Full Report for Hex (12*) by Esa Koskinen

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!

Place a piece. Connect opposite sides.

Miscellaneous

General comments:

Play: Combinatorial

Mechanism(s): Connection

BGG Stats

BGG Entry	Hex (12*)
BGG Rating	6.70278
#Voters	701
SD	1.84893
BGG Weight	2.7818
#Voters	55
Year	1942

BGG Ratings and Comments

User	Rating	Comment
yakshto	10	The most elegant and engaging game I've encountered so far. Perhaps Y is more elegant, but it requires huge boards to be interesting. If you think Go is king of low complexity and high depth, you haven't played this. For all its apparent dryness, Hex plays incredibly wet and tense. Crazy to think that it wasn't invented until mid-XX century, as it has this timeless, universal elegance about it. One of its advantages, as opposed to Go and many other games, is how easy is to introduce this game and have new players immediately, intuitively seeing what to do and test their intuitions. Go, while its rules are short and clear, suffers from newbies not knowing how to get there, how to surround, where to start on an empty board, not to mention the square grid and the rule that you can't connect stones diagonally, which takes many games to get used to, due to how our visual perception works.
Butterbob	9
amatyarakshasa	10	A simpler version of Twixt. So simple and so hard. Defense = Offense = Defense. A totally awesome game.
rauwolfa	9.9
eljo	7	1990 HOM
mrraow	10	Beautifully simple connection game. Flawed, in that a pie rule is necessary to offset the first player advantage, but full of surprises.
jrsquee	10
Arctic Jack	8	Attic Box #2 14x14 Hex seems to give you a little breathing room but still probably only between evenly matched players. If not, 14x14 is just prolonging the inevitable.
bayspiel	N/A	08.02.02.04
dosxtres	9
fogus	6.5	2016 ==== Hex is another abstract that's seen less play because of newer discoveries, but wow is it a beauty. These days I play almost exclusively pen-and-paper and it really shines as a core entry in my travel-set. [2015.06.01] As time passes I find myself appreciating elegant rulesets and there are fewer games more elegant than Hex. For a time I thought that Havannah would subsume this game, but as it turns out the feeling of both are very different. Hex is almost entirely unforgiving and subtle, whereas Havannah feels like a race with some slack built-in. [2014.10.10] 8.75 Probably the most elegant game ever created. There's just one rule (two if you include the Pi rule)... but it's a lifetime game despite this. Amazing.
cannoneer	6	I don't like the swap rule in games. I respect this design but it's not something I clamor to play. If there's nothing else going on on IG Game Center I'll sometimes jump into a game of this. I'm not very good, and maybe the rating will increase with more play. At least it's very simple to learn!
fhsIV	9
danky	1	homemade. buggy game, it have an easy winning strategy
dolzandavid	5.5	A connection game, inferior to Twixt by a country mile.
adamscott	7	Might be the easiest game ever made to teach/learn, but has lots of depth. Go players will pick this game up very quickly. It feels like a lighter version of Go to me.
Altugas	N/A	(Not played yet).
freechinanow	7	Finally, a chance to try one of the more significant games in abstract history- if only because it was one of the first known "connection" games- a concept that has been duplicated numerous times, oftentimes successfully. Hex is certainly a connection game at its most purest. The 7X7 board is fine, but I can imagine this game being much more interesting with an 11X11 or 13X13 board. Its simplistic rule-set belies its depth. Why this game has completely died, while Connect Four gets to be the primary big-box toy store abstract of the last 40 years- I have no idea. There are expensive copies available through the larger independent abstract publishers, because this deserves a larger release again.
birdbolter	5	This game was immensely amusing to me in my first dozen plays, less so now.
jeep	9
Stephen Glenn	9	Homemade copy
hikwaitek	10
Aiken Drum	8	If you like abstract strategy games, you will probably know this game. It's very deep and one of the simpliest games in terms of rules out there. --May 07
emike	7	Classic.
The Nerdy Girl	10
donkst	N/A	3M Paper Version
LukeJS	10
matthulgan	10	The ideal abstract.
Songok	10	Very easy to learn, not sure about mastering it eheh Love the pie rule at the start
Pionek	9
2d20	6	PnP Not my preferred style of Abstract, but would still play occasionally.
davidme	6.9	"Own" in The Book of Classic Board Games by Sackson.
Draxonfly	4	garden
aslaksen	7	Classic abstract!
simpledeep	10
gabriel_k	10
Emmekappa	9
nickmoniker	10	Very likely, Hex is my favorite game of all time. It's certainly in my top five.
4characters	6	For such a simple game it can be difficult to play well. At first glance you might be tempted to think it's as simple as tic-tac-toe, but it's surprisingly deep.
Calpurnio	7	Played over the web. Nice abstract
ampelman	10
BobDodgerBlue	N/A	876
thelegendarybeng	10	This game fits the "seconds to learn, years to master" description to the maximum level. This game has so so much depth despite being so quick, and I still am finding new strats to use over 7 years after first learning it. Every gamer should try this game out.
Dingus	N/A	3M paper pad version and wooden marble version
HexNash	10
El Diabolo	8.5	This game is bizarrely subtle. Like go, without serious study, looking at a board does not convey the spirit between the players.
bcnevan	4.5	Hex provides a rule set about as bare bones as you can get. Emerging from that sparse rule set is a deep game of positional understanding. This often manifests itself in the feeling that Hex is a game of positional chicken that can end upon the first observed error. Now that game of chicken has depth, but that depth is shared by many, many abstract games. Hex requires you to constantly analyze the board state, shift your connection goal in view of that understanding, and also work to block your opponent's apparent connection goal. For the standard 11x11 board, the relatively small number of placement positions combined with the static end-game goal seem to cause the placement of the first piece (with equally skilled players) to be highly influential to the game's outcome. At the least, Hex's implementation requires the player that places the second piece to avoid isomorphic placements and to more readily take advantage of the other player's mistakes. A larger board (e.g., 14x14) would seem to make the computations more difficult, but the issue is pretty baked in, so we're really just discussing how far down it gets buried below the difficult calculations. For at least these considerations, Hex seems pretty low on the list of abstracts that I would want to devote a large amount of time to. For even just connection games, Twixt, Slither, and Havannah seem much more worthy of long-term investment. Sometimes a simple ruleset is too simple and results in a system that is not robust enough. [update] played it some more; and even the positional puzzles become less interesting. Positional chicken; rote call-and-response play; etc. I can confirm the gist of my original comment. Outside of Hex, there are much more interesting abstract games out there.
dalton-almeida	N/A	PnP
The Player of Games	9.09	Print and play board. Stones from [thing=11997] [/thing]. Excellent connection game! One of the purest and simplest abstract games from a rules perspective. Just connect your two sides of the board by playing one stone at a time in the cells of the hex grid, and you win. However, deep and feels like a "knife fight in a phone booth" (or "in a wardrobe" now cell phones make phone booths go extinct).
DalimThor	6	it's quick and easy to learn.
Getzen	9	Hex (and its cousins Y and Unlur) is a beautifully simple game -- the rules are no more complex than tic-tac-toe -- with tantalizingly deep gameplay, especially on larger boards (say 11x11 on up). Easily learned and played by youngsters too. It might seem dry to most gamers, but for abstract lovers it doesn't get much better. See Unlur, Havannah, Twixt, or even Punct for games with a similar connection theme, but which are a little higher on the fun factor.
birdsong703	6	The PnP version is a good one to take on flights.
drunkenKOALA	10	Simple and beautiful. Great strategical depth that may rival even that of Go's. [url=http://www.boardgamegeek.com/article/1070318#1070318]My favorite game.[/url] I think hundreds of years from now, Hex will hold the same place that Go does now.
CarlosLuna	10
Mingy Jongo	9.8	One of the greatest perfect-information games of all time.
cackleton2	10	Hex is a wonderful game of surprises, tension, witfulness, the long journey of improvement and insight that absorbs those who take it. Join the Hex discord server: https://discord.gg/Rj37fuw
aionman	9	Comparable depth and excitement to Go but can be played in less than an hour. Would like to buy wooden board and pieces with 11 X 11 on one side and 13 X 13 on the other side.
byturn	6	the pure connection game.
cdunc123	9.25	An elegant game with tremendous depth. The rules are nearly as simple as can be. And I like the decisive win condition (no counting up scores). Not a perfect 10 because it needs the swap rule to balance it. One other downside is that you can lose the game in, say, the third move without realizing it. That can be frustrating for beginners. But once you learn to prevent the early losses, the game starts to shine. And to learn to avoid early losses, all you need to do is read and understand [url=https://boardgamegeek.com/article/20527868#20527868]this brief tutorial. [/url]
chriskaspar	N/A	Would love to make my own version of this game.
Anakin1981	5	Decent abstract game with very easy rules to teach and play but not exactly my cup if tea...
Kasimuzz	10	Maybe the best ever game!
r4t4t0sk	10
struggler1	10
camb	10	This is to my mind the ultimate game: among the simplest rules of any game, but among the deepest to play. I've played it for many years now, and every game still seems to throw up new situations and problems to solve. Great stuff.
Drek_Overlord	5	The more the field is filled in, the higher the risk of placing chips incorrectly and letting the opponent win.
nestorgames	9	Publisher ;-) The perfect abstract.
filou	9	One of the pioneering connection game, and still one of the best. The rules look so natural, the use of an hex board too... It looks like this game should have been invented 2000 years ago. It's not that strange that it was independantly invented by two different persons.
epicgamer	7	I like this abstract connection game. I think I should try out some others like it.
Fenriz	4	I prefer Twixt.
dancingdanslc	4	DIGITAL PLAY: iPad Air Connect sides by placing tokens one at a time. Boring Out of my collection
fiddly_bits	N/A	Homemade Nash set(s) in several of the traditional sizes.
takeoutweight	10	I wish there was thousands of years of analysis backing this game, it would be fun to study. I find the geometric pattern matching and reading of long forcing continuations fun. It's always a dramatic game. Eg even Go can come down to a find-pennies-in-the-couch-cushions endgame. Not hex.
dysjunct	4	Mediocre. Another boring abstract.
ericlosiewicz	6	Classic abstract that feels like it's almost solvable and could be deterministic (maybe there's some obvious opening plays and counterplays).
ctalbot	5	This abstract doesn't have much to offer. It's not fun.
Erniepaul	N/A	?
jg27	10	If the ratio of strategic depth to rule complexity is the measure of a game, then hex may be the best game ever created. Games are typically short and sweet (or bitter), and it's impossible for players to draw. You don't need to worry about cycles like in chess or go. I see some users complaining that the game is shallow and the first player has an easy win. If this were the case there wouldn't be a Hex Research Group at University of Alberta :) Just make sure you play on a board of at least 11x11, and start with the swap/pie rule.
Deleted010518	9	There's a lot of complexity in here. From 'splitting the pie' fairly at the start, to blocking sensibly to progressions like Go's ladders... and there's undoubtedly a lot more that I've not yet uncovered.
DornianCollection	N/A	Russell
darrenmac	9
AnttiR	9.63
big_buddha	7	Very simple, very deep, and has that special something that just makes it pleasant to play
ChristianDK	6	Rules don't get any simpler than the rules for Hex yet the game is deep. A very strategic game.
halladba	10
bucklen_uk	6	Elegant abstract - but there are many more 2 player games I'd rather play.
Friendless	9	I think I play at an intermediate level now, but I have lots to learn. It's hard to find a regular opponent, so I wrote a Facebook app to play on. http://apps.facebook.com/hexgame/ With more experience I still find the game to be exceedingly dry. In an abstract game like Chess or Go a move can still have character, e.g. be an aggressive attack or a nervous defence. In Hex a move is just a move, and I don't see any passion in the play. The game is also unforgiving. On an 11x11 board a bad move can spell doom. In many other games there's time to fight back, but in Hex you can put yourself into a losing position and spend a long time doomed without realising it. I will continue playing but the game is not showing me the hidden beauty I had hoped for. There's a downloadable AI opponent called Hexy which plays a very good game. In fact it's too good - I can't beat it on even the easiest level so I find it very very boring and unhelpful.
fantum	10	Very, very, very, very good.
RDReilly	9	Simple, deep, beautiful. Made two wooden boards for myself.
bootleby	10
morphles	10	Rich gameplay from very simple rules. In this regard I doubt you get more bang for a buck! Very good game.
Akeem	6	I have tremendous respect for what this game is, what this game has spawned, and what this game takes to play it well. I just do not find it fun (maybe it's an innate prejudice against diamond shaped boards or some other ridiculous reason). There are other connection games out there with a similar feel that are far more interesting to me (e.g. Mind Ninja, Gonnect, *Star) that I would much rather spend my time on.
donaldrnelson	N/A	W
Brederic	N/A	@ BGA
FlatWorm	7	Pure abstract strategy. A challenge for the most jaded strategist, but also can be used to introduce kids (or others) to strategy boardgames.
salva	9	Some say it makes no sense to have a Hex board because it should be played on paper, but anyway I made an 11x11 wooden board myself and I play it with Go stones.
twixter	10	I've played over a thousand Hex games on the Internet. I hope to play thousands more.
bekudno	10	I am a huge fan of the pure connection game genre, and Hex is the only such game I've played much of. Pure connection games have an amazing elegance that I've never seen matched anywhere else. They are also deceptively deep. I'm good enough at Hex to understand that I could study it for many years and keep finding new insights. The largest board I've played on is 13x13, but I have a feeling that 19x19 Hex is to 11x11 Hex as 19x19 Go is to 9x9 Go, i.e. almost a different game with all the layers of strategy it adds. I believe that Hex and related pure connection games are around for the long haul, and that by the standards of a few hundred years from now, the current best players in the world are beginners. I like to play at www.littlegolem.net
Tony van der Valk	10	www.hexboard.com
ensor	7	Must play with pie rule. Simple rules yet challenging underneath, like dots and boxes.
Punainen Nörtti	10
FauxSloMo	9
n0v4___	10
darker	N/A	[Own a hex-battlemat suitable for play, not published edition] Entertaining. Only played once or twice - some reminiscinces of Go, some completely different dynamics. Enjoyed.
bothros	10
megamau	9	The greatest complexity in relation to the rules. It can literally be explained in 30 sec., but it is full of tactics and strategy.
Pocc	9
Butsudoka	7	Please see [url=http://www.boardgamegeek.com/thread/1166936/a-wicked-and-seductive-witch]my review[/url]. I've been less interested in playing this game since I found Havannah, which I think is a more stimulating and entertaining game.
AdamMcD	6	Great strategy, but games that rely only upon dots, boxes, lines, etc. (hexegons in this case) always seem cold and formal - takes the fun out of it.
Josemastill	10
Adyry	10
artyomch	9
BeyondMonopoly	8	Mine is homemade set - Go stones on a Chessex mat.
familywontplay	5.5	The first person advantage is too great.
rayzg	9	Homemade version -- plastic sheet protector, printout, and dry-erase markers. Make sure you play this with very large boards, like 19x19.
aarondesk	7.5	#to-play
Chironis	9	2 player
mynameiswillem	10
demongod	N/A	Printed
mzmzmz	10	This is an awesome abstract game, easily my favorite.
clayhaus	9	Simple. Elegant. Classic.
rorschah	10
pled	9.5
fofluff	N/A	Klutz Board Games book.
folko	6.9	[S]
ed_in_play	N/A	printed rhombus shaped board 11x11 Hex to use with go pieces or pieces from two Othello sets
Formersd	6	Connection abstract with a simple single rule but deep strategy.
jmastill	10
psikonauta	10
BoardGameGeek42	N/A	BGA
Furan	6	There's something wrong with me, or it doesn't seem to be so briliant...
gmoralesor	10
XMJA	10
DSeagraves	7	Great abstract game. Very challenging.
chaosbreaker	7	Simple rules yet a complex game. Own a laser printed board on a self adhesive, vinyl bathroom tile that I bought from a hardware store.
T0afer	10
twerkface	9.5
DanielBeaver	8	Very simple, deceptive depth. It requires a bit of coaching for new players, or else they will flounder around without discovering the basic tactics, but this is a relatively small hump compared to other abstracts.
dispatch134711	9.4	From one rule springs endless delight. The simplest and purest of all abstracts. The most mathematical and one of the most difficult. Connect two sides of a hex board. Discovered by two different mathematicians, Hex is truly a universal game. Even a child could tell if the game was won. If extraterrestrial intelligence exists, they play this game. On larger boards, its depth will rival Go itself. Fascinating. Most computer programs are rubbish. A windows program "Hexy" presents a stiff challenge, but only on 11x11. This is the size at which computers will eventually overwhelm humans (if they haven't already). Luckily, moving up to a bigger board is always an option.
clark94	8	Simple game, which explains why it is so difficult. If you make a mistake early it is often irrecoverable.
aaronseeber	6	A classic, but a bit too dry for my taste.
Hexer	10
ypercube	10
amortera	N/A	Print
Gamegrunt	6	Beta Games "Banochee" version. Obtained in a thrift store. The components fit nicely into my Pente tube. This one is neglected in favor of Twixt, a better connection game.
alekerickson	10
Thesse1955	9
KalebAllinson	9
CDRodeffer	8	Beautifully simple abstract connection game. If you don't already have it, Cameron Browne's book on this game is excellent.
mxpf	10	My favorite 2-player classic abstract.
Chris Sjoholm	9
pleclenuesse	10
ludopath	10	It may not be as much "fun" as, say, Gyges, Tzaar, Dvonn, or even Amazons and Lines of Action, but there is no question that this is a brilliant game design. Boards should be 13x13 at least, though.
ddyer	8	More than a mathematical curiosity. Go players will find the positional and pattern matching pretty familier.
Gruff Mckenzie	9	simple and superb...
AmassGames	4	Too basic and odd: even approach
Scrabblette	9
Quadell	9	I usually play this on a homemade board with makeshift pieces. In my opinion, this is the world's best abstract strategy game, both perfectly simple and magnificently complex.
Hjallti	9	Great game
Bob Waters	9	Simple.
D Beau	7.5	I've always been under the impression that I didn't enjoy connection games, but playing Hex has brought that into question. Perhaps I simply couldn't grasp the fundamental concepts of the genre until I saw them boiled down to their essence. With Hex, there's a great clarity, which was missing for me in games like Punct or Twixt. Regardless, my few games so far have been very fun and exciting, and I look forward to playing more.
Panglott	10	Such a fascinating game, so simple and yet so much interest. I would love to play this more.
adebisi	3	One of those classic games that are simple but ingenious, like tic-tac-toe. However, after playing once I just don't want to play again.
drbobjack	8	Hex is the ultimate connection game, and possibly the abstractest abstract. On a theoretical level, the way very simple rules create something that works so well is fascinating. But Hex is more than a cool theoretical construct -it's incredibly sharp and interesting to play. The back and forth of cuts, early plays to gain control of areas, figuring out just where to play your stones -it's brilliant. And in a game that can be taught in 10 seconds! It's not the most exciting game, admittedly, and it can be difficult for new players to "get". You can play it with them, giving them stones as a handicap, but it's probably not the best introduction to abstracts. And as a placement game, positions can feel a little static. Still, Hex is a fantastic game that should be played by anyone who's interested in abstracts.
epicurus	10
HrFrosk	10
Ottia	9	It's biased towards the first player (the smaller the board, the bigger the edge) but otherwise Hex is a deserved classic. It's the sleekest connection game there can be, one of the very few games whose elegance can be remotely compared to Go's, and one of the other few that are even more minimalistic.
Checkallday	7	I'm still learning but I like Twixt better.
almo2001	8	I have the nestorgames 14x14 portable edition. Great game!
tkvaran	9.5
Thrift Thopter	10
gwylim	10	Probably my favorite game. The rules are very simple, but the strategy is far from trivial. Only play online.
wtanaka	9	http://games.wtanaka.com/hex
boomtron	8	The most basic connection game. But, that just allows the decisions to boil to their essence. Great.
Iguanoman	9
Tiwsman	10
bop517	N/A	Pen and Paper 3M game.
kupad	10	An amazing game - I'm surprised there are no versions commercially available. It can be taught in perhaps a minute, it's incredibly deep - a truly elegant game. It's also very cutthroat and completely unforgiving. I plan to get better at this one.
Apple Paul	5	A basic abstract game without much gaming excitement. Feels like an experiment in math theory at best I suppose.
garbagefan	7	iPad
FiveStars	10	One of the best games ever invented. Was called "Polygon" by its Danish inventor, the poet Piet Hein, and "Nash" by John Nash, winner of the Nobel Prize.
qswanger	10	Quintessential connection game.
aprolepsis	9	the purest connection game

Kolomogorov Complexity Analysis

Size (bytes)	28242
Reference Size	10293
Ratio	2.74

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 second	15766.80 (63.42µs/playout)
Reference Size	389514.28 (2.57µs/playout)
Ratio (low is good)	24.70

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.

Playout/Search Speed

Label	Its/s	SD	Nodes/s	SD	Game length	SD
Random playout	20,726	96	3,146,321	14,506	152	14
search.UCB	20,434	367			67	11
search.UCT	20,199	352			76	13

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: Player 1 (White) win %	46.10±3.07	Includes draws = 50%
2: Player 2 (Black) win %	53.90±3.10	Includes draws = 50%
Draw %	0.00	Percentage of games where all players draw.
Decisive %	100.00	Percentage of games with a single winner.
Samples	1000	Quantity 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

Match	AI	Strong Wins	Draws	Strong Losses	#Games	Strong Score	p1 Win%	Draw%	p2 Win%	Game Length
0	Random
2	UCT (its=3)	631	0	274	905	0.6665 <= 0.6972 <= 0.7263	49.72	0.00	50.28	149.32
13	UCT (its=14)	631	0	353	984	0.6108 <= 0.6413 <= 0.6706	47.66	0.00	52.34	147.33
24	UCT (its=25)	631	0	365	996	0.6031 <= 0.6335 <= 0.6629	48.69	0.00	51.31	146.77
34	UCT (its=35)	631	0	321	952	0.6322 <= 0.6628 <= 0.6921	46.53	0.00	53.47	145.28
39	UCT (its=40)	572	0	428	1000	0.5411 <= 0.5720 <= 0.6023	39.40	0.00	60.60	143.43
40	UCT (its=40)	522	0	478	1000	0.4910 <= 0.5220 <= 0.5528	41.20	0.00	58.80	143.97

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 length	56.81
Branching factor	141.09
Complexity	10^121.64	Based on game length and branching factor
Computational Complexity	10^7.58	Sample quality (100 best): 22.64
Samples	1000	Quantity 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 actions	169	Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves	83	A good move is selected by the AI more than the average
Bad moves	86	A bad move is selected by the AI less than the average
Response distance	4.37	Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples	1000	Quantity of logged games played

Board Coverage

A mean of 33.62% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean	56.81
Mode	[47]
Median	55.0

Change in Material Per Turn

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 14% of the game turns. Ai Ai found 4 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

Measure	All players	Player 1	Player 2
Mean % of effective moves	41.87	36.09	47.86
Mean no. of effective moves	60.12	52.14	68.39
Effective game space	10^57.38	10^27.60	10^29.78
Mean % of good moves	48.42	77.77	18.01
Mean no. of good moves	67.89	105.66	28.79
Good move game space	10^60.27	10^48.78	10^11.50

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

Measure	Value	Description
Hot turns	71.93%	A hot turn is one where making a move is better than doing nothing.
Momentum	35.09%	% of turns where a player improved their score.
Correction	38.60%	% of turns where the score headed back towards equality.
Depth	5.66%	Difference in evaluation between a short and long search.
Drama	0.00%	How much the winner was behind before their final victory.
Foulup Factor	49.12%	Moves that looked better than the best move after a short search.
Surprising turns	0.00%	Turns that looked bad after a short search, but good after a long one.
Last lead change	36.84%	Distance through game when the lead changed for the last time.
Decisiveness	3.51%	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.)

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

0	1	2	3
1	169	28561	2399293

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 3.