Thue-Morse Go is a Go variant in which the order of stone placements follows the Thue-Morse sequence. Each turn contains either one or two placements, with the changing order creating new tactics and changing which threats require an immediate answer.
The game is normally played without komi. It has been conjectured that the Thue-Morse order balances the game without a first-player advantage or disadvantage, but this has not been established. Mathematical results about fair sharing do not by themselves settle the question: in Go, making a move changes the value of other moves.
The idea appears to have been proposed independently by atimholt, TheElvenAngelCatboy, and BHydden, with further development by the Online Go Forum community.
These rules assume familiarity with Go. Except where modified below, play uses Tromp–Taylor-style placement, capture, and area scoring.
In the ordinary game, Player 1 plays Red and Player 2 plays Blue by default. The Kill-All variant instead assigns colors to the Attacker and Defender roles. These defaults can be changed via Abstract Play's paintbrush customization screen.
The available sizes are 11×11, 16×16 (default), 19×19, and 23×23. Each size has the same number of points under either connectivity option.
As the number of placements goes towards infinity, the average number of placements per move approaches 1.5, so as a first order approximation a board 150% of the size should give Thue-Morse games of comparable length to Normal Go games. Applying this estimation to the number of points on 9×9, 13×13, and 19×19 gives the 11×11, 16×16, and 23×23 results.
Square is the usual Go grid: points connect orthogonally.
Snub square uses a tiling of squares and triangles. Interior points have five neighbours; boundary points have fewer. Connections, liberties, captures, and territory all follow the lines of this board. Points are not connected merely because they appear diagonally adjacent.
Thue-Morse, the default, begins:
R B B R B R R B B R R B R B B R ...
Grouping those placements into moves gives:
R | BB | R | B | RR | BB | RR | B | R | BB | ...
The sequence can be constructed by starting with R, then repeatedly appending a copy of everything written so far with R and B interchanged:
R RB RBBR RBBRBRRB RBBRBRRBBRRBRBBR
Equivalently, number placements from zero and write the placement number in binary. An even number of 1 digits gives Red a placement; an odd number gives Blue a placement. Passing and taking the button still consume their allotted placements and advance the sequence.
Balanced Marseillais repeats the first four terms, RBBR, indefinitely:
RBBR RBBR RBBR RBBR ...
Across the boundaries of those four-term blocks, this means that Red's first move has one placement and every subsequent move has two:
R | BB | RR | BB | RR | BB | ...
This order is also known as ABBA or 12* or T(2). It changes only the allocation of placements; capture timing remains a separate option.
With Weak eyes unchecked, resolve each stone placement separately:
On a two-placement move, the second placement therefore sees the result of the first, including its captures. Placement order matters. Two genuine eyes retain their usual protection: an attempted invasion of one eye is removed before the opponent can fill the other.
With Weak eyes checked, defer both removal and repetition checking until the end of the move. Place both stones, or place one and pass the other opportunity, then remove opposing strings without liberties before removing your own strings without liberties. Only the resulting board is checked for repetition.
Consequently, a two-placement move can fill both one-point eyes of an opposing string and capture it. Three separate secure eyes provide protection against this attack. A stone temporarily without liberties can also survive if the rest of the move saves it. Stones awaiting capture remain on the board until the move ends, so their points cannot be reused for the second placement.
Choose one of the following:
A position means the arrangement of stones on the board. The player to move, location in the placement sequence, button ownership, and scores are not part of the comparison.
The initial board counts as an occurrence. With Weak eyes unchecked, the positions after both placements of a double move count separately. With Weak eyes checked, only the position after the move's final clearing counts. Passes and taking the button do not add occurrences merely because they leave the board unchanged.
These rules also govern suicide. For example, placing an isolated stone that immediately removes itself recreates the current board. PSK forbids this; the other repetition settings may allow it, with the resulting occurrence counted normally.
The button is a single scoring bonus available to whichever player takes it first. Taking it uses one placement instead of placing a stone or passing. It does not count as a pass for ending the game.
Under the default setting, there is a 1-point button if the number of board points is odd, and no button if it is even. Thus 11×11, 19×19, and 23×23 ordinarily have a button, while 16×16 does not. This makes the combined nominal value of the board and button even; tied scores remain possible.
When Reverse komi is enabled, include that komi when determining parity. Let p be the number of board points and k the reverse komi:
Default button value = 1 if p + k is odd; otherwise 0.
The default button cannot be taken until Player 2 has chosen the reverse komi.
With 0.5 point button checked, there is instead a half-point button on every board size, regardless of reverse komi. It is available from the beginning. Once claimed, it prevents a tied score, because all other scoring contributions are integers.
Kill-All games have no button and cannot be combined with the 0.5 point button option.
This option is intended for players of unequal strength and makes the game unrated. Its operation differs between ordinary and Kill-All games.
Player 2 is the stronger player. At the beginning of their first move, they declare a positive number h of handicap stones. They then give up their first h placement opportunities by automatic passing, while Player 1 (the weaker player) plays their allotted placements normally.
The declaration itself consumes the first of these h opportunities. It is not an additional pass on top of the declared handicap. The placement sequence continues throughout the handicap; it is not restarted afterward. Compulsory handicap passes do not count toward ending the game.
If h = 1, Player 2 (the stronger player) may use the second placement of their opening double move normally. If h ≥ 2, that whole move is given away; any remaining compulsory passes are served at the beginning of Player 2's later moves.
Let p be the number of board points. The permitted range is:
H = round(p / 25) 1 ≤ h ≤ H
Here, round means rounding to the nearest whole number.
Player 1 is the stronger player. Before the opening begins, they declare h extra Attacker stones. Player 2 (the weaker player) then takes the first turn of the alternating opening described under Kill-All below.
If Player 2 (the weaker player) claims the Attacker side, they immediately place the h extra Attacker stones on empty points of their choice. If Player 1 (the stronger player) claims the Attacker side, no extra stones are added.
The permitted range is:
1 ≤ h ≤ 2 × round(p / 25)
The maximum can equivalently be written as p / 12.5 rounded to the nearest even integer. This means rounding to a multiple of two, not the rounding convention sometimes called “ties to even.”
| Board size | Maximum ordinary handicap | Maximum Kill-All handicap |
|---|---|---|
| 11×11 | 5 | 10 |
| 16×16 | 10 | 20 |
| 19×19 | 14 | 28 |
| 23×23 | 21 | 42 |
This is another handicap option for ordinary games. Player 2 is the stronger player and chooses a positive whole number k at the beginning of their first move. That many points are added to Player 1's (the weaker player's) final score.
Declaring reverse komi uses no placement. Player 2 (the stronger player) still has their normal opening double move, except for any placements given away under Handicap stones. When both options are enabled, both declarations must precede the actual placements; the declarations may be entered in either order.
With H = round(p / 25), the permitted range is:
1 ≤ k ≤ 14H
The numbered selection stones offer multiples of seven:
7, 14, 21, ..., 14H
Any whole number within the permitted range may instead be typed into the move box; the multiples of seven are shortcuts, not a restriction on legal komi.
Reverse komi makes the game unrated and cannot be combined with Kill-All. Its effect on the default button is described above.
A player may pass any placement. On a double move, submitting only one placement passes the unused opportunity. The Pass control passes the whole move.
To end normally, one player makes a move containing a voluntary pass, and the opponent then passes their entire move while agreeing on which strings are dead. The first move may contain both a stone placement and a pass; the final move must pass every available placement. Thus simply counting two individual passes is insufficient: two passes belonging to the same player's double move do not end the game.
When passing, a player may mark whole strings as dead. The opponent may accept those markings with a whole-move pass, propose different markings while passing, or continue play. Two whole-move passes agreeing that no stones are dead also end the game.
Changing the proposed dead strings keeps the game going. Once a nonempty set has been proposed, responding with a move that contains no voluntary pass, or clearing all the markings, ends dead-stone marking for the rest of the game. Any dead stones must then be captured on the board before the players pass to finish. A move containing both a placement and a pass can preserve the agreement process if it retains or revises the markings rather than clearing them.
When agreement ends the game, remove the agreed dead strings and use area scoring:
The higher score wins; equal scores are a draw. Prisoners are not counted separately, since they're implicit in the number of stones on the board.
Kill-All replaces area scoring with asymmetric goals. One player is the Attacker, who begins with stones on the board; the other is the Defender, who tries to establish just one unconditionally alive string. The opening determines both the initial position and who plays each role.
Begin with an empty board. Starting with Player 1, players alternate turns. On each turn, the player either:
All stones placed during the opening belong to the eventual Attacker, regardless of who placed them. The other player becomes the Defender. There is no requirement to place a stone before claiming the Attacker side.
With Handicap stones enabled, Player 1 (the stronger player) first declares the handicap and Player 2 (the weaker player) begins the alternating opening. If Player 2 claims the Attacker side, they add the declared extra stones immediately, as explained above.
AP caps the alternating opening at (p − 1) / 2 rounded down to a whole number: 60, 127, 180, or 264 stones for the four available sizes. Upon reaching that limit, the next player must claim the Attacker side.
After the opening, start the chosen placement sequence from its beginning. The Defender receives the first placement and takes the A/0 role; the Attacker takes the B/1 role. This applies whether the selected order is Thue-Morse or Balanced Marseillais. Setup stones do not advance that sequence.
Passing is forbidden. Every allotted placement must be used to place a stone, subject to capture and repetition rules. There is no button, reverse komi, dead-stone agreement, or scoring.
The Defender wins by forming an unconditionally alive (ie pass-alive) string: one that can survive without answering the opponent. Life dependent on seki or winning a ko is insufficient. AP detects this using Benson-style analysis, requiring two vital eye regions normally or three with Weak eyes enabled.
The Attacker wins when their own pass-alive stones leave no room for the Defender to establish the necessary eyes. AP checks for such a win automatically, although this test does not recognize every hopeless position.
An early documented proposal is atimholt's Reddit post of 16 April 2017, suggesting the Thue-Morse order as an alternative to komi after watching the Stand-up Maths video about fair sharing. The post also suggested dispensing with ko restrictions, on the grounds that the future placement order changes even when a board position recurs.1)
Abstract Play also credits TheElvenAngelCatboy's separate Reddit proposal. Both earlier Reddit discussions were linked from the subsequent OGS discussion.2)
On 15 August 2019, BHydden opened the Online Go Forum discussion that became a center for playing and developing the game. Players used ordinary OGS games, inserting passes when necessary to give the other player consecutive placements. These administrative passes were a way to accommodate OGS's alternating turns, rather than extra placements in the Thue-Morse sequence.3)
The community developed written move lists, browser scripts, and physical trackers. Samraku established an OGS group in October 2019, and Vsotvep posted a script that displayed upcoming placements. In spring 2020, Samraku and Vsotvep demonstrated physical trackers, including hexadecimal tracking. A round-robin tournament was organized in 2020 using New Zealand rules with zero komi.4)
Periodic alternatives were also explored. In October 2019, antonTobi described a repeating order with a double move every third turn. In June 2020, the discussion explicitly considered repeating the first eight Thue-Morse terms, 01101001, as an easier sequence to track. This eight-term option is not among AP's current variants.5)
AP's Balanced Marseillais option instead repeats the first four terms, 0110. Its name and allocation of placements come from chess. Marseillais Chess, published in 1925, gives each player two moves per turn. Robert Bruce's balanced version, introduced in 1963, reduces the first player's opening turn to one move, producing the ABBA ABBA… order used here. The credit concerns that move order, not the invention of Thue-Morse Go as a whole.6)
The early discussions already raised whether two consecutive placements could fill two eyes, and whether changing the move order removed the need for a ko rule. AP treats capture timing and repetition as independent choices: Weak eyes changes when captures occur, while the repetition group offers PSK, double delayed PSK, or fivefold-repetition draws.7)
The Kill-All option combines the placement-order variants with the asymmetric life-and-death objective of Kill-All Go. Its opening is Pieboxing, credited to MXHero, including the optional handicap in which the weaker player receives extra stones only if they choose the Attacker side.8)
AP also provides square or snub-square connectivity, two button conventions, and optional stone or point handicaps. These are independently selectable rule choices, subject to the incompatibilities described above; they should not be read as one universally established historical ruleset.
The default tracker shows the next sixteen placements. The TMS tracker display option instead represents the next placement's zero-based index with three hexadecimal digit columns. Tracker runs downward reverses the tracker direction.
Click points to enter a move's placements. With Weak eyes unchecked, their order technically matters nearly always, but in practice is only likely to matter when one order is illegal or results in a different result than intended. With Weak eyes checked, their order is completely meaningless, so AP normalizes it automatically to facilitate smoother premoving. To pass the rest of a partially entered ordinary move, submit it early; to pass the entire move, use the Pass control. When a pass has been entered, clicking an occupied string can mark or unmark it as dead while agreement remains available.
The Hide territory dots option hides the dots in empty territory which would be scored under Tromp-Taylor rules. Territory dots otherwise show the score of the position as it stands, with proposed dead strings removed; they are how the position would be scored if both players passed with the current markings of dead groups, not a prediction of the final result with intelligent play.
In Kill-All games, Mark pass-alive stones throughout the game shows the recognized pass-alive stones faded in every position. Otherwise those markings are shown in the ending position.
This draft describes the upstream develop implementation inspected on 19 October 2026. The game is marked experimental. Source reference: Thue-Morse Go engine and associated tests.