of Japanese is that [...] you can have a ruleset with only simple basic rules that already allows play - up to the first stop.

This is a strong point not only of Japanese rules or only territory scoring rules but of all rules.

Most importantly, the normal ko rule works.

1) If you mean that the effect of the basic ko rule applies, this is so for all rules.

2) If you mean that the basic ko rule would cover all kos, you are wrong.

The price of this is that you need extra rules AFTER the stop, i.e. about L&D.

The price of not having (1)? Since (1) applies for all rules, there is no price.

The price of not having (2)? Since (2) is wrong also for Japanese rules or territory scoring, your point is void.

The Chinese approach eliminates L&D,

It should. Well designed area scoring rules eliminate L+D. The Chinese Rules do not.

normal ko (forbidding immediate recapture, i.e. a time-wise restriction) doesn't work anymore.

See above.

You inevitably need some ko rules trickery, even in the main game.

It depends on what you call trickery. If you call the practical application of superko trickery, you must call that of any ko ruleset trickery because any requires detection whether repetition occurs / has occurred / is about to occur.

Area scoring does NOT require superko. There are alternative ko rulsets, such as the Basic-Fixed-Ko-Rules.

And the moment you start to fiddle with the ko rule

See above. Each ko ruleset needs detection whether repetition occurs.

to fix a known problem,

What problem?

you usually end up with introducing a new problem elsewhere.

Bad rules design is not mandatory.

Since disputes are rare

You make the assumption that one should not talk about the problems of applying territory scoring rules in each game. Their correct application creates disputes in each game. Only the informal, implicit agreement NOT TO APPLY THE RULES STRICTLY avoids disputes in each game.

All anomalies are rare

Except for the systematic anomalies occurring in each territory scoring game.

you either have flawless rules with no anomalies (like chess)

Or like go with carefully written area scoring rules.

RobertJasiek wrote:Bad rules design is not mandatory.

Indeed.

Bill Spight wrote:

The strong point of Japanese is that (with a small, easy-to-accept addition of forbidding suicide) you can have a ruleset with only simple basic rules that already allows play - up to the first stop. Most importantly, the normal ko rule works. The price of this is that you need extra rules AFTER the stop, i.e. about L&D.

The Chinese approach eliminates L&D, so you don't need extra rules after the stop.

This is why Button Go basically uses Japanese/Korean rules until the point where play would normally stop, at which point the button is taken, after which the game is played by Chinese rules. Adding the button is a simple way to marry the different approaches.

I agree it is an interesting approach. But I also recall some earlier discussions where the outcome of some otherwise identical positions would depend on ko threats. I wouldn't call this an anomaly, but is still a surprising difference from both the Japanese and Chinese game.

After a quick look at your above text I'm also not sure using superko like that would be free of all cases of the 1-eye flaw.

Like the modern Chinese rules, territory is counted in seki, however.

Unlike the "no suicide" rule, I am not aware of theoretical necessity behind "no territory in seki". Without one the natural choice is the simpler one, oc.

Well, both types of the game were played without written rules until the mid-twentieth century. I think ko rules trickery is of recent vintage.

Certainly, just like written rules themselves. Somebody mentioned above less rigid rules where (for example) the treatment of repetition is up to the referee. Such are flawless by nature, the only problem is practical application.

RobertJasiek wrote:

moha wrote:The strong point of Japanese is that [...] you can have a ruleset with only simple basic rules that already allows play - up to the first stop.

This is a strong point not only of Japanese rules or only territory scoring rules but of all rules.

No, as I wrote above with area scoring you need more than the simple basics just to have the game progress correctly. At the very least something to cover unbalanced cycles. This is very different from territory scoring.

You inevitably need some ko rules trickery, even in the main game.

It depends on what you call trickery. If you call the practical application of superko trickery, you must call that of any ko ruleset trickery because any requires detection whether repetition occurs / has occurred / is about to occur.
...
Each ko ruleset needs detection whether repetition occurs.

This is only a popular fallacy, at least in the theoretical sense. Go rules do not necessarily need to detect repetition (just like two eyes for example). In long cycles the theoretical game may keep on repeating the moves in question infinitely, leaving the game without an end position (like perpetual check). OC this may also be undesirable for some, and for practical application you certainly want at least some way to be able to say "and so on". But making the distiction between theoretical and practical rules is important here. (And is a point where basic ko with hot stone and time-based restriction shines.)

For area scoring, you need not rule unbalanced cycles specifically but must ensure a game end nevertheless. For territory scoring, for might create a rules exception that no ko rule applies to unbalanced cycles;) So what?