WallGo is a recently introduced strategic board game popularized by the 2025 Netflix series
The Devil's Plan. Although played on a small 7 × 7 board, its combination of stone movement
and wall placement yields high game-tree complexity and intricate strategic interactions. Despite its
growing popularity, WallGo remains underexplored. This paper presents WallZero, an AlphaZero-based agent
for the two-player WallGo setting. We introduce tailored action and feature designs to improve playing
performance significantly. In the evaluation, WallZero defeats two professional Go players who
participated in this study, securing on average 1.98× more territory per game. Beyond its strength,
we use WallZero to assess game fairness and identify key strategies for mastering WallGo. Interestingly,
our results show that the opening used in the Netflix series yields a more balanced game. Our code is
available at rlg.iis.sinica.edu.tw/papers/wallzero.
The Rules of WallGo
WallGo is played on a 7 × 7 board. In the two-player setting considered in this work, Red and Blue each
control four stones and seek to enclose more territory than the opponent.
(a)(b)(c)(d)(e)
Overview of WallGo rules. (a) Empty mode. (b) 4-stone mode. (c) Reachable area of Red stone labeled 4
(light green). (d) Two-step upward move with wall placement. (e) Endgame: Blue wins by 1 point
(19–18).
Setup phase: In empty mode, all eight stones are placed during setup. In 4-stone mode, four
stones are pre-positioned and each player places the remaining two stones. In both modes, Red places
one stone first, then players alternately place two consecutive stones, starting with Blue.
Play phase: On each turn, a player selects one stone, moves it by zero, one, or two orthogonal
steps, and then places one wall adjacent to the stone's final position.
Scoring: A region is assigned to a player only if it contains that player's stones and no opponent
stones. Neutral enclosed regions do not count for either side.
Game end: The game ends when all stones are enclosed within regions containing stones of only
one player. The player with the larger total territory wins. If totals are equal, the player with the
largest single region wins; otherwise, the game is a draw.
Although the board size is small, each turn combines stone movement and wall construction, resulting in an
estimated game-tree complexity of approximately \(10^{87}\).
WallZero
WallZero follows the AlphaZero training pipeline in the MiniZero framework, where Monte Carlo Tree Search
is guided by a policy-value network. The agent adds two WallGo-specific designs: a unified action space
that covers both setup and play phases, and a feature representation tailored to stones, walls, territory,
reachability, and recent history.
Feature design in WallZero.
Feature
# of planes
Description
Stone
2
Red / Blue stone
Horizontal Wall
2
Red / Blue horizontal wall
Vertical Wall
2
Red / Blue vertical wall
Player Turn
2
Indicates the player to move
Territory (T)
3
Red / Blue / Neutral territory
Reachability (R)
2
Positions reachable within one turn for each player
History (H)
36
Four-step history of stones, walls, and territory (9 per step)
Experimental Results
Human-AI Evaluation
To evaluate practical playing strength, WallZero uses a 10-block residual network and is tested against
two Taiwanese professional Go players, Wei Huang (3-dan) and
Chun-Hsun Chou (9-dan), across both modes and both colors. Before the formal matches, both players played
practice games to familiarize themselves with WallGo. The formal matches used a 90-second time limit per
move and 2,000 MCTS simulations per move for WallZero.
Game results between professional Go players and WallZero. Scores are reported as Human-WallZero
territory counts. Values in parentheses denote the ratio of WallZero's territory to the human's.
Empty Mode
4-Stone Mode
Red
Blue
Red
Blue
3-dan
16-33 (2.06×)
20-29 (1.45×)
14-32 (2.29×)
19-30 (1.58×)
9-dan
12-37 (3.08×)
17-30 (1.76×)
20-29 (1.45×)
12-34 (2.83×)
WallZero won all eight formal games. Across the matches, it gained 1.98× more territory than the
human players on average, and its estimated win rate exceeded 90% before move 20 in every evaluated game.
Opening Analysis
The analysis examines whether the 4-stone opening used in The Devil's Plan is aligned with the
opening preference of the empty-mode model, and compares the opening distributions learned in empty and
4-stone modes.
The most frequent openings show different behavior across the two modes. Empty-mode openings
are diverse but consistently center-oriented, with both players clustering around the opponent's
stones to restrict reachability. In 4-stone mode, openings converge to a smaller set of
patterns: Red first consolidates regional influence, Blue counters with two consecutive
placements, and Red's final placement maintains containment over Blue's stones.
Top 4 openings in empty and 4-stone modes. Percentages denote frequencies over 1,000
self-play games. Numbers indicate move sequence.
When the 4-stone opening is progressively introduced from empty mode, the empty-mode policy
does not converge toward the predefined opening. It concentrates probability mass near the
center and assigns near-zero probability to the fixed 4-stone locations. Even so, the symmetric
empty mode exhibits a stronger first-player advantage, with Red win rate 55.95%, compared with
51.35% in 4-stone mode.
Win rate (from Red's perspective) and policy probabilities predicted by the policy and value
networks. For the policy, only probabilities larger than 10% are displayed. (a)-(e) use the
empty mode model with the 4-stone opening; (f) uses the 4-stone mode model.
Strategic Analysis
A central contribution of this work is the use of WallZero not only as a strong playing agent, but also as
an analysis tool for understanding WallGo strategy. The paper analyzes WallZero self-play games in 4-stone
mode together with feedback from professional Go players, identifying two core strategies: reachability
control and passing strategy.
Reachability refers to the set of positions a player can access under the current board. Since
both stones and walls affect reachability, maintaining future access is essential in WallGo.
The following cases illustrate how reachability guides movement and wall construction.
After Red moves from E5 to E3, different wall placements lead to distinct future
reachability. Placing the wall to the right or below loses two reachable positions,
while placing it to the left or above loses one. However, the left placement leaves
D3 exclusively reachable by Blue, so WallZero prefers placing the wall above.
(a)46%47%49.5%52.5%
Reachability Control - Case I. (a) Initial position (Red moves E5 to E3).
(b)-(e) Wall placed to the right, below, left, and above, respectively.
Percentages denote the win rate from Red's perspective.
In this midgame position, Red at E2 and Blue at E1 compete for the lower region.
Placing the wall above preserves Red's reachability while limiting Blue's expansion.
The Red stone at D1 itself acts as a temporary barrier, showing that stones can
serve as implicit walls while preserving flexibility.
(a)(b)0.5%8%64.5%
Reachability Control - Case II. (a) Initial position. (b) Red moves E2 to D1.
(c)-(e) Wall placed to the left, right, and above, respectively. Percentages
denote the win rate from Red's perspective.
Case III shows that sacrificing immediate territory can be correct when it preserves
access to a more important future contest. Moving to E7 allows Red to gain one
additional point, but keeps Blue closer to the central battle around B4: reaching C5
takes three steps from F7 but only two from E7. This changes the eventual outcome by
one point.
Reachability Control - Case III. (a) Initial position (Blue to move). (b)-(c)
Blue moves to F7 and E7, respectively. (d)-(e) Final outcomes under continued
play. Percentages denote the win rate from Blue's perspective.
Because each turn requires both movement and wall placement, entering a valuable region first
can be disadvantageous. In the analyzed late-game position, Blue leads by one point and the
lower-right region has 10 unclaimed points. If Blue plays there first, it can obtain at most 3
points and loses; if Red plays there first, both players secure 5 points and Blue wins. WallZero
reveals an implicit passing technique in which players sacrifice small amounts of territory to
manipulate move order in the endgame.
Pass Strategy. (a) Initial position (Blue to move). (b)-(c) Outcomes if Blue or Red
plays first in the lower-right region, respectively. (d)-(h) Sequence illustrating the game
progressing to a draw. (R:x, B:y) indicate territory scores.
