Full Report for Murus Gallicus (standard version) by Phillip Leduc

Full Report for Murus Gallicus (standard version) by Phillip Leduc

Towers (2 high) can move, walls (1 high) are immovable - get a piece across the board to win.


Towers (2 high) can move, walls (1 high) are immovable - get a piece across the board to win.


General comments:

Play: Combinatorial

Mechanism(s): Race,Capture,Stacking

BGG Stats

BGG EntryMurus Gallicus (standard version)
BGG Rating7.70517
BGG Weight3.25

BGG Ratings and Comments

Arcangelurbano8.9(ESP) De los más interesantes juegos abstractos que he jugado.
mrraow8There is a lot more going on here than the simple rules suggest. Impressed :)
bravucon8Played on www.iggamecenter.com Preliminary rating, right now I'm impressed with this game, looks like here is a lot of space for intelligent moves (and stupid ones too)... I respect pure abstract strategy games when they are good, I respect this game ---> This game is good.
dolzandavid6.5It's an excellent abstract of trying to reach the opponent's home row by constantly balancing the defensive and attacking moves, while at the same time always trying to create new towers so that you do not run out of moves. It's pretty short, but it appears to have a lot of strategy. Great!
retrosoldier8very cool...abstracts are so appealing in part due to their minimal rules. I like the "military" theme here and "no draw" results.
Aiken Drum8
leffe dubbel5
Lunga7.5Homemade copy. Very interesting game, and while fairly short playing time, offers some good depth and coaxes the gray cells to think through each potential move. Really a simple idea behind the game, but not so simple to play well!
Jean_Leviathan9I discovered this game in the end of 2010 and I have fallen in love with it! Abstract games are not my favorite kind of games but this one has joined my “elite” club. Simple but very interesting rules and a great dynamic of game play guarantee an interesting experience.
luigi878.6Lovely mechanism.
Tigrillo8Simple abstract that is about gaining momentum without overstretching yourself. That gives it a nice balance between attacking and defending where defending seems easier.
clayhaus9Interestng movement -- towers to walls -- can create some tricky play. Need to be aware of creating too many walls that in turn can limit your own ability to maneuver. After 3 plays can easily say that this is challenging winner of a game.
Schachtelhalm7An original abstract stacking game.
nconcN/A微妙な闘いが続く気がする 分かりやすいルールと以外な展開が体験できるんだけどさ 良いゲームだと思うのだけど少しだけ弱い気がするな 何が足りないんですかね?
Wentu7.3After some games against AI I find the game pretty interesting and i raised my rating to 7.3 ; rules are simple and give origin to a game with different chances, different strategies, surprises and all in a rather short game. I still have some reserve about the frustration of losing because you remain without towers... but maybe it's ok
tckoppang6Solid abstract that only suffers from a somewhat limited replay value. Luckily, this effect doesn't kick in until you've more than gotten your "value" out of the game. Surely worth a try.
seneca29N/A16x2 pedine 8x7 board
gmcnishN/A8x7 board, 2x16 stackable stones
bc847rating after ~6 games. hate to have a 33% share in this obscure game's ratings, but OTO it deserves to reach 30. can't tell yet how many opening strategies are possible. love the basic mechanic.
ludopath9Weird and fascinating game with ultra-simple rules.
russ7Clever Roman-themed abstract that sort of chess-like, sort of mancala-like. Check out the downloadable playable version in the Files section. Very nice easy way to get a feel for the game against an AI player if you have no live opponent at hand.
whac36Rating may change with more play.
nestorgames9Home made. Very interesting!
no_where_dense8One of my favorites from Nestorgames. Quite unique.
trapeze7Unusual abstract. We're still learning how to play the game. The game develops in surprising ways.
slovo7.5Beautiful. Hope to see it for ipod touch soon. And I would love a big table a la Epaminondas...or maybe i'll put the Murus Gallicius in front of my Epaminondas foot-men?
dave doma9
Kaffedrake6Working abstract that seems to be characterized by an initial rush to the centre followed by a slow process of repositioning, potentially to attack but more likely to outlast the opponent as the available moves run out.
Talisinbear7.5This games appears to have some interesting strategies. Having played online, first impression is very good.
Jugular8Wow! Outstanding abstract. I have yet to plumb it's depths and with so few pieces I suspect it isn't all that deep but it looks to be a great ride ahead. Really has a great feel to it.
lhapka6i played with AI (swf)
Carabama9A truly excellent game. The movement of the pieces is very simple yet very pleasant. My favorite chess-like game so far. It is important to play and keep the possibilities of making towers as long as possible through the game. Sacrifice can be a right path, if you can make two towers in your next turn for example. Diagonal openings or movements/attacks tend to be better choices. This game has a very good strategic richness despite the relative shortness of a game-play (up to 20 mn or so). And the best in games : it becomes more and more intuitive the more you play. As Phil Leduc himself says : his best creation so far. And now catapults were added with "Advanced Murus Gallicus" !

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0033.3338.14
Grand Unified UCT(U1-T,rSel=s, secs=0.07)36094580.0053.3376.80

Level of Play: Strong beats Weak 60% of the time (lower bound with 90% confidence).

Draw%, p1 win% and game length may give some indication of trends as AI strength increases; but be aware that the AI can introduce bias due to horizon effects, poor heuristics, etc.

Kolomogorov Complexity Estimate

Size (bytes)25527
Reference Size10293

Ai Ai calculates the size of the implementation, and compares it to the Ai Ai implementation of the simplest possible game (which just fills the board). Note that this estimate may include some graphics and heuristics code as well as the game logic. See the wikipedia entry for more details.

Playout Complexity Estimate

Playouts per second46016.58 (21.73µs/playout)
Reference Size416077.22 (2.40µs/playout)
Ratio (low is good)9.04

Tavener complexity: the heat generated by playing every possible instance of a game with a perfectly efficient programme. Since this is not possible to calculate, Ai Ai calculates the number of random playouts per second and compares it to the fastest non-trivial Ai Ai game (Connect 4). This ratio gives a practical indication of how complex the game is. Combine this with the computational state space, and you can get an idea of how strong the default (MCTS-based) AI will be.

Win % By Player (Bias)

1: White win %46.20±3.07Includes draws = 50%
2: Black win %53.80±3.10Includes draws = 50%
Draw %0.00Percentage of games where all players draw.
Decisive %100.00Percentage of games with a single winner.
Samples1000Quantity of logged games played

Note: that win/loss statistics may vary depending on thinking time (horizon effect, etc.), bad heuristics, bugs, and other factors, so should be taken with a pinch of salt. (Given perfect play, any game of pure skill will always end in the same result.)

Note: Ai Ai differentiates between states where all players draw or win or lose; this is mostly to support cooperative games.

Playout/Search Speed

LabelIts/sSDNodes/sSDGame lengthSD
Random playout46,9402491,578,6368,199348

Random: 10 second warmup for the hotspot compiler. 100 trials of 1000ms each.

Other: 100 playouts, means calculated over the first 5 moves only to avoid distortion due to speedup at end of game.

Mirroring Strategies

Rotation (Half turn) lost each game as expected.
Reflection (X axis) lost each game as expected.
Reflection (Y axis) lost each game as expected.
Copy last move lost each game as expected.

Mirroring strategies attempt to copy the previous move. On first move, they will attempt to play in the centre. If neither of these are possible, they will pick a random move. Each entry represents a different form of copying; direct copy, reflection in either the X or Y axis, half-turn rotation.


Game length89.94 
Branching factor14.45 
Complexity10^101.93Based on game length and branching factor
Samples1000Quantity of logged games played

Computational complexity (where present) is an estimate of the game tree reachable through actual play. For each game in turn, Ai Ai marks the positions reached in a hashtable, then counts the number of new moves added to the table. Once all moves are applied, it treats this sequence as a geometric progression and calculates the sum as n-> infinity.

Move Classification

Distinct actions592Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves2A 'killer' move is selected by the AI more than 50% of the time
Killers: c6xc7,e2xf1
Good moves216A good move is selected by the AI more than the average
Bad moves375A bad move is selected by the AI less than the average
Terrible moves56A terrible move is never selected by the AI
Too many terrible moves to list.
Samples1000Quantity of logged games played

Change in Material Per Turn

This chart is based on a single playout, and gives a feel for the change in material over the course of a game.


This chart shows the best move value with respect to the active player; the orange line represents the value of doing nothing (null move).

The lead changed on 15% of the game turns. Ai Ai found 18 critical turns (turns with only one good option).

Overall, this playout was 77.53% hot.

Position Heatmap

This chart shows the relative temperature of all moves each turn. Colour range: black (worst), red, orange(even), yellow, white(best).

Good/Effective moves

MeasureAll playersPlayer 1Player 2
Mean % of effective moves47.8445.3850.36
Mean no. of effective moves6.756.626.89
Effective game space10^67.6010^33.2210^34.38
Mean % of good moves14.3422.725.78
Mean no. of good moves2.063.290.80
Good move game space10^18.4910^15.0010^3.49

These figures were calculated over a single game.

An effective move is one with score 0.1 of the best move (including the best move). -1 (loss) <= score <= 1 (win)

A good move has a score > 0. Note that when there are no good moves, an multiplier of 1 is used for the game spce calculation.


Table: branching factor per turn.

Action Types per Turn

This chart is based on a single playout, and gives a feel for the types of moves available over the course of a game.

Red: removal, Black: move, Blue: Add, Grey: pass, Purple: swap sides, Brown: other.

Unique Positions Reachable at Depth


Note: most games do not take board rotation and reflection into consideration.
Multi-part turns could be treated as the same or different depth depending on the implementation.
Counts to depth N include all moves reachable at lower depths.
Inaccuracies may also exist due to hash collisions, but Ai Ai uses 64-bit hashes so these will be a very small fraction of a percentage point.

Shortest Game(s)

No solutions found to depth 7.



Opening Heatmap

Colour shows the success ratio of this play over the first 10moves; black < red < yellow < white.

Size shows the frequency this move is played.



Black to win in 3 moves

Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.