Thoughts about Go ruleset elegance

1. Introduction

It is the opinion of many players that the Go ruleset should be as elegant as possible. Defining the "elegance" of a ruleset is something quite subjective, though. Undoubtedly the properties of an "elegant" ruleset should the following:

People who advocate simple rulesets often prefer the New Zealand, Tromp-Taylor or AGA rules. Traditionally the Japanese rules are said to be extremely complex and exact opposite of "elegant".

I agree that a ruleset should be elegant as defined above and that a simple and elegant ruleset makes the game easier to grasp, and I also agree that the three rulesets mentioned above are quite fine. However, in my opinion people usually fall into the fallacy of thinking that elegant rules should be as short as possible. I also think that overly despising the Japanese rules is a slight exaggeration.

I intentionally did not mention shortness in the list of "elegance" properties above. Shortness does not always equal to simplicity. Sometimes shortness can even cause the ruleset to break the above properties. In my opinion elegance by shortness might not always be the best solution.

2. Superko

One example of definining elegance by shortness is the positional superko rule. This rule is certainly short, easy to formulate and simple to understand: "A move must not repeat an earlier board position."

One advantage of this rule is that it takes care of the simple ko rule at the same time and thus we don't need to specify that rule separately.

2.1 Can superko be problematic?

The elegance by shortness advocates will usually tell that the superko rule does not cause any problems and thus completely complies with the elegance properties above. When they are presented with the few problems superko introduces to the game, they will usually argument that these problems are extremely rare and do not affect the game practically at all. While this argument is certainly true, this is already a contradiction to the initial claim.

Since they still maintain that the superko rule is elegant, that means that the elegance properties described above should be modified and an additional "unless the problematic situation is extremely rare" should be added.

The (once again) contradictory thing is, however, that they will still think that for example the game voiding in the Japanese rules (which is caused by the lack of superko) is not elegant, even though it happens extremely rarely as well.

One could argument that, "OK, both have problematic cases, but the superko is simpler to formulate and thus complies with more of the elegance properties and is thus more elegant". I'm not going to say this is not true, but in my opinion whether the superko rule really complies with the above properties or not is quite subjective and is a matter of opinion.

Certainly the superko rule is easy to understand, there's no doubt about that. However, is it easy to play according to this rule (specially for a beginner)? In a complex repeating position it may well be quite difficult for a beginner (or even for a bit more experienced player) to be sure which one is the first move not allowed by superko.

Dia. 1
Dia. 1
For instance, consider the situation in Dia. 1 at the left. How fast can you tell the status of the groups (supposing superko is in use)? Imagine two beginners playing a game like this; how difficult would it be for them to follow strictly the superko rule if it's difficult even for a more experienced player? This is a very simple thing for a computer to check, but certainly not for a human.

Even though quite rare, there really are situations where following the rule can be more difficult than necessary. This, in my opinion, does not comply with the properties of an elegant ruleset.

And this is not the only problem with the superko rule. It also breaks the property of not having problematic cases.

Dia. 2
Dia. 2
Consider the black group in Dia. 2. Normally this kind of group with one eye and a half-point ko false eye is considered dead in all rulesets. However, if superko is in use then in this situation black can capture the ko (by playing at the marked point) but white can't capture back because of the superko rule. Thus there's no way white can capture the black group according to the rules, thus black is alive with 4 points of territory (plus the two prisoners) and wins the game. Black is not dead simply because white doesn't have any legal move (except filling his own eye, which he can't do lest black capture all the white stones, of course). If white had even one extra move (eg. a dame) black would be dead (white can make the extra move, after which black can only pass, after which white can capture the ko after which black can't recapture and white captures all the black stones).

In my opinion this is an undesirable side-effect of the superko rule (and that's why some rulesets try to fix this problem by making certain exceptions to the superko rule). Granted, it happens very rarely, but reportedly this type of situation has happened in real games on small boards, so it's not an impossible situation in practice. This oddity clearly breaks the principle of an elegant rule not giving unfair or illogical solutions to certain problems.

The following two diagrams show other two anomalies caused by the (positional) superko rule.

Dia. 3
Dia. 3
The one in Dia. 3 is not even a rare occurrence, even though it usually doesn't cause any problems. This is a seki and all the stones are alive (supposing the outer black stones are alive). However, if white would happen to play at the marked point that would be a grave mistake: When black captures the two white stones white can't capture back because of the positional superko rule. Unless there are bigger threats elsewhere on the board black can capture all the white stones.
Dia. 4
Dia. 4

The position in Dia. 4 is a double-ko seki. It would be, however, a grave mistake for either player to take a ko: The other player will take the other ko, the first player will have to pass and then the other player will take the first ko. Now the first player can't capture the other ko because of the superko rule and he will lose all his stones.

These two problems do not happen with the so-called situational superko (nor in rulesets without superko, naturally). In short, situational superko means that a play must not repeat an earlier board position left by the player (that is, the turn ie. sente was also the same). This is a slightly more complicated superko rule than the one discussed here. It makes the rules slightly more complicated (which was the thing to avoid in the first place) and it isn't infalible either since it also has its problems (such as Dia. 2).

These are not the only problems caused by superko. There are several others not presented here. The point is, however, that the superko rule is certainly not free of problems and thus not a perfect rule in the sense of elegance.

Not having a superko (such in the Japanese rules) causes problems in itself, basically the few infinite looping situations which cause the game to be declared void (but this happens very rarely). It's certainly not elegant either (slightly complicated wording, causes some problematic situations) but neither is the superko rule. Thus deciding which one is more "elegant" is a question of opinion.

In my personal opinion not having superko is better because it doesn't cause additional burden to the players (ie. having to check which move in a long loop is the first which breaks the rule).

2.2 Is lack of superko a bad thing?

As already said, many people have quite strong opinions about the lack of superko in Japanese rules being a really stupid thing and they feel that game voiding due to an endlessly repeating position is completely arbitrary and unjust and stupid and whatnot.

But is it really all that bad?

One such endlessly repeating situation is the so-called eternal life (chosei). It happens so rarely that a Chinese Go text says:

You should buy fish, vegetables, meat and wine
and have a good party to celebrate yourself

It seems more common that the attitude of professional players and also amateurs, specially in the "big" go countries is not to get outraged and offended by such rule, but they may even celebrate such rare occurrence. Game voiding because of this doesn't seem to be generally deemed as braindead, as many westerners seem to think.

Moreover, let's consider superko more profoundly: Does it really give a fair result both players can be happy with? While this may be more a question of opinion, consider this:

When does the need of game voiding or applying superko happen? That is, when does an endlessly repeating position happen?

It's not enough that just a triple-ko or eternal life position happens on the game. It's quite common that, specially at the end of the game, there may be even more than three kos (most of them half-point kos) on the board, yet no repeating happens. It's thus wrong to say that "triple-ko voids the game" as many do.

What is needed, besides such position happening, is that it happens in such a situation that neither player can stop the loop and tenuki instead. That is, there's so much profit at stake that the first one who plays elsewhere will lose the game and thus neither player can stop, but they will continue playing the repeating position over and over (or lose the game if they don't).

What happens if superko is used? What happens is that one of the players is forced to lose. It's more or less random who happens to be player who would make the first illegal move. It's usually quite impossible to control the sequence of moves leading to the repeating position in such way that a player could intentionally avoid losing if superko was in use.

Thus, usually, he did not lose because he was weaker than his opponent but only because he had bad luck.

And that is the point: Is Go a game of luck or a game of skill? If one of the players can lose the game practically at random, does that make the game fair?

In this light, is game voiding so bad? Granted, it voids the game equally at "random", but at least neither player suffers from it. The only negative consequence of this is that they might need to play another game. That is, the players get a new opportunity.

Not so with superko: If superko is in use, then one of the players loses basically at random, the other one wins, period. Many superko advocated seem to think that superko somehow avoids problems and lets the game to be continued normally. However, what will usually happen in this situation is that the losing player will just resign and the game will be thus ended anyways: Thus the situation is practically the same as with the game voiding rule, except that now one of the players has lost and the other won.

It may also happen that one of the players didn't have the entire game at stake in the repeating position and he could have played elsewhere instead but he inadvertedly played a move breaking the superko rule. In a tournament game this usually results in him immediately losing the game (because of making an illegal move) just because of this tiny mistake. If Japanese rules had been used, he would have just noticed that it's a repeating position and that he doesn't have anything to lose from it and could just play elsewhere, even if the same position had repeated itself a couple of times already.

I personally do not think superko is any more fair than game voiding. The disadvantage of superko is that it burdens beginners with a sometimes difficult-to-impose rule (which may be accentuated in small boards). With game voiding there's no such problem: The players will eventually see that the game is repeating, and if it was someting innocuous, one of the players will just stop the loop, and if it wasn't, then there will be no problems in resolving who made the first illegal move (a task which may be quite difficult for beginners if the loop has been continuing for some time): The game is just ended with no result and they can get going on with a new game.

In this way lack of superko actually makes the game simpler than superko (a rather surprising point of view which is not accepted by many).

3. Area scoring and pass stones

3.1 Area scoring

Area scoring (that is, your score is the number of free intersections surrounded by your stones plus the number of stones you have on the board) is often thought as more elegant than territory scoring (number of free intersections surrounded by your stones plus the number of prisoners you have captured). This is because it makes several things easier to understand for a beginner.

For instance, using territory scoring it may be difficult for a beginner to accept that dead stones inside enemy territory don't need to be explicitly captured but can be taken as prisoners at the end of the game (capturing them explicitly would cost points).

However, using area scoring this is natural: Capturing the dead stones explicitly at the end of the game would not change the score (empty intersection or own stone, it doesn't matter, it's one point anyways) so that unneeded step can be simply skipped.

Also if there's some controversy about the status of a group, the situation can be played explicitly without costing points to either player and that way it will be clear whether the group can be captured or if it lives.

In most situations either scoring method results in the same score difference and thus it doesn't really matter which one you use. However, since area scoring makes it a lot easier to understand the dead stone removal process as well as it makes it easy to demonstrate the status of a group, it is thought to be more "elegant".

In this way the area scoring really is very nice compared to territory scoring.

However, play a 19x19 game with a beginner and after the game is over and there are more than a hundred stones on the board tell the beginner "now count all your stones on the board". Talk about burden...

The nice thing about territory scoring is that it's easy to count even for a beginner: The beginner simply needs some advice about rearranging territories in easily countable multiples of 5 (and preferably of 10) and then counting is extremely simple. After rearranging the territories counting usually takes just a few seconds.

Area scoring advocates say it's very easy to perform area counting. However, I have yet to be taught a way which is as easy as territory counting. Maybe there is, but I don't know any.

3.2 Pass stones

Territory scoring certainly has the problem that in some rare cases resolving the status of certain groups after the game has ended can be complicated (the bent-four in the corner situation discussed later is one such case). Fortunately these situations are rare, but nonetheless they exist.

The pass stones rule tries to fix these problems while still preserving territory scoring. This rule states that when a player passes he gives a prisoner to his opponent. It may not be immediately obvious, but this rule makes territory scoring virtually identical to area scoring but without the burden of having to count all your stones on the board.

This is a certainly nice thing since it has the best of both worlds: Counting is easy and there are no problems in demonstrating the status of a group by playing explicitly, and it's even probably easy for a beginner to accept dead stone removal. I personally like this rule.

However, this doesn't mean it's completely problem-free, even though these problems are only cosmetic in nature, which isn't very bad.

The simple pass stones rule introduces as a side-effect the so-called pass-fighting. This is a side-effect of the rule and shouldn't really by itself be part of the game.

Pass-fighting happens at the end of the game when one of the players passes and gives a prisoner. If the second player just passed as well he would also give a prisoner and that's it. However, if he makes a move which the first player must respond to (ie. threats to get some points eg. by capturing something), after the first player has responded he can pass (giving a prisoner). Now if the first player also passes he will give a second prisoner. Thus the second player would now have two prisoners while having given only one, that is, he has an extra point. Naturally if the first player does not want to give him the extra point he will make a threat move himself and this cycle continues until there are no more threatening moves left. If the first player who passed needs to pass last because of losing this fight, he will have given an extra prisoner to his opponent, worth one additional point. (Naturally this is only relevant if the score difference would be half point, but it still can happen.)

A variant of the pass stones rule states that white must pass last in any case (which means that there will be three passes if white passes first), thus giving the extra point advantage to black right away without a fight. This certainly avoids having this odd pass-fighting, but it can be hard to accept that white needs to give an extra point to his opponent if he doesn't have any move left on the board and it's his turn. If white would have been winning by half point before passing it would certainly feel very unfair to lose the game simply because of this odd rule. (In all other rulesets he would win.) White would most probably want to pass-fight instead of this. I'm not very convinced this white-passes-last rule can be called "elegant".

Of course a small additional point is that it may be hard for a beginner to understand why he has to give a prisoner to his opponent when he passes (this may seem illogical and even unfair at first), but this shouldn't be a very big problem.

If we disregard the pass-fighting phenomenon, then the pass stones rule is quite nice and certainly elegant.

4. Bent-four in the corner

This is perhaps one of the most controversial situations which is not very infrequent. Probably every player who has played hundreds of games have had this situation in his games (unlike for example an infinite loop situation which is very rare and may not happen even in tens of thousands of games).

Dia. 5
Dia. 5
Dia. 5 shows one of the few arrangements which exhibit this peculiar situation (the other arrangements are very similar, with three invading stones in the corner and two common liberties in a very seki-like shape).

Japanese rules are often criticized and blamed as illogical because they have a dead-stone confirmation rule which has the direct consecuence that in this situation black is dead (without white having to prove it). It is usually thought that having such rule is extremely "non-elegant" and ugly. In my personal opinion this opinion is a bit unfair and greatly exaggerated. I will give my arguments below.

Putting aside all rulesets for a moment, let's look at why this situation is so special (it certainly looks like a seki, but isn't).

Dia. 6
Dia. 6
Dia. 7
Dia. 7
The key feature of this situation is that black can't do anything there but white can start a ko-fight whenever he wants. The diagrams 6 and 7 at the left show how this happens. White's move 5 is a ko capture which puts the black's group in atari.

Why is this situation so special? This is because of the abovementioned feature that white can decide when to start the ko and black can't do anything about it. In rulesets where playing inside your own territory after the game has practically ended (ie. there are no moves worth points nor dames left) does not cost points, such as the ones using area scoring or pass stones, white can explicitly protect all his weak points where black could make ko-threats and then play out the sequence above. Since black doesn't have any ko-threats he must simply pass after which white captures the black group.

Capturing the black group this way didn't cost white any points (in the same way as protecting for ko-threats didn't either) and thus this whole process can be skipped by mutual agreement and the black stones simply considered dead.

In this light the Japanese rule which causes black to be dead doesn't seem so unfair after all. It simply makes Japanese rules closer to other rulesets.

There is, however, certain situations where a big difference can happen between rulesets in this matter. Fortunately this situation isn't very common so in practice it's rather rare that it really happens (even though it can happen sometimes, probably more often than eg. infinite loops). These few situations truely make the Japanese rules a bit inferior in terms of "elegance" to the other rulesets. However, I personally think this doesn't make the Japanese rules so much "non-elegant" as many purists would like me to believe.

Dia. 8
Dia. 8
The difference can raise when there's a situation elsewhere on the board where white can not remove a black's ko-threat. Dia. 8 at the right presents such a situation.

At the upper right corner of the board there's a seki. If white plays the ko in the upper left corner as described above, black can make a ko-threat by playing at a. This threatens to capture 20 white stones which is much more than the 7 black stones on the left. Thus white cannot ignore this threat but must capture the three black stones.

After this black will take the ko. If there are no more ko threats on the board black will live in the left by capturing the invading stone (which makes two eyes). White will have got seven points on the right (four points of territory plus three prisoners) but in exchange black saved his seven stones on the left (which is worth at least 15 points compared to the situation where black's group was dead). Even if black's threat was smaller than the left corner black would still get some compensation. (In most rulesets white can also choose not to play the left corner and thus it's left as a seki.)

White cannot possibly remove black's ko-threat at a, so it's an unremovable ko-threat. This is one of the few cases where there's a very pronounced difference between rulesets, which is certainly a shame. Fortunately this situation doesn't happen very often.

When there are no unremovable ko-threats the Japanese rules are exactly as fair as any other rulesets in this regard. It's thus in my opinion quite unfair to despise the Japanese rules because of this.

One could ask: "Why do the Japanese rules have such odd rule? Why not do it in the same way as the other rulesets?" This is a fair question and it's discussed in the next section below.

5. Pass for ko-threat

The Japanese ruleset has two special rules for the dead stone confirmation stage (after the game has finished): Demonstrating the status of a group can be done without continuing the actual game (that is, any moves made after the game has been ended are not part of the game itself) and the only valid ko-threat in this stage is a pass.

The first rule means that the status of a group can be demonstrated by playing it out, but after it has been demonstrated, the moves can be taken back to the point where the game actually ended. (This is very rarely needed in practice, though.) It brings the Japanese rules closer to other rulesets (but doesn't really help the problem of a beginner accepting this as logical and fair).

The second rule is the one which causes controversy. It means that if there's a ko at the confirmation stage, no ko-threats can be made (even if there would be some). Among other things it causes the bent-four in the corner situation to be dead (ie. black in Dia. 5 would be dead because he can't make a ko-threat if white plays as in diagrams 6 and 7).

One could ask why have such an odd rule. In spite of what it might seem at first, this rule is not arbitrary and it has its own elegance.

Dia. 9
Dia. 9
Dia. 9 shows a situation where the usefulness of this rule is clear. At the right there's a double-ko seki. Such seki provides an infinite amount of ko-threats to both players (capturing one of the kos puts the opponent's group into atari forcing him to take the other ko).

The black group in the left corner is dead. However, supposing there's no pass-for-ko-threat rule: How would white demonstrate it's dead? If he takes the ko (by playing at a) black can make a ko-threat in the double-ko seki forcing white to reply there, after which black retakes the ko. Black could continue doing this forever and thus white couldn't capture him.

In other rulesets superko causes the black group in the left corner to be dead: After two ko-threats in the double-ko seki black can't recapture the ko in the left corner because it would repeat an earlier position, thus black is dead.

In Japanese rules the pass-for-ko-threat rule at the confirmation stage causes the black group to be dead (because black can't make the ko-threat in the double-ko seki).

Then why not use superko instead of pass-for-ko-threat? One good thing about not having superko is that for example, black in Dia. 2 is automatically dead. Thus this rule achieves in this case the same effect as the superko rule but without introducing the problems inherent to superko.

Although this special rule is not problem-free either, one cannot decisively argument that it's a bad and "non-elegant" rule. It has its own elegance because it simplifies some things in the confirmation stage. One cannot completely disregard the opinion that it might even be more elegant than superko for this purpose. (I'm not claiming it is, I'm just stating that it really is a question of opinion.)

6. Suicide

In some rulesets (such as Tromp-Taylor) suicide is allowed. It's often argumented that it makes the ruleset shorter and simpler without affecting drastically the game (and it indeed has some special behaviour only in a few rare cases).

I find this argument odd. When suicide is not allowed, this has to be said in the rules. However, when suicide is allowed, also this has to be said specifically (in the form that you have to remove your own stones without liberties after a play, after removing opponent stones without liberties).

Thus allowing suicide simply replaces one rule with another. The amount of rules hasn't really changed, so it's odd to claim that it makes the rules shorter.

It is often argumented that not allowing suicide requires a rule which wording is more complicated. This is a question of opinion. I don't think it's very complicated to say that a move is not allowed if after removing opponent stones without liberties one of your own groups would not have liberties. It's basically the same thing as with the suicide rule but instead of removing stones it just says you are not allowed to make such play.

7. An extreme example in New Zealand rules

There's one rule in the New Zealand ruleset which I personally find an extreme example of a rule created for the sake of simplicity which can result in horrendously unfair and arbitrary results.

The New Zealand rules have been clearly developed with the elegance by shortness principle. They are short almost to the extreme (even though Tromp-Taylor rules are even shorter), in some cases even at the expense of clarity: Some rules are quite hard to understand at first (and seem to be developed for programmers instead of the average people). I'm not saying this is bad, though. I personally am a programmer and like these kind of recursive definitions the NZ rules use.

But anyways, my main point was this one rule which I consider too extreme to be reasonable. This is what the rule says:

The game is finished when both players agree that there are no more worthwhile moves. 'Dead' stones may then be removed from the board by mutual agreement. If they cannot agree which stones are dead they must play on. If they cannot then agree who shall move next, all stones stay on the board (are alive) and are counted.

The fundamental point is the last sentence. It clearly has been written to "get rid" of this problem with a rule which is as short and simple as possible. However, in my opinion it can have completely unfair consequences.

Suppose that after both players have passed, one of the players (say, black) notices a weakness in one of his opponent's (white's) groups which he could exploit to capture some stones or even kill the whole group. This weakness was missed by both players during the game, but black noticed it after both have passed.

Naturally black will want to continue playing and move first to get profit from this weakness, specially if it will allow him to win the game (supposing he would lose if the game was ended as it is).

Of course if white now spots this weakness as well it will be him who wants to play first in order to reinforce. White doesn't want to continue the game (it would be fine for him if it ended like it is), but if it is continued he naturally will want to play first.

So both players want to play first now (because the one who plays first wins the game). What do the rules say? Something really outrageous! Since there's no agreement, the game is simply ended and, believe it or not, no dead stones are removed from the board! All the dead stones on the board are now alive.

What does this mean? It means that if there's even one single dead stone inside a huge territory, the big group surrounding the territory and the single opponent stone will form basically a seki, and thus the owner of the territory gets no points from the territory. He will thus potentially lose tens of points completely arbitrarily (it's just a matter of luck whether or not there would be dead stones inside a territory or not), which makes this rule very unfair. You could as well toss a coin to see who wins the game. This is completely against the basic principles of Go.

And before you flood my email with hate mail, I'm sure that, even though I haven't checked, this is not handled in practice like this when playing with the NZ rules but all dead stones are removed by mutual agreement regardless. However, if we read the rules strictly, this is prohibited: All stones stay, period. The rules don't say anything else.

I believe that the spirit of the rule is that the stones which are being disputed stay on the board and this rule does not apply to dead stones not disputed. However, once again, if you read the rule strictly, it says all stones, nothing else.

Thus this is an extreme example of a rule wanting to be short and clear ending up being unambiguous and very unfair, giving completely arbitrary results in some cases if followed strictly.

Note: If I'm not completely mistaken, in the Japanese rules the one who wants to continue the game (in this example black) cannot move first, but his opponent (here white) gets the first move. If white spots the weakness he can protect it and loses only one point doing so (which he should have lost anyways during normal play). I think this is very fair.

8. Conclusion

Even though some players have very strong opinions about certain rulesets being "elegant" and other rulesets not, I think these opinions are sometimes a bit exaggerated and biased.

The fact is that all rulesets have their little problems. Go is such a complicated game that it's not possible to create a reasonable ruleset which is completely free of problems and is perfectly "elegant". (The infamous Ing rules are a good example of what happens when one really tries...)

In my opinion this fact is not bad. It's one of the things which make Go such an interesting game. It's very fascinating how a game which in principle has simple rules can have situations which cause headaches to even strong players and call into question every ruleset. All rulesets have their strong and weak points, their own "elegance", and defining one ruleset as better than another is a question of opinion.

I believe that if Go was a game where short, simple and elegant rules were possible, it would be a much more boring game.

Copyright 2004 Juha Nieminen

Valid HTML 4.0!