Full Report for Nine Men's Morris by Traditional

Full Report for Nine Men's Morris by Traditional

Traditional game, popular during the Middle Ages.

Generated at 04/08/2021, 07:50 from 1000 logged games.

Rules

Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!

RULES

Placement Phase: Players alternate adding pieces to the board.

Movement Phase: When all pieces are in play, players may move a piece to an adjacent space (along board lines).

When a player makes a line of three in any phase, the opponent loses a piece.

GOAL

When a player is reduced to only two pieces, they lose.

VARIANTS

Flying: When a player is reduced top three pieces, they may move a piece anywhere, not just along board lines.

Move any time: A player can move their pieces before the placement phase is complete.

Miscellaneous

General comments:

Play: Combinatorial

Family: Mill games,Traditional

Mechanism(s): Capture,Line

Components: Board

BGG Stats

BGG EntryNine Men's Morris
BGG Rating5.35671
#Voters1353
SD1.62502
BGG Weight1.8347
#Voters121
Year-1400

BGG Ratings and Comments

UserRatingComment
drcsaba10
deees8
baub647.5Received a beautiful hand-crafted set of this game for the Winter Solstice -- I like the simplicity of the game which belies the clever nuances of this classic abstract.
Audiofreek10Classic "old world" game for two.
John McKevitt8
Balzaams6Palyed a lot via in game game of Assassin's Creed 4: Black Flag
bayspielN/A06.03.05.04
pertm7.5
Altugas5.5Natural evolution of TicTacToe. Interesting... But very limited (homemade version).
TheWisefool138
ahoodedfigureN/AI own it, in that I made my own board and used backgammon pieces. It was fun, but I always felt like there was some sort of figurable system to it.
Bottle of Port6Can see the appeal over the centuries - makes you think!
Nappe18
Bombadillo5The mandatory game to complete a classic tern with Chess and Checkers, as its board - usually printed on the back of the former’s - suggests. By modern standards, this game would be rated as a filler: and as a filler it plays quite well.
Tolkana10
gamov8
BacchusN/AActually a Green Box Version
damjes10
matango10very nice game
2d206.5My wife and I mostly play this on the iPhone once in a while. Good game.
danithaca4Game proven to be solved.
captaincomic4I'd rather play other abstracts, especially since draws are pretty common. [microbadge=131] # of players: [bgcolor=#00CC00]2[/bgcolor]
cookieeemonster5I play this often with my father.
BobDodgerBlueN/A634
Crime3Bon jeu abstrait. Très rapide.
Daddys_Home5Played at the art museum. Seemed like a great game for it's age.
Hrothwell8.5
Kraar8
blanor7Very good diversion for odd occasions.
aquarian4Boring.
drunkenKOALA8Dynamic game where [url=http://www.boardgamegeek.com/article/1066768#1066768]maintaining mobility[/url] is prime. More depth than it first appears. Much more than a fancy take on tic-tac-toe.
jamesdavis7.7I like this game, its so fun and allows alot of tactics and thinking.
rudi12349
TheIgel699.1
BowlofBGG3Plays at time of review - 2 win/lost at time of review - 0/2 This game is interesting and can easily be made out of anything at home, its also simple so its easy barrier to entry. It is a lot like Tick Tac Toe, what I mean by that is it comes down to how your pieces are placed and the first few moves will decide the winner. This game while innovating for the age of which it was played, it has not aged well. When you think of Chess and Go (both equally ancient in their own rights) they have millions (go has billions) of variables, possibilities and board states. So much so that they still are widely played today and enjoyed at all levels. These games (and all games) have "God Moves" where a player does a critical move at a particular point amount all the possibilities that it shifts the very nature of the game (typically the move that makes the winner the winner in the long run). This game does not have that, do to its small board and rules and age, this games puzzle has been cracked the world over. AI can play this game and win shut off is how basic this puzzle can boil down. This game is both players know the game and play perfectly will lead to a draw, like tic tac toe. Games like this, while maybe great for their time, do not stand the test of time due to a skill ceiling causing games to end in draws. These games while fun to experience, are not something fun to play more then a few experience and beyond the history value are not worth more then that.
BSG75CAG10Very fun game...though it seems a lot of folks never heard of it. Considering this game has been around longer than any of us, that's kinda sad. Trust me, it's worth your attention.
byturn5part of a 10-classic-games compilation.
ChrisScottxD6A fun, but simple 2-player strategy game.
clwesley6Used to have a IRL version of this.. not sure when I lost it. First played it in one of the Hero's Quest or King's Quest video games as a mini game you needed to win to pass part of the story. Was enthralled by it then.
Yesman Tim8
Anakin19812Another simple children's game.
amelija10
bobborobboN/Adi Emma
teamxavier9
casualgod7Have great memories of playing this as a child, although it is not a kid's game. I should really get a copy of this someday.
Ded_Zhupan9
GreatBeast8
uhlaw9710My all-time favorite abstract strategy game. Love bringing it to parties, and teaching other people to play it. Also have an excellent computer version. NO WONDER this is likely the oldest continually played abstract strategy board game. Its appeal is TIMELESS!!
Szamek10
daxaer8
Fenriz8.5One of my favorite abstracts. EXTREMELY underrated, and plays quicker than most abstracts. At first glance, it looks like a glorified version of Tic-Tac-Toe, but it has much, much more depth than one initially thinks. Depending upon who you play it with, you can take this game as a quick filler, or a brain-burner. Outstanding classic. Only complaint: lots of draws among expert players.
dancingdanslc4DIGITAL PLAY: iPad Air Abstract strategy game. iOS app is called Morris. I'm not an abstract game fan. Out of my collection
ctrievel10
AlienDjinn6.75This was one of the first head to head strategy games I learned to play in my youth. It even came up in a Robin Hood PC game, where you had a to play and win a game in Sherwood forest. Every noble warrior of the realm should posses competent Nine Men's Morris skills.
Ujal_192110
bigbarge506Have a copy I picked up at Monticello (Thomas Jefferson's home). It is a good game that is really really old, and I like it a lot, but the end game can get a little long.
snigfarp8An excellent game that I don't get opportunity to play enough.
andreferr1É com joga da velha. Uma vez que se detecta os movimentos corretos, não há como perder.
chrboesen1Played a lot as a kid. I can always beat the wife and girls (ages 5-10). Not much interest to them. Played 1,000 times.
ctalbot4Sadly, it's a dull abstract.
randalthompson7.5
BlueCherryFaerieN/Awe have a special handmade leather edition of this game that we picked up at the Renaissance Festival
leslauber8
SVK_PETO8
svenmees8
Artax5Az ismert malom jatek.
Engoduun8I just rediscovered this ancient game for me, and have to say it somehow went under my radar for unknown reasons. In fact, it's a very relaxing strategy game, light, but deep. And fun, too.
Elixer18.5Slaves building the pyramids can't be wrong.
BhikkhuJoJo8
big_buddha5Good game for kids
andrewhodkinson9
Renars1239
Cheshire Swift6About the simplest game I still enjoy playing. Portable wood/metal set.
brianeikunst1Maybe I've used the wrong rules, but there hardly seems to be a game here.
dagny218I used to play this game years ago and really enjoyed it. Haven't played it in years but now own it in the form of the Klutz Book The 15 Greatest Games in the World.
aaarg_ink8151117 Rating for 10 Men's Morris (Lasker's Morris) where the two phase structure is eliminated you can start moving the pieces immediately as soon as they are placed.
Litwood9
biboulecoyote8
dcgogo9one of the first games i ever played
jmduran9Great game.used to have my students build their own boards and pieces
LiamAcquiesce9
BredericN/A@ Yucata
Pinook10Classic, essential, as some of the low voters point out you can lose this game in the set-up. Which makes it even more thrilling. Does have aspects of Go to it - the power of individual pieces is determined both by their location on the board and their relationship to other pieces on the board.
Bad News [bnw]7Solved you say? I don't care because I don't know the solution. This is a nice take on the tic-tac-toe-mecanics.
clintnesmith9
jmay8
Tutis10
cardshark288009
Asmoridin2Frustrating as a game can be.
Andy MerrittN/AThis is to at least a fair degree incorrect. Mulinello Quadruplo is played on a different board, and with 5 men each. This is No. 6 in Whittlecraft's 'Miniboard' series, and to show it is distinct from Nine Men's Morris, Whittlecarft published Nine Men's Morris as No. 1 in the same series...
maharaja8
Carissa5Made my own board for this one too.
Indy4189I learned this game when I was playing a computer game (Conquests of the Longbow) and you have to beat one of the character at the game to advance the storyline. I got quite good, but haven't played in years. I had several sets, one wooden board with marbles and a magnetic travel copy. I recently picked up the game for my tablet.
Clatch9
cssmith6239Lost
megamau8More interesting than what appears at first.
3pic_Win6Took me a few plays to realize it, but this game has some complex strategy. I would get bored of it if I played it too often, but it's fun to play occasionally.
Avron5I don't think I've played this since I was a kid, the set I own was one of my parents gifts to me one recent year because they have trouble knowing what to get me. I would like to play again, once, to see how my memory compares to reality.
svetozar8
Chris Coyote8classic
ColumBuzz4Okayish game, and since it’s solved fun to play for the first few times. Gave it to a kid.
rickhatch7.55B+
Butsudoka3A decent abstract game, but it has one serious weakness, and that is that it's too easily solved, i.e. the replay value is very limited.
relvar998
The Duke of Kestrel8My version of this game allows for diagonal movement at the corners, though you still need to mill orthogonal. I find it improves the game significantly, my rating is based on this version and I highly recommend you try this alternate rule.
Basto5A fun abstract, more notable for its historical value than its gameplay.
Shadow Overkill8
CodeAndReloadN/ACustom Spaceship themed version (includes Six Men's Morris and Twelve Men's Morris).
Skasian8
Ray_of_Light10
Wolfram8Historisches Spiel
BeezeeN/AGAMEBook game
popartgirl8
preiselbeer8
MrKorky8
Bayushi Sezaru4.5Ancient traditional game, played on a board with lines, using only 9 playing pieces per player. It's a very light abstract game, so simple it can be used to teach games to kids. Will play this with the daughters!
salish999Can quickly be drawn on any kind of paper on thgeh road, and be played with shells and rocks found on the roadside. Awesome. (note: I suck at it, though)
clayhaus6Quick, relatively light game with little depth, but still enjoyable to break out now and then.
flyboy168Underrated abstract.
BrutalDolphin797Classic.
rsb762gm9
Algernon884Another of the classic abstract. Not one I would play very often.
Be4tngU8
Augustine10Handmade board for sale.
CardboardGBGN/APB
XMJA9
crimescene8The children love it, but you can also have fun as an adult. We do.
leithian8
arcplayer8Clemens Gerhards excellent craftsmanship.
criss_mcs35My wife loves it.
DanielBeaver7Interesting abstract, quick to play.
Black SaintN/AXmas 2019 from Jon
boydweigerN/APnP
hmmfred9
Roidesire8
CartoonCat7Many a pleasant afternoon spent playing this with my brother when we were kids.
AdlerCivN/ANo cards
CDRodeffer7I like abstracts in general, and this one is a classic. It doesn't matter to me that it's been solved, because I don't have the solution memorized. Nor does anyone I know.
BloodfreakN/AWell used
anttighost4Strategy game for two.
Bluenose6Great entry game. Simple, solvable. A 2 player puzzle.
AmassGames6Blimey, can be tough
Daddy5As a medieval re-enactor, I've played this a lot at meetings all over England. Take it on picnics, relax and enjoy its simply pleasures.
dukivladus9
Kersus9My version is called Tecumseh.
amacleod2.5It's a good introduction to strategic thought for very young children. Certainly chuck it by the time they're eight, though.
Scrabblette8
counter example8
Hapexamendios8
D Beau7.25Cool old abstract. Few moments in gaming are more satisfying than building an unstoppable mechanism by which you can simply move a piece back and forth, forming a mill with each turn.
kingcrim059
adebisi2Aesthetically quite pleasing when played on a nice handcrafted board and polished stones. Unfortunately, that is how far it goes. Basically, the game is tic-tac-toe in a disguise since the initial setup is very similar and the game can be lost there. Once the pieces start moving, your choices are very limited, which is usually a good thing but here it can be quite frustrating since you can keep the game going on forever or see that you have already lost the game even before the first stone has been removed from the board. Once one player starts losing the game usually unravels very quickly. I have a feeling that the game can be solved so that it always ends in draw, but I am not sure I would invest the time on finding that solution. At least this is marginally better than tic-tac-toe.
ahorn5The problem of this game: The number of strategies is very limited. After playing it intensively for a while (and I mean intensively!), you will find that there is only one single strategy that will end in a tie. Any variation will lead to a loss if the opponent knows the game well enough.
BozoDelN/AQuero jogar a versão do Lasker.
BaSL5--------------------------------- Best with: 2 >10 plays
theophillusjuan9
bwingrave5My step-son made this game board at school.
cdwood448
BaluMG10great!!! doesn't require studies, like chess...
crnj_cmpbllN/A(Mill) Dad's
arnest_r6Surprisingly tactical sometimes.
BlueAngel05683The concept is interesting, but I always found it too restrictive and linear.
Iguanoman8
CommonGroundsCCC8
bluebee27Home made version
Twinhamm3r8
amcbethN/AYe olde game
k0ll4ps8
Duch8It is not so simple as it seems.
Skreczi8
tosione9
finallyiamnoone9
redclay10
FiveStars9A very good game. As deep or as shallow as you are yourself! Highly underrated.
trawlerman8
AndrePOR4Classic (Before 2000)
Cardboard Conundrum6.5Got a lovely edition at the UKGE 2015. Very nice slice of history - and fun game for the pub.
CHRISDH3*3*(Jan 2013) Very dry abstract game that is highly repetitive and boring. There's nothing to excite me in this game and would much rather play another abstract title.

Kolomogorov Complexity Analysis

Size (bytes)27810
Reference Size10293
Ratio2.70

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 second24521.04 (40.78µs/playout)
Reference Size494315.37 (2.02µs/playout)
Ratio (low is good)20.16

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.

State Space Complexity

% new positions/bucket

State Space Complexity108916642 
State Space Complexity (log 10)8.04 
Confidence52.960: totally unreliable, 100: perfect
Samples1176763 

State space complexity (where present) is an estimate of the number of distinct game tree reachable through actual play. Over a series of random games, Ai Ai checks each position to see if it is new, or a repeat of a previous position and keeps a total for each game. As the number of games increase, the quantity of new positions seen per game decreases. These games are then partitioned into a number of buckets, and if certain conditions are met, Ai Ai treats the number in each bucket as the start of a strictly decreasing geometric sequence and sums it to estimate the total state space. The accuracy is calculated as 1-[end bucket count]/[starting bucklet count]

Playout/Search Speed

LabelIts/sSDNodes/sSDGame lengthSD
Random playout33,1785763,211,59355,697979
search.UCT33,4281,024458

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.

Win % By Player (Bias)

1: White win %54.90±3.10Includes draws = 50%
2: Black win %45.10±3.06Includes draws = 50%
Draw %1.40Percentage of games where all players draw.
Decisive %98.60Percentage 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.

UCT Skill Chains

MatchAIStrong WinsDrawsStrong Losses#GamesStrong Scorep1 Win%Draw%p2 Win%Game Length
0Random         
4UCT (its=5)350562689800.6134 <= 0.6439 <= 0.673222.1457.3520.5191.46
11UCT (its=12)5002622169780.6147 <= 0.6452 <= 0.674640.1826.7933.0383.79
21UCT (its=22)5741132869730.6175 <= 0.6480 <= 0.677445.6311.6142.7575.12
24UCT (its=65)619241497920.7673 <= 0.7967 <= 0.823348.613.0348.3661.92
25UCT (its=177)63021437750.7853 <= 0.8142 <= 0.840053.550.2646.1950.78
26UCT (its=482)63011407710.7890 <= 0.8178 <= 0.843454.600.1345.2745.12
27UCT (its=1310)63101587890.7704 <= 0.7997 <= 0.826257.290.0042.7143.45
28UCT (its=3562)63102118420.7190 <= 0.7494 <= 0.777556.060.0043.9444.58
29
UCT (its=3562)
517
0
483
1000
0.4860 <= 0.5170 <= 0.5478
54.70
0.00
45.30
46.19

Search for levels ended: time limit reached.

Level of Play: Strong beats Weak 60% of the time (lower bound with 95% confidence).

Draw%, p1 win% and game length may give some indication of trends as AI strength increases.

1st Player Win Ratios by Playing Strength

This chart shows the win(green)/draw(black)/loss(red) percentages, as UCT play strength increases. Note that for most games, the top playing strength show here will be distinctly below human standard.

Complexity

Game length52.58 
Branching factor10.05 
Complexity10^48.50Based on game length and branching factor
Computational Complexity10^6.16Sample quality (100 best): 17.74
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

Board Size24Quantity of distinct board cells
Distinct actions89Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves64A good move is selected by the AI more than the average
Bad moves24A bad move is selected by the AI less than the average
Response distance%48.48%Distance from move to response / maximum board distance; a low value suggests a game is tactical rather than strategic.
Samples1000Quantity of logged games played

Board Coverage

A mean of 86.58% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean52.56
Mode[50]
Median51.0

Change in Material Per Turn

Mean change in material/round0.14Complete round of play (all players)

This chart is based on a single representative* playout, and gives a feel for the change in material over the course of a game. (* Representative in the sense that it is close to the mean length.)

Actions/turn

Table: branching factor per turn, based on a single representative* game. (* Representative in the sense that it is close to the mean game length.)

Action Types per Turn

This chart is based on a single representative* game, and gives a feel for the types of moves available throughout that game. (* Representative in the sense that it is close to the mean game length.)

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

Trajectory

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 3 critical turns (turns with only one good option).

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 moves66.3362.8470.22
Mean no. of effective moves6.195.506.96
Effective game space10^33.2110^15.1810^18.03
Mean % of good moves32.6934.2330.96
Mean no. of good moves2.092.211.96
Good move game space10^14.5110^8.0410^6.46

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 space calculation.

Quality Measures

MeasureValueDescription
Hot turns81.13%A hot turn is one where making a move is better than doing nothing.
Momentum20.75%% of turns where a player improved their score.
Correction28.30%% of turns where the score headed back towards equality.
Depth4.56%Difference in evaluation between a short and long search.
Drama6.77%How much the winner was behind before their final victory.
Foulup Factor33.96%Moves that looked better than the best move after a short search.
Surprising turns0.00%Turns that looked bad after a short search, but good after a long one.
Last lead change83.02%Distance through game when the lead changed for the last time.
Decisiveness30.19%Distance from the result being known to the end of the game.

These figures were calculated over a single representative* game, and based on the measures of quality described in "Automatic Generation and Evaluation of Recombination Games" (Cameron Browne, 2007). (* Representative, in the sense that it is close to the mean game length.)

Openings

MovesAnimation
a7,f4,d6,e4,g4,f6,f2
a7,f4,d6,e4,g4,f6
a7,f4,d6,e4,g4
a7,f4,d6,e4
c5,d7,g7,e5
a1,f2,d7
a1,f4,d2
d1,e4,b2
b2,d2,c3
b2,e4,d1
b2,b6,d1
d2,b4,e5

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.

Unique Positions Reachable at Depth

01234567
124576664870404495444316944415230012

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.

Puzzles

PuzzleSolution

Black to win in 14 moves

Black to win in 12 moves

Black to win in 12 moves

Black to win in 10 moves

White to win in 12 moves

White to win in 13 moves

Black to win in 12 moves

White to win in 11 moves

White to win in 10 moves

Black to win in 11 moves

Black to win in 11 moves

Black to win in 10 moves

Weak puzzle selection criteria are in place; the first move may not be unique.