Lasker-Maas Rules

"The Lasker-Maas rules for the game of Go" is a modern territory-scoring ruleset (like Japanese rules), but in which the (implicit) definitions of life and death status of groups, and of which points actually count as territory, are settled by actual play in the same way as in the Chinese rules.

This ruleset was drafted in March 19, 1995 by Robert Elton Maas, being a slight modification to the original rules published in the appendix on Go in the book "Modern Chess Strategy" by Edward Lasker. Maas modified the writing to be more precise regarding how to end the game and decide final life and death and count the score fairly.

General basic definitions:

• Go is played on a square matrix (usually represented by grid of crossing lines where the intersections of the lines are the points of play, usually physically slightly elongated from a square grid in the direction that makes it appear square when viewed in perspective from players seated across it, but exactly square when drawn on a computer screen or printed representation or public display board).

• One player places black stones on the points on the board while the other places white stones.

• The board starts empty, then players alternate placing a stone of their color on some unoccupied point of the board, black going first. Players may pass at any time in the game rather than place a stone. There is an infinite supply of black and white stones available for play (although in practice only a few hundred are needed to play on a full-size i.e. 19-by-19 board). There is also a place to put "captured" stones, which is initially empty (usually this is actually two separate places, one for each color stones).

• At any time, two stones of the same color which are orthogonally adjacent (along rows or columns of matrix, i.e. along the grid lines of physical representation of board, not diagonally) are "directly connected". If there is a chain of such direct connections S1 S2 ... Sn such that each Si is directly connected to S(i+1), then S1 is "connected" to Sn. Otherwise no stones are connected.

• A "group" is a maximal set of mutually connected stones, that is, a set of stones each connected to each other, and such that no other stone is connected to any of them.

• For any stone, a "direct breathing space" for that stone is an unoccupied space orthogonally adjacent to that stone. For any group, a "breathing space" for that group is any direct breathing space of any stone of the group.

Rules:

• Rule 1: On each turn, a stone may be placed on ANY unoccupied point on the board, except as restricted by rule 2 or rule 4.

• Rule 2 (no suicide): A stone may not be placed such that in the resultant position the group of which that stone is a member doesn't have any breathing space.

• Rule 3 (capture): When a stone is placed, if it occupies the last breathing space of one or more opponent's (oppositely-colored) groups, i.e. after placing the stone the opponent's group(s) have no breathing space whatsoever, such opponent's groups are "captured", i.e. removed from the board immediately and placed in the prisoner's place. Even if the stone that was placed was part of a group that didn't have any breathing spaces initially, after removing the opponent's group(s) the group now does have breathing space, so the play is allowed.

• Rule 4 (positional superko): If, after placing a stone and removing any opponent's groups that are accordingly captured according to rule 3, the position of the whole board is exactly the same as it was any previous time of the same game, that move is not allowed.

• End of the main phase of the game: when both players pass consecutively (without any intervening non-pass plays), the first (main) phase of the game is over. Play then continues just as before except that stones to be placed on the board are taken not from the infinite supply but from the prisoner's place. (Note: Rule 4 applies just as if the two passes had never occurred.) If either color of prisoners becomes empty, a pair of stones one of each color is moved from the infinite supply to the prisoners' place (so that neither player will be prevented from playing due to lack of prisoner stones). When both players pass consecutively again (which must be two NEW passes, not one of the first two passes plus an immediate third, but may be the third and fourth consecutive pass immediately after the first two), the second phase is finished.

• Counting: At the end of the second phase, empty points are treated as if they were a third color of stones for the purpose of defining "connected" and "group". Any group of empty points such that one of the points is orthogonally adjacent to any white stone, and one of the points (same or other) is orthogonally adjacent to any black stone, is not counted. Otherwise, any group of empty points is counted as "territory" for whichever color stones some of its points touch, the number of points counted being equal to the number of empty points in the group. For each color, the number of stones remaining in the prisoner place is subtracted from that color's score. The color with the largest score is the winner.

Commentaries:

• The first phase is territory ("Japanese style") play, where placing stones in one's own territory reduces it, while the second phase is area ("Chinese style") play, where placing stones in one's own territory does not reduce it and is necessary to remove dead enemy stones from the board in order to claim the territory they occupied and the adjacent formerly empty territory.

• Score is territory style, whereby plays inside your own territory reduce the number of empty points thus reduce your score, and may be "counted" at the end of the first phase of the game.

• The second phase is merely the method of resolving questions of life and death that the players couldn't simply agree upon at the end of the first phase. Because plays during the second phase are from the prisoner place instead of from the infinite supply, such resolution (typically) doesn't change the Japanese-style score, because each such move both fills a spot (reducing territory or increasing number of dead stones eventually in prisoner place) and consumes a prisoner (thus decreases the number of stones in prisoner place), which effects cancel.

• At any point in the game the two players can agree to the result of the game and cease play beyond that point. For example a player can resign at any point.

• In practice, the second phase can be totally omitted when players agree on which points to score as territory and which stones to remove as extra prisoners for counting, and that will happen in the vast majority of games. Thus, in this vast majority of games, these rules are played and counted exactly identical to Japanese rules, and an external observer would not be able to tell which of the two rulesets is being used.

Differences with Japanese and Chinese rules

• Traditional Japanese rules have a lot of pecular situations that have special rules that go against these more clean rules, such as bent four in corner, triple ko, etc.

• Traditional Chinese rules discard the low-order bit of the score-difference, thus not allowing as fine control of komi as Japanese and Lasker-Maas rules.

• A consequence of the Lasker-Maas rules is the existence of DameKoThreats. If in approaching the end of the first stage, one player has more surplus ko threats than the total number of dame pairs, that player can gain an extra point by not filling the last one-point ko. He takes the ko, and the oppoinent uses a dame as a ko threat, player answers with another dame instead of filling the ko, and opponent takes the ko. This player then makes a ko threat and retakes the ko. This continues until all dame are exhausted, then the opponent must pass rather than play a dame, and this player immediately passes also to end the first phase without filling the ko. During stage two, the other player still can't retake the ko, so fills one of his own points of territory to capture some dead stones, and this player immediately fills the ko. This is completely analogous to Chinese rules, which also allow to keep this extra point of territory if the ko is left open until after filling all dame (implicitly, by not changing the score at all when filling after there are no more dame). See ChineseKo for another example of ko fight that is worth fighting under Chinese and Lasker-Maas, but not modern Japanese rules. Also, counting this extra point of territory has not always been unanimously ruled against by Japanese players, see RuleDisputesInvolvingGoSeigen.

• OneSidedDame will in practice (assuming that players understand the rules and play correctly) score as territory points for the player, as in Chinese rules, and unlike Japanese. For that, all that a player has to do is to just wait until the second, "area-scoring" phase, and fill those dame using prisoners, thus gaining points for them exactly as if they were actual territory.

• TorazuSanMoku will in practice work out as 3 points of territory, like the historical Shuwa ruling and unlike modern Japanese rules, when played in the second phase (and no player has a reason to play it during the first phase).

• Points of territory inside sekis are counted as territory, as in Chinese rules, and unlike Japanese.

• Lasker-Maas rules use superko throughout the game. Unlike in Chinese, Japanese and Korean professional games, where a triple ko, eternal life and similar typically voids the game and forces a replay, under Lasker-Maas rules those are played by the superko rule. For example, triple ko becomes a normal ko-fight.

• The score is typically equivalent to the Japanese score, but without the fiat rules about what's alive and what's dead. Playing stage two from the prisoner's storage is equivalent to deciding what's alive and what's dead by the Chinese or Lasker "kill it, or else it's alive" rule, without screwing up the essentially Japanese score. Therefore, score is in 1-point increments instead of the 2-point increments of the Chinese area scoring method. As a result, komi can be meaningfully adjusted in 1-point increments to have a better chance of matching the difference in skill and advantage of first move.

• If adopted in practice for tournament play, a slight modification can be made to the rules to allow more than a single "area scoring phase" at the end, or to allow to end this final phase once players come to an agreement and there is not more dispute, similar to the AGA rules, so that if only a few extra points of territory must be filled to prove that they are indeed territory (say, a one-sided-dame dispute) or if a small life and death dispute must be resolved, it is not necessary to capture all the groups in the whole board too, but just solve the dispute and then proceed to scoring.

Equivalence with Button Go:

• The essence of Lasker-Maas rules is almost equivalent to ButtonGo. It can be made fully equivalent by a very slight change: make the second phase (the "area scoring" phase, in which stones are played from prisoners) start immediately after the FIRST pass of any player. Let's call it "Adjusted-Lasker-Maas".
• With this modified version, it can be mathematically proved that if black wins by X points (X might be negative if black loses) by "Adjusted-Lasker-Maas", they win by X+0.5 points in button-go (all before komi, so adjusting komi makes the scores actually identical).
• Thus, best play (score-maximizing) is always identical under both versions.
• This equivalence holds as long as taking the button has identical consequences to passing with respect to ko bans. In this equivalence, taking the button maps to the first pass under Adjusted-Lasker-Maas rules, and vice-versa.

Santo?: An interesting question is whether pass-fights can occur under these rules. I think that these rules are equivalent to Ikeda Territory Rules 1 (but Lasker-Maas "playing from the opponent's prisoners" might be considered more natural and easier to remember than the passing-stones used by Ikeda, as those also have the special provision to make sure that players play/pass exactly the same number of times, and thus one must remember who played first in the second phase to make that final adjustment, something that one does not need to remember and take care of under Lasker-Maas). Is there any example of a pass-fight under Lasker-Maas rules?

Santo?: I reformatted this whole page, as it was essentially correct but very hard to read (it was formatted like "a huge wall of text", and the text had some quite superfluous non essential parts that most other pages about rules simply not mention, like going into a lot of detail about how handicap can be used in a game of go and such). Feel free to revert or to fix anything that you think I "screwed up" during the reformatting :)

See

• http://www-2.cs.cmu.edu/~wjh/go/tmp/rules/Lasker.html.
• Message-ID: <40auic$g8s@openlink.openlink.com>
  • http://groups.google.com/group/rec.games.go/msg/f9f792a7b32cc00c
• Message-ID: <40ausl$gd8@openlink.openlink.com>
  • http://groups.google.com/group/rec.games.go/msg/ac0d0fbf7dd9a8ff

Nobrowser?: Where does the part about one-sided dame come from? It is not in the archived Maas posts, and it seems very much at odds with the rest of these rules. That is, such points definitely do not count as territory if you just follow the plain language of the rules, so there would have to be a special case rule added for them. Has that been done by Lasker or by Maas or anyone? Santo?: I added some clarification to the one-sided dame part. That is basically my commentary about how the rules should work with correct play: it is not that the rules necessarily define those one-sided dame points as "normal territory for counting", but players can easily "force" those points to count for them (by filling them in the second phase, just as in Chinese Rules you can force them for you by filling them last, after normal neutral dame), thus when correctly played, they end up behaving the same as if they were territory.

Nobrowser?: The two posts (one from March, the other from September) have different superko rules. The earlier one specifies positional but the later specifies situational superko.

Nobrowser?: Returning here after some time, I hope I understand these matters a bit better now. It seems to me that counting or not counting territory in seki is the one way area and territory rule sets differ which cannot be reconciled -- not even with a technical gadget like the Button. So I lean toward classifying any rules that do count seki points as area rules, even Lasker-Maas (and same with AGA and Ikeda Toshio's "territory" rules I).