Full Report for Hex(dimension 11) by Piet Hein,John Nash

Full Report for Hex(dimension 11) by Piet Hein,John Nash

Possibly the simplest deep game ever invented

Generated at 23/04/2020, 05:26 from 1000 logged games.

Rules

Start Position

Place a piece. Connect opposite sides.

Miscellaneous

General comments:

Play: Combinatorial

Mechanism(s): Connection

BGG Stats

BGG EntryHex(dimension 11)
BGG Rating6.75095
#Voters633
SD1.81172
BGG Weight2.7358
#Voters53
Year1942

BGG Ratings and Comments

UserRatingComment
Butterbob9
amatyarakshasa10A simpler version of Twixt. So simple and so hard. Defense = Offense = Defense. A totally awesome game.
rauwolfa9.9
eljo71990 Home Made
mrraow10Beautifully simple connection game. Flawed, in that a pie rule is necessary to offset the first player advantage, but full of surprises.
Arctic Jack8Attic 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.
bayspielN/A08.02.02.04
dosxtres9
fogus6.52016 ==== 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.
cannoneer6I 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!
fhsIV9
danky1homemade. buggy game, it have an easy winning strategy
dolzandavid5.5A connection game, inferior to Twixt by a country mile.
adamscott7Might 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.
AltugasN/A(Not played yet).
freechinanow7Finally, 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.
birdbolter5This game was immensely amusing to me in my first dozen plays, less so now.
jeep9
Stephen Glenn9Homemade copy
hikwaitek10
Aiken Drum8If 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
emike7Classic.
The Nerdy Girl10
donkstN/A3M Paper Version
LukeJS10
matthulgan10The ideal abstract.
Songok10Very easy to learn, not sure about mastering it eheh Love the pie rule at the start
Pionek9
2d206PnP Not my preferred style of Abstract, but would still play occasionally.
davidme6.9"Own" in The Book of Classic Board Games by Sackson.
Draxonfly4*garden*
simpledeep10
gabriel_k10
Emmekappa9
nickmoniker10Very likely, Hex is my favorite game of all time. It's certainly in my top five.
4characters6For 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.
Calpurnio7Played over the web. Nice abstract
ampelman10
BobDodgerBlueN/A876
thelegendarybeng10This 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.
DingusN/A3M paper pad version and wooden marble version
HexNash9
Dindor9
El Diabolo8.5This game is bizarrely subtle. Like go, without serious study, looking at a board does not convey the spirit between the players.
dalton-almeidaN/APnP
The Player of Games9.09Print 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).
DalimThor6it's quick and easy to learn.
Getzen9Hex (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.
birdsong7036The PnP version is a good one to take on flights.
drunkenKOALA10Simple 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.
CarlosLuna10
Mingy Jongo9.8One of the greatest perfect-information games of all time.
cackleton210Hex 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
aionman9Comparable 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.
genji2569
byturn6the pure connection game.
cdunc1239.25An 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]
chriskasparN/AWould love to make my own version of this game.
Anakin19815Decent abstract game with very easy rules to teach and play but not exactly my cup if tea...
Kasimuzz10Maybe the best ever game!
r4t4t0sk10
struggler110
camb10This 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.
nestorgames9Publisher ;-) The perfect abstract.
filou9One 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.
epicgamer7I like this abstract connection game. I think I should try out some others like it.
Fenriz4I prefer Twixt.
dancingdanslc4DIGITAL PLAY: iPad Air Connect sides by placing tokens one at a time. Boring Out of my collection
fiddly_bitsN/AHomemade Nash set(s) in several of the traditional sizes.
takeoutweight10I 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.
dysjunct4Mediocre. Another boring abstract.
ericlosiewicz6Classic abstract that feels like it's almost solvable and could be deterministic (maybe there's some obvious opening plays and counterplays).
ctalbot5This abstract doesn't have much to offer. It's not fun.
boulderman4Too basic and odd: even approach
ErniepaulN/A?
jg2710If 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.
Deleted0105189There'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.
DornianCollectionN/ARussell
darrenmac9
AnttiR9.63
big_buddha7Very simple, very deep, and has that special something that just makes it pleasant to play
ChristianDK6Rules don't get any simpler than the rules for Hex yet the game is deep. A very strategic game.
halladba10
andrewhodkinson6Abstract Strategy
bucklen_uk6Elegant abstract - but there are many more 2 player games I'd rather play.
Friendless9I 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.
fantum10Very, very, very, very good.
RDReilly9Simple, deep, beautiful. Made two wooden boards for myself.
bootleby10Totally enthralled by this game and I hope the connotation of "frightened" comes off in my use of the verb "enthrall"
morphles10Rich gameplay from very simple rules. In this regard I doubt you get more bang for a buck! Very good game.
Akeem6I 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.
donaldrnelsonN/AW
BredericN/A@ BGA
FlatWorm7Pure abstract strategy. A challenge for the most jaded strategist, but also can be used to introduce kids (or others) to strategy boardgames.
salva9Some 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.
twixter10I've played over a thousand Hex games on the Internet. I hope to play thousands more.
bekudno10I 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 Valk10www.hexboard.com
ensor7Must play with pie rule. Simple rules yet challenging underneath, like dots and boxes.
Punainen Nörtti10
FauxSloMo9
darkerN/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.
bothros10
megamau9The greatest complexity in relation to the rules. It can literally be explained in 30 sec., but it is full of tactics and strategy.
Pocc9
Butsudoka7Please 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.
AdamMcD6Great 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.
Josemastill10
Adyry10
artyomch9
BeyondMonopoly8Mine is homemade set - Go stones on a Chessex mat.
familywontplay5.5The first person advantage is too great.
rayzg9Homemade version -- plastic sheet protector, printout, and dry-erase markers. Make sure you play this with very large boards, like 19x19.
aarondesk7.5#to-play
Chironis92 player
mynameiswillem10
demongodN/APrinted
mzmzmz10This is an awesome abstract game, easily my favorite.
clayhaus9Simple. Elegant. Classic.
rorschah10
pled9.5
fofluffN/AKlutz Board Games book.
Bonejar9
folko6.9[S]
ed_in_playN/Aprinted rhombus shaped board 11x11 to use with go pieces or pieces from two Othello sets
Formersd6Connection abstract with a simple single rule but deep strategy.
jmastill10
psikonauta10
BoardGameGeek42N/ABGA
Furan6There's something wrong with me, or it doesn't seem to be so briliant...
gmoralesor10
XMJA10
DSeagraves7Great abstract game. Very challenging.
chaosbreaker7Simple rules yet a complex game. Own a laser printed board on a self adhesive, vinyl bathroom tile that I bought from a hardware store.
DanielBeaver8Very 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.
dispatch1347119.4From 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.
clark948Simple game, which explains why it is so difficult. If you make a mistake early it is often irrecoverable.
aaronseeber6A classic, but a bit too dry for my taste.
Hexer10
ypercube10
amorteraN/APrint
Gamegrunt6Beta 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.
alekerickson10
Thesse19559
KalebAllinson9
CDRodeffer8Beautifully simple abstract connection game. If you don't already have it, Cameron Browne's book on this game is excellent.
mxpf10My favorite 2-player classic abstract.
Chris Sjoholm9
pleclenuesse10
ddyer8More than a mathematical curiosity. Go players will find the positional and pattern matching pretty familier.
Gruff Mckenzie9simple and superb...
Scrabblette9
Quadell9I 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.
Hjallti9Great game
Bob Waters9Simple.
D Beau7.5I'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.
Panglott9Such a fascinating game, so simple and yet so much interest. I would love to play this more.
adebisi3One 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.
drbobjack8Hex 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.
epicurus10
HrFrosk10
Ottia9It'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.
Checkallday7I'm still learning but I like Twixt better.
almo20018I have the nestorgames 14x14 portable edition. Great game!
tkvaran9.5
Thrift Thopter10
gwylim10Probably my favorite game. The rules are very simple, but the strategy is far from trivial. Only play online.
wtanaka9http://games.wtanaka.com/hex
boomtron8The most basic connection game. But, that just allows the decisions to boil to their essence. Great.
Iguanoman9
Tiwsman10
bop517N/APen and Paper 3M game.
kupad10An 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 Paul5A basic abstract game without much gaming excitement. Feels like an experiment in math theory at best I suppose.
garbagefan7iPad
FiveStars10One 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.
EllenM6Like that owing to the hex shapes a game cannot end in a draw. It's clever. Rating considers likely repeat plays-
qswanger10Quintessential connection game.
aprolepsis9the purest connection game

Kolomogorov Complexity Estimate

Size (bytes)31068
Reference Size10293
Ratio3.02

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 second64621.19 (15.47µs/playout)
Reference Size3063725.49 (0.33µs/playout)
Ratio (low is good)47.41

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

LabelIts/sSDNodes/sSDGame lengthSD
Random playout70,1433787,541,72540,18810811
search.UCB122,4114,194328
search.UCT119,4442,997348

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 %57.00±3.09Includes draws = 50%
2: Black win %43.00±3.04Includes 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.

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Random       
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0033.3373.06
Grand Unified UCT(U1-T,rSel=s, secs=0.03)36074383.7244.1937.33
Grand Unified UCT(U1-T,rSel=s, secs=0.07)36094580.0057.7835.38
Grand Unified UCT(U1-T,rSel=s, secs=0.20)360104678.2656.5239.39
Grand Unified UCT(U1-T,rSel=s, secs=0.55)360104678.2667.3946.93

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.

Complexity

Game length45.55 
Branching factor98.76 
Complexity10^89.97Based 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 actions122Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves55A good move is selected by the AI more than the average
Bad moves67A bad move is selected by the AI less than the average
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.

Actions/turn

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.

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 2% of the game turns. Ai Ai found 1 critical turn (turns with only one good option).

Overall, this playout was 59.09% 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 moves49.0054.4443.56
Mean no. of effective moves44.6850.9138.45
Effective game space10^55.8210^31.4210^24.41
Mean % of good moves41.370.2382.51
Mean no. of good moves39.820.2779.36
Good move game space10^38.7910^0.7810^38.02

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.

Swap Heatmap (Full Scan)

Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.

Based on 100 trials/move at 0.1s thinking time each.

Openings

MovesAnimation
j2,j3,i3,i4,h4,h5
j2,j3,i3,i4,h4
h5,h4,i4,j2
j2,j3,i3,i4
h5,h4,i4
g5,j6,k3
j2,j3,i3

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.

Swap Heatmap (Historic)

Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.

Size shows the frequency this move is played.

Unique Positions Reachable at Depth

0123
112114641878581

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.