Version 2, 2006-04-28 last update, 2006-04-28 first day, Robert Jasiek

INDEX | GO | RULES |

Introduction to Ikeda Territory I Rules

General Nature
Necessary Study
The Rules Core
Meaning of the Passes during the Playout
Remarks about Ko Rules
Strategic Behaviour in Standard Positions
Probably No Frequent Pass-Fights

General Nature

The scoring of Ikeda Territory I Rules is a promising compromise between a) Area Scoring and b) Life and Death Territory Scoring. Removals can be done by alternate play in the playout. During the playout, an equal number of moves is compensated by paying 1 prisoner per pass. Generally, two-sided dame are unvaluable because they can be occupied already during the alternation.

The behaviour of some shapes is like under Area Scoring while the behaviour of some other shapes is like under Life and Death Territory Scoring. The behaviour of endgame positions with only two-sided dame and basic endgame kos left depends on which ko rules are used.

Necessary Study

Unlike Area Scoring or Life and Death Territory Scoring, Ikeda Territory I Scoring has not been tested in millions of played games. Instead theoretical study is necessary. During the previous months, quite some study has been done, however, still a significant amount should be done.

Since the rules have the two phases alternation and playout with different rules, particular attention must be paid to 1) strategic behaviour in standard positions, 2) the precise details of ko rules and their consequences for strategic behaviour, and 3) pass-fights. Current research suggests that strategic behaviour in standard positions is reasonable, the details of ko rules can be chosen to avoid technical problems, and frequent pass-fights do not occur. However, a more exhaustive study of all standard endgame positions with only two-sided dame and basic endgame kos left is strongly recommended for whichever ko rule(s) should be chosen. This is much more important than study of any scarce or rare non-standard position like bent-4 or like both a basic endgame ko and a double disturbing death on the board.

The Rules Core

Basic Rules

The game consists of the alternation, then the playout, then the scoring.
The alternation stops with two successive passes.
The playout continues the alternation and ends with two successive passes.
During the playout, one prisoner is paid per pass. However, a prisoner is not paid for the last pass if the same player started the playout.
During the scoring, a player's score is the number of empty intersections surrounded only by his stones plus the number of prisoners of opposing colour.

Rules of Agreement Option

In between the alternation and the playout, the players may make an agreement about all strings that shall be removed and to omit the playout in that case.
If they agree, they remove those strings, their stones become prisoners, the playout is omitted, and the scoring follows.
If they disagree, the playout follows next.

Meaning of the Passes during the Playout

The passes during the playout have these meanings:

Like in every Go ruleset or like during the alternation, usage of both plays and passes as moves avoids the otherwise occurring very frequent and long pass-fights.
For an equal number of moves of Black and White, possibly different numbers of plays are compensated by costly passes. Thereby it is no disadvantage to approach liberties of stones to be removed.
A succession of two passes ends the playout sequence.

If the playout has an unequal number of moves (i.e. plays or passes) of Black and White, then the last pass has only one meaning: it contributes to the succession of two passes that ends the playout. This last pass does not have the meaning to compensate the previous opposing pass. Since the last pass is free, there is no fight about its own value.

Remarks about Ko Rules

In principle, Ikeda Rules can be combined with 1) a Superko rule, 2) Basic-Fixed-Ko rules, or 3) Basic-ko and Long-cycle-ko rules. However, since Ikeda Rules have two phases, one has to be careful about the details.

A Superko rule can apply either to both phases together or to each phase separately. Ikeda Toshio has used Positional Superko applied to both phases together. This is natural for a ruleset where the one and only playout is a continuation of the alternation.

The Basic-ko rule could require at least either an intervening play or an intervening play or pass. The latter can be problematic together with Long-cycle-ko rules: If the alternation ends with basic-ko capture, pass, pass, then the first move of the alternation could be a recapture in the basic-ko and already this could create a long-cycle-tie. Therefore the Basic-ko rule that requires an intervening play seems safer. - Unfortunately, this does not end all troubles: If ko rules have Long-cycle rules at all, then there is the general threat of an unexpected, unwanted game end due to a long cycle. Formal proofs that such could not occur would be helpful. For logical rules, it is not a good solution to leave the rules ambiguous by reintroducing the traditional verbal player agreement for an exceptional game end due to a long cycle.

Strategic Behaviour in Standard Positions

Ikeda Territory I Rules have in particular the following strategic behaviour:

Two-sided Dame

This is like under Life and Death Territory Scoring.

Generally, two-sided dame are unvaluable
If there are an odd number of two-sided dame or minimally necessary teire, then at least one of them should be filled during the alternation.

Example (1)

Black to move

. . . . . . .
# # # # # # #
. . . . . . .
O O O O O O O
. . . . . . .

Alternation

. . . . . . .
# # # # # # #
1 3 5 7 6 4 2
O O O O O O O
. . . . . . .

White 8 passes, Black 9 passes.

Position at the end of the alternation

. . . . . . .
# # # # # # #
# # # # O O O
O O O O O O O
. . . . . . .

Agreement: The players agree not to remove any strings.

Score = 7 - 7 = 0.

Remarks: The easiest strategy is to fill as many dame as possible during the alternation. Thereby both players ensure that they are unvaluable.

One-sided Plays

This is like under Area Scoring.

One-sided plays (like one-sided dame, intersections in asymmetrical sekis, for removal of dead stones from sekis, or defense in a capturable-2 seki) provide points during the playout.

Example (2)

Black to move

# # # # # # O O O O O # .
# # O O . # O . O O O # #
# . O O . # O O . O # # .

Alternation

Black 1 passes, White 2 passes.

Position at the end of the alternation

# # # # # # O O O O O # .
# # O O . # O . O O O # #
# . O O . # O O . O # # .

Agreement: The players disagree.

Playout

# # # # # # O O O O O # .
# # O O . # O . O O O # #
# 4 O O . # O O . O # # .

Black 3 passes (pays 1 stone), Black 5 passes (pays 1 stone), White 6 passes (pays 1 stone).

Position at the end of the playout

# # # # # # O O O O O # .
# # O O . # O . O O O # #
# O O O . # O O . O # # .

Prisoners: 2 black stones, 1 white stone.

Score = (2 + 1) - (2 + 2) = -1.

Remarks: Playing a one-sided dame during the alternation would not get any points. Playing a one-sided dame during the playout gains 1 point because the opponent has to pass in the meantime and pay 1 stone for that pass. Therefore White disagrees during the agreement phase, thereby makes the playout possible, and plays the one-sided dame during the playout. The stones paid for passes during the playout become prisoners. The playout has an equal number of moves; so also the last pass is costly. The prisoners of a particular colour score for the opponent. White wins by 1 point, what is indicated by the score being negative.

Example (3)

White to move

# . # . O O . O .
# # # O O # O O O
# # # # # # O O O

Alternation

White 1 passes, Black 2 passes.

Agreement: The players agree not to remove any strings.

Score = 1 - 2 = -1.

Remarks: Empty intersections surrounded only by one player's stones score for that player. It is superfluous to fill some of them during a playout. The easiest strategy to get scored points in such simple asymmetrical sekis is to pass and leave as many one-sided empty intersections empty as possible. Here it is 1 one-sided empty intersection that White could but does not need to fill during a playout. Thus a playout is not necessary if the players simply agree during the agreement phase.

Basic Endgame Kos - Behaviour under Superko

If the positional superko rule is used, then the behaviour is in between that of Area Scoring and Life and Death Territory Scoring: The available ko threats might decide whether a basic endgame ko should be connected during the alternation or whether it can be connected during the playout to gain 1 extra point.

A basic endgame ko can be a fight about either only the captured ko stone or about both the captured ko stone and the empty intersection filled during the playout.
Scarcely, a basic-ko bigger than an endgame ko can be left open until the playout and resolved then.
If a basic endgame ko is next to teire, then besides the empty ko intersection itself it might become bigger by the number of the teire that could be filled during the playout.
If a basic endgame ko can be created on two adjacent dame, then also this ko might survive open until the playout.
It is sometimes perfect play of both players to leave two basic endgame kos with a ko stone of the same colour open until the playout.

Remark: Since this is only an introductory page, only very few examples are shown to illustrate the basic strategic variety.

Example (4)

White to move

. O O # . # .
O O O O # # #
. O . # # # .

Alternation

. O O 3 1 # .
O O O O # # #
. O 2 # # # .

Black 4 passes, White 5 passes.

Position at the end of the alternation

. O O O O # .
O O O O # # #
. O # # # # .

There is 1 black prisoner stone.

Agreement: The players agree not to remove any strings.

Score = 2 - (2 + 1) = -1.

Remarks: This is the usual case that the winner of the ko gets the 1 point for the captured opposing ko stone but has to connect the ko already during the alternation. The opponent uses a play on a dame to force the player to connect the ko before a playout could start. White wins by 1 point.

Example (5)

White to move

. O O # # .
O O # . # #
. O O # # .

Alternation

. O O # # .
O O # 1 # #
. O O # # .

Black 2 passes, White 3 passes.

Position at the end of the alternation

. O O # # .
O O . O # #
. O O # # .

There is 1 black prisoner stone.

Agreement: The players disagree.

Playout

. O O # # .
O O 5 O # #
. O O # # .

Black 4 passes (pays 1 stone), Black 6 passes (pays 1 stone), White 7 passes (pays 1 stone).

Position at the end of the playout

. O O # # .
O O O O # #
. O O # # .

There are 3 black and 1 white prisoner stones.

Score = (2 + 1) - (2 + 3) = -2.

Remarks: After White wins the ko fight, there is not even any dame left that Black could play as a ko threat. Such a heavily one-sided ko threat environment occurs only occasionally. If it occurs like in this example, then the winner of the last basic ko postpones its connection until the playout. Then, besides the already captured ko stone, he gains a second point when the opponent has to pay for passing in the meantime. Due to the superko rule, the opponent Black may not recapture the ko if only passes are made since the last capture by the player White. At the end of the playout, the prisoners can include some made during the alternation and some made during the playout. Since there are an equal number of moves of Black and White in the playout, also the last pass is costly. White wins by 2 points.

Whether a basic endgame ko has to be filled already during the alternation or can be filled for an extra point during the playout depends on the ko threat situation. During the alternation, filling a dame does not provide a point but it might be a ko threat or ko threat answer. Typically, dame provide ko threats for only one player while the opponent, who tries to leave the ko open until the playout, needs more regular ko threats than the player has regular ko threats plus dame ko threats together. Therefore it is only occasional rather than frequent that the playout starts while a basic endgame ko is still open.

For comparison, under Area Scoring it does not make a difference whether the ko remains open or filled. However, in a one-sided ko threat situation, the winner of a basic endgame ko can also try to fight the dame threats, although for the different reason that the dame are valuable. - Under Life and Death Territory Scoring, the value of a basic endgame ko itself lies only in the captured ko stone. The ko is then connected mostly because of rules technical reasons, e.g., to avoid a nearby group remaining in-seki.

Basic Endgame Kos - Behaviour under 3 Passes and a Basic-ko Rule

If the alternation ends with 3 successive passes and if a basic-ko rule prohibits repetition after two successive plays, then the behaviour approaches that of Life and Death Territory Scoring. During the alternation, passes serve as ko threats, ko recapture is possible after an intervening pass, and hence an open ko is defended by connecting it already during the alternation. However, study of further examples is necessary. (Also note that some further rule restricting long cycles is needed.)

Example (6)

White to move

. O O # . # .
O O O O # # #
. O . # # # .

Alternation

. O O 3 1 # .
O O O O # # #
. O 2 # # # .

Black 4 passes, White 5 passes, Black 6 passes.

Position at the end of the alternation

. O O O O # .
O O O O # # #
. O # # # # .

There is 1 black prisoner stone.

Agreement: The players agree not to remove any strings.

Score = 2 - (2 + 1) = -1.

Remarks: This is the usual case. White wins by 1 point.

Example (7)

White to move

. O O # # .
O O # . # #
. O O # # .

Variation 1

Alternation

. O O # # .
O O 3 1 # #
. O O # # .

Black 2 passes, Black 4 passes, White 5 passes, Black 6 passes.

Position at the end of the alternation

. O O # # .
O O O O # #
. O O # # .

There is 1 black prisoner stone.

Agreement: The players agree not to remove any strings.

Score = 2 - (2 + 1) = -1.

Remarks: This variation is a possible perfect play. White wins by 1 point. Although Black does not have a ko threat on the board, this last basic endgame ko fight was about only 1 point - the captured ko stone.

Variation 2

Alternation

. O O # # .
O O 4 1 # #
. O O # # .

Black 2 passes, White 3 passes, White 5 passes, Black 6 at 1, White 7 passes, Black 8 passes, White 9 passes.

Position at the end of the alternation

. O O # # .
O O # # # #
. O O # # .

There are 1 black and 1 white prisoner stones.

Agreement: The players agree not to remove any strings.

Score = (2 + 1) - (2 + 1) = 0.

Remarks: White 3 is a strategic mistake. White tries to keep the ko open until the playout to gain an extra point then. However, after intervening passes, Black may recapture the ko. This variation 2 leads to the score 0, which is worse for White than variation 1.

Further Remarks

Strategy related to basic endgame kos is more demanding under Ikeda Territory I Rules with superko than under some Area Scoring ruleset: Under Ikeda Rules, there is the additional strategic aspect of every strategic action whether to postpone it until the playout. Since Area Scoring has consistently the same rules for all moves of the game, strategy of the late endgame is simpler.

A little further study is necessary to see whether there are further strategic differences to Area Scoring or Life and Death Territory Scoring in standard positions. Of course, there are further differences in rare positions (like bent-4 or 1000-year-ko). Non-standard kos are influenced more by the ko rules or pass rules than by the scoring rules.

Probably No Frequent Pass-Fights

Recently on rec.games.go, Robert Jasiek has proven for Ikeda Territory I Rules formally and generally what is stated in the following informal simplification:

Normally there are no pass-fights during or shortly before the playout if a) Black and White control the same areas at the start and at the end of the playout, b) the two-sided dame and teire (and nothing else, in particular no basic-ko captures) are played shortly before the playout, and c) long cycles are not carried over from the alternation to the playout.

This means that during the playout the players can remove stones from their territories and can fill useless stones inside their or opposing territories however they like. If only they use perfect play, they cannot create a pass-fight. In other words, useless plays are merely useless - they cannot become harmful. After removal of all useless stones, the score is the same as if useless stones had not been played at all.

Although the proven fact is pretty mighty, it does not cover basic endgame ko fights during the late endgame of the alternation. Study of a lot of examples has not revealed any pass-fight there, either. However, further examples with basic endgame kos should be studied. This is a matter of a few weeks of work.

One should note that it is not considered a pass-fight if there is a ko fight about not connecting a basic-ko during the alternation so as to connect it during the playout. It may be called a phase-fight, though.