Rules and Area and Territory Scoring

Table of contents Using simple ko (or ban lifting passes) under area scoring (or areafied encore) Using superko (or no ban lifting passes) under territory scoring Using territory scoring without excluding sekis Using komi 7 under area scoring - issues with B's surplus stone Using a button or first pass compensation rule under area scoring

"When you have eliminated the impossible, whatever remains ... must be the truth."

Area and territory scoring have some natural differences. Minor things like valuable dame or black's extra area point if he gets a surplus move. But despite those the two scoring methods are fundamentally still the same game, with nearly identical gameplay and behavior. This principle also has implications about the "correct" or universal rules of the game, in a reasonably objective way.

Below are some rules design problems and mistakes - rule components and combinations that would artificially CREATE a significant divergence and behavior difference between the area and territory game. Note that here territory scoring refers to the common type with L/D and hypothetical play, but for completeness, the hybrid type (a territory phase followed by an areafied encore using pass stones) can also be considered.

Using simple ko (or ban lifting passes) under area scoring (or areafied encore)

This would allow prisoner-unbalanced area repetition thus draw or no result in common positions, which are plain sekis under territory scoring with its natural immunity to such.

 

One example is the non-ko line of sending three returning one.

For area scoring to overcome this, one possibility is some kind of prisoner-aware long cycle rule (like Chinese ko which prevents unbalanced repetition), or something like the Spight stop rule. Another potential alternative would be a complete superko rule without ban lifting passes - but this in itself would create a difference, see below.

Using superko (or no ban lifting passes) under territory scoring

This would lead to ko play pathology with territory scoring, diverging from both area scoring and common sense in ordinary positions.

Under area scoring (or areafied encore), even if the rules don't have ban lifting passes, the players usually have equivalent substitute - plenty of 0 pt ban lifting moves, plays inside territory. So ko play can still follow a natural path, recapture of open kos remains possible, and a lack of passes could only matter on very crowded and small boards - not in daily practice.

Under territory scoring, however, only dame could substitute, which are not always available (or enough). The players often have no means to change the board without losing points. So without complete and ban lifting passes, ko play could change drastically from both area scoring and normal go logic, creating permanently un-recapturable kos - even on 19x19 board, and even in common positions like a mannenko, or kos like this:

no komi no prisoners  

Lacking threats, normally B can only connect and let W do the same and win by his territory advantage. The outer ko could only give a temporary gain for B. This assumes W can eventually retake the outer ko should B make a futile attempt to take it. Which is true under area scoring (or areafied encore) - regardless of passes. Common (L/D based) territory scoring rulesets work similarly - but need ban lifting passes. (And possibly resumptions - note that if B tries the ko line, W needs to actually recapture in the game for the prisoner, it is not enough to declare B ko stone dead.)

Using territory scoring without excluding sekis

This would make territory scoring unstable, and unable to score some multi-state seki positions that are no problem for area scoring. Additionally, dead stone removal from sekis could change the cost of some plays into them (depending on how L/D is defined).

Correct scoring needs a final position with an unambiguous score, and sekis are a threat to that. They can take various forms with special properties, and some - like a double ko seki - have multiple stable (possibly scorable) states, between which it can be pushed around. Which is still ok as long as these states all have the same score - but this is where territory scoring start to have problems.

Under area scoring there is no scorewise difference between filling an intersection (like a ko mouth) or leaving it open and surrounded by live stones. Thus multi-state sekis usually still have - or can be stabilized to - an unequivocal area score. Under territory scoring, however, filling worth less than surrounding, which reduces possible stabilizing moves as they may lose points. Thus - if territory scoring would include sekis - some positions would have a stable area score, but undefined (oscillating) territory score.

 

Mannenko is probably the most common example where this could break territory scoring, with its unique one-sided ko and consequently alive ko stone - see here.

The standard solution - excluding sekis - can be restated as territory is only granted in completely controlled (independently alive, or freely-pass-aliveable) regions. This can be formalized without even defining sekis. Another possible alternative is an areafied encore, which can score sekis similarly to area scoring.

Using komi 7 under area scoring - issues with B's surplus stone

Less significant than earlier points, and is not about creating a new difference but about an existing one that is usually fixed with the standard 7.5 area komi. The root problem is B plays one more stone than W in half of the games (since he plays first, and has chance to play last as well). This surplus stone has no direct effect on territory scores, but is an automatic extra point in area. This introduces a problematic element into area scores, with various consequences - and various ways in which area rules try to correct it.

The potential B surplus stone means that the area score is usually either the same as the territory score or one point better for black. Territory komi is 6.5, and increasing area komi by the average value of the extra stone (0.5) to 7 is a possible approach. This would balance winning chances (better than the standard 7.5), but besides allowing ties, it has some problems. The surplus stone is not random (nor skill-based either). Due to how parities work out on an odd board, B will normally (without special sekis or one-sided passing) get his extra stone specifically when the territory score (thus the sum of territories as well) is even:

board (odd) = territories (odd or even, after prisoner backfill) + stones played (odd if B had extra)
 

Getting a surplus stone on B+6 boards but nothing on B+7 leads to rounding both B+6 and B+7 (territory) outcomes to B+7 area. The same happens with B+4 and B+5 and so on - creating superposed score pairs rounding to equal area score. Their difference remains visible even in area terms though, as the first case becomes B+7 with B getting the last move (so B one more stone than W) while the second case is B+7 with W last move (so both sides equal moves).

Achieving the same area score with one surplus stone is not really equal performance as without it. Thus this rounding affects the accuracy of how well scores measure performance, and makes area granularity coarser.

This problem also manifests as allowing free 1 point mistakes within a score pair without consequences. This is best known near the endgame - like the common granularity examples, or FreeTeireIfEvenDame (B may have free teire on odd, W on even territory parity). But the same is actually true throughout the game. A move that loses one (territory) point also flips who gets the last area play/dame (with flawless play onwards), which - depending on the current territory parity - can stay within a score pair thus cancel out in area.

See for example KataGo's evaluation of W's possible responses to the best B 9x9 opening moves under area vs territory (compare 1.A to 1.T, or 3.A to 3.T). Katago thinks the territory solution of 9x9 is B+6. This is even, which means B can expect to get the last play for his extra stone. Which in turn means that in the opening B cannot, but W can make a free 1 point mistake under area scoring. Such W mistake moves from B+6 to B+7 territory, thus remains within the same pair and will get masked - its only effect is letting B reach the same area score without the extra stone he needed originally.

Due to the above effects some area rulesets exclude the surplus stone from area scoring, with a last move or first pass compensation. The Taiwan rule, as well as Ikeda's rule, WMSG rules or button go all let area scoring distinguish the two cases (^[1]).

But the simplest fix is the standard 7.5 komi (or 5.5 as in the past, ODD+0.5 generally). This draws the komi line between score pairs, so while it does not distinguish B+6 and B+7 territory, it makes both lead to the same area winner, with or without rounding. Thus the effects of coarser granularity are mitigated: the extra stone (or the free mistake / free teire) - when present - can at most affect winning margin, not win/lose/draw. The price is a difference in balancing winning chances: this komi cannot produce the same winner as territory scoring with territory komi (6.5), but produce the same winner as territory scoring would with this komi (7.5).

In contrast, komi 7 would allow the surplus stone to actually change the area winner, leaving the effects of coarser granularity unmitigated. While this would indeed make a difference to territory scoring, whether this is ok is a debated question. One practical effect would be extending the tie outcome from a single score/performance to the entire [B+6,B+7 territory] pair (thus twice as wide and frequent).

Using a button or first pass compensation rule under area scoring

This would create unintended behavior differences to the original Taiwan rule (last play compensation), as well as to both area and territory scoring.

Due to the problems with the potential extra B stone, some area rulesets try to exclude it from area scores, or compensate somehow. This needs a method to judge if such compensation is due or not - whether a given game had the surplus stone, did B play both first and last.

Things like teire may complicate this question, but it can usually be answered from factors like the number of played stones, or by checking the last few moves. Ing mentions the historical Taiwan rule as "black gave up half a stone when he played last". Ikeda quotes the original rule as "half a point is deducted from Black's score and added to White's score whenever Black makes the last competitive move".

This kind of last play adjustment is equivalent to using a dynamic komi that differs by 1 in games with the extra B stone and without it. For example, both 6.5 and 7.5 area komi can be meaningful and correct in their half of games, and this would make the area score almost always equal to the territory score, with a reasonably robust solution.

However, a newer idea is to replace "have B played an extra stone" or "who played last" with "who passed first" (or to introduce a half point button which is essentially the same). This normally still works fine - the first passer is usually the opponent of who played last. But sometimes this makes the wrong call.

no prisoners  

B just connected in response to a W atari. The normal conclusion of this game is W connects at a, B ataris at b, W connects at c.

But W also has another way to play, starting with a W pass. This leads to B b, W a, allowing B to take the corner ko once at c, but since W has a threat at bottom, he can count on winning the ko afterwards to recover the original result.

This line makes little sense in normal go, neither under territory or area scoring (with or without Taiwan rule). But is not strictly inferior either, as it has the same result as the simple main line.

Note that the number of stones played by W and B are equal in both lines, and it is always W who makes the last play in either case. So there is never a surplus B stone - nothing to compensate for. Area and territory scoring naturally agree here - as well as area + Taiwan rule, which makes no adjustment in either line.

However, the early W pass makes first pass rules believe this game had a B last play, and thus the compensation point is due. Another painful thing is that this behavior (and the game result) depends on a type of connection played earlier on the bottom (see here).

[1] This practice to compensate for the extra B stone is also mentioned by Ing (in preface/7), apparently it was reasonably common at the time.