Full Report for Y(dimension 19) by Ea Ea and Charles Titus

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 all three sides.

Miscellaneous

General comments:

Play: Combinatorial

Mechanism(s): Connection

BGG Stats

BGG Entry	Y(dimension 19)
BGG Rating	7.08657
#Voters	108
SD	1.66384
BGG Weight	2.5
#Voters	10
Year	1953

BGG Ratings and Comments

User	Rating	Comment
mst3k4L	7
yakshto	8.5	Played on a regular triangular hex board, Y is probably a bit more elegant than Hex (making it the most elegant game ever?), but somehow less engaging nevertheless. Requires huge boards (I'd go for base-17-18-19 at least). Base-14 Y feels like 9x9 Hex.
mrraow	7	Good connection game, but loses out to hex in terms of simplicity and elegance.
Willward	7	Debate continues over whether this game is better than its great-uncle [I]Hex[/I]. I vote "yes".
fogus	6.4	[2014.11.26] I printed out a ton of Mudcrack Y boards for travel and it's my favorite "airplane tray table" game. Elegant, simple to teach, and strategically deep.
rschmucker	6
gregcrowe	7
diecarpitur	5
Scortez	5.25
Stephen Glenn	9	Homemade copy
skybison	9	It's not Go. It doesn't need to be. Why? Y.
Aiken Drum	6	I love connection games, and this one is excellent.
fuchsundbrunnen	8.5
matthulgan	10
Pionek	7
jirka bauma	7
matango	9	hex variant
simpledeep	9
cousinIt	8
schwarzspecht	8
David Greene	8
jayzen	7
fivecats	6.5
jrodman	8	I really enjoy this connection game, only I can't find enough players.
Peter Loop	9
Wentu	6.4
Nehm	6
HexNash	10
dakarp	N/A	Very nice abstract connection game.
The Player of Games	8	Interesting game. I really enjoy the wooden board from Kadon. Comes with rules for: 1) The Game of Y 2) Aliens and Amazons 3) Singularity 4) Leap Over 5) Tetra 6) Quinta 7) Sexta 8) Solitaires
mattcmaddox	N/A	Handmade board.
Orphius	6
metobillc	7
unic	8
KnightTim	N/A	In The 15 Greatest Board Games in the World
Mingy Jongo	9.9	I use a homemade 19-hexagons-wide regular board. The curved ones with pentagons mixed in just seems wrong.
wizhyun	7
pattonre	6
AbstractStrategy	3	I found it really quick to reach a conclusion and boring. Am I missing something? Not sure... If Hex is worse than this then I can't be bothered playing...
cdunc123	8.5	Provisional rating since I've only played a couple of games, and on a small board at that. But I enjoyed it as much as Hex, and maybe even more. Since both players have the same objective, it had a different feel to Hex; it seemed like I often had more interesting options each move. And it's even more elegant than Hex, since there is no distinction between sides. Among "deep games," it may be the most elegant there is.
ecoboardgeek123	N/A	diy version
Kaelistus	8
scih	6
lulu35	N/A	2J abstract
Drek_Overlord	6
MatroidX	4	I prefer Hex to this close variant.
Phil Bordelon	6	(The rating is an average of two different forms of the game.) I actually think I like Y a bit more than Hex, but it needs to be played on a large board (like, say, 13-17 to a side) to really shine. At that scale, I think Y is probably a high 8. In its most common published form, it's a take-it-or-leave-it game (a 5 in BGG parlance) in that any single misstep can cost you the game, and going first almost guarantees a win. So: 13/2, or 6.5. I'll round that down to a 6, since I actually spent money on a nice Y board... that is the clearly inferior form. Sigh.
fiddly_bits	N/A	I have a homemade "straight" Y board.
MadSad	8
damonstea	5
kc2dpt	7
BankofDracula	7
djnesq	7	Connoisseurs of this genre of games probably can point out the strategies that distinguish Y/Hex/Havannah one from another. I enjoy them all, but they feel pretty much the same to me. The Y board is small; an early disadvantage is hard to overcome because you don't have the opportunity for counterplay at the other end of the board that some of those other games give you.
glanfam	9	Beautiful Kadon wooden edition
fehrmeister	5
uigrad	6	Too expensive for what is included. I made my own version. (shhhh)
Friendless	7	Similar to Hex, and I similarly struggle to find opponents.
steadym	8	Always up for some of this. Elegant and beautiful connection game.
hippiephysicschick	N/A	lost board?
RDReilly	10	One of my favorite abstracts. Considerable depth; doesn't take too long to play.
keithw	9
Ludo le gars	8.5	Home-made version
BoardGameBarrister	8	The game that the LovelyWife and I played while dating.
lyman	7	I like the Kadon (non-uniform) board. Have not played by email partially since I think the regular board is less interesting. Generally I mostly play Unlur when I play connection games.
seandavidross	6
twixter	8	Very similar to Hex, one of my addictions. The Kadon board is very aesthetic. I would prefer an even larger extension of such a grid, however. Maybe 17 points along each edge, 345 total...?
Tony van der Valk	9	I like the bent-Y board
DaMarsh	7	Good game, beautiful board, and rules for additional games. All of these descriptions apply to many games from Kadon Enterprises (//www.gamepuzzles.com).
Punainen Nörtti	10
latindog	N/A	Currently Unplayed :(
antlersantlers	9
Avaer	8
JazzFish	7	Learned this one out of a book in second grade, so it holds a special place in my heart.
megamau	8	Not much different from Hex.
Helian	7
dooz	7
leffe dubbel	7
molnar	10	Addictive abstract strategy, with mathematical elegance that cannot be matched. It's impossible. The connection games (also [gameid=4112], [gameid=2759], [gameid=949], [gameid=3826]...) appeal to me because when they're done, they're done - no keeping score. This is my favorite of the genre, both players have the same goal (not quite true of Hex) and someone has to win (Sperner's Lemma). Can be played with pencil and paper, but the Kadon board is exquisite. Generally, my ratings take into account the physical product not at all. I rate the idea, the thought processes that one goes through while playing. On strictly that basis, I am no longer certain that Y is actually a better game than [gameid=34221]. Honest. For all I know, [gameid=11997] is even better. The attention-getting wood board though, the black and white stones, the 'clack' - that all pushes it up for me. The published version also differs somewhat from the version you'll find online. The seeming curvature introduced on the Kadon board has more than aesthetic significance: by shortening the distance along the edges relative to the distance from the center to the edge, the power is spread more evenly throughout the board, which makes for a game where the hot spots can move around quite entertainingly. (And it also looks cool.) I'll mention here that the book "Mudcrack Y & Poly-Y" (which is not in the database, because it is specific to one game) has an excellent discussion of strategy. Like everything that I've read from Ea Ea, the themes of that discussion can be applied elsewhere as well.
AdamMcD	6	Like Hex - the game lacks character. Only lines and dots are present. Like chess - I won't play with someone who takes long turns.
brian	6
Jim Tarnung	6
BeyondMonopoly	9	A very involved, and involving game that takes Hex and grows forward with it. Excellent gameplay.
rayzg	8	Homemade version -- plastic sheet protector, printout, and dry-erase markers. Also own book "Muddcrack Y and Poly Y." Tricky to create aesthetically pleasing board with graphics programs.
mrgodot	6
The Abstractionist	N/A	Wooden board.
erak	6	Seemed a little basic. The board was beautiful however.
ed_in_play	N/A	printed triangle shaped board 16x16x16 to use with go pieces
XMJA	9
T0afer	4	Edit: After several plays of this I find Y to be much less fun to play than Hex, greater elegance be damned. I'm told you need very large boards to reduce the First player advantage in a meaningful way and honestly I don't know why I wouldn't just play Hex. It's not like Hex is a bad game or is in great need of more elegance.
Forianst	6
bellowski	8	Nice, fairly quick game. Kind of expensive, but components are outstanding and add to the experience(gotta love go stones on wood). Worth adding to a collection.
Pirxtrurl	7
Thesse1955	6
CDRodeffer	N/A	I've heard good things about it, and would like to trade for a copy.
greg4413	6.5
AngusBull	7.5	Very Good abstract connection game. Can be played with pencil and paper which makes it quite portable.
paynentt	7
Scrabblette	9
dabeshouse	8
pieces09	7
yzemaze	6
Zickzack	6.1	In a way, the rules are simpler than Hex. However. there are more symmetry axes which allow less variety. If you want to avoid swaps, there are only 2 (!) opening moves in Y compared to at least 5 in Hex. Further, the edge areas cover larger parts of the board than in Hex. Games are shorter in Y than on a Hex board of a similar size (e.g. Hex on 11x11 and Y with an edge length of 15). The two effects together leave Hex as the richer game. The strategic advice contained in books like "Mudcrack and Poly-Y" is trivial at best. The designers do not understand their own game. This shows in board sizes that are too small for meaningful play, especially when played as Master Y, and in board geometries that cannot be balanced by a 1-move swap rule.
rseater	3	degenerate first player advantage. Using pie rule is unsatisfying and the state state is still too small to be interesting. update: the game is mathematically interesting and adds some core mechanics to the connection genre, but that doesn't save this particular instance from being boring imbalanced computation
yolandavi	7
Ritz1974	9	Very elegant, but lost my home-made wooden game board when I last moved
Iguanoman	8
bop517	6	Solid abstract...need to try again.
Kytty	6
Javest	6.8
Slounger	5	DIY
dbucak	9
zdim	7
FiveStars	10	A most elegant game closely related to Hex!
bankrupt	7
pezpimp	6	Based on one play: Connect the three sides to win. A little more complex then its cousin of connecting two sides since you cannot forget about any side, but still leaves you wishing there was more to it.
steveoliverc	N/A	3-sided Hex. Print & play, but get a nice wooden set.

Kolomogorov Complexity Analysis

Size (bytes)	32172
Reference Size	10293
Ratio	3.13

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	34436.33 (29.04µs/playout)
Reference Size	2028809.09 (0.49µs/playout)
Ratio (low is good)	58.91

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	34,617	276	6,010,343	48,257	174	13
search.UCB	NaN	NaN			0	0
search.UCT	NaN	NaN			0	0

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 %	49.90±3.09	Includes draws = 50%
2: Black win %	50.10±3.09	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	293	924	0.6522 <= 0.6829 <= 0.7121	50.76	0.00	49.24	171.13
12	UCT (its=13)	631	0	351	982	0.6121 <= 0.6426 <= 0.6719	51.73	0.00	48.27	170.17
22	UCT (its=23)	631	0	355	986	0.6095 <= 0.6400 <= 0.6693	50.30	0.00	49.70	168.59
31	UCT (its=32)	631	0	349	980	0.6134 <= 0.6439 <= 0.6732	51.12	0.00	48.88	166.77
39	UCT (its=40)	631	0	342	973	0.6180 <= 0.6485 <= 0.6779	53.24	0.00	46.76	165.94
46	UCT (its=47)	631	0	359	990	0.6069 <= 0.6374 <= 0.6667	55.35	0.00	44.65	165.17
49	UCT (its=50)	559	0	441	1000	0.5281 <= 0.5590 <= 0.5895	54.50	0.00	45.50	164.35
50	UCT (its=50)	507	0	493	1000	0.4760 <= 0.5070 <= 0.5379	51.10	0.00	48.90	163.82

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	78.38
Branching factor	151.33
Complexity	10^170.21	Based on game length and branching factor
Computational Complexity	10^7.81	Sample quality (100 best): 11.37
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	191	Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves	94	A good move is selected by the AI more than the average
Bad moves	97	A bad move is selected by the AI less than the average
Response distance	5.91	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 41.25% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean	78.38
Mode	[77]
Median	78.0

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 24% of the game turns. Ai Ai found 2 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	2.72	2.71	2.73
Mean no. of effective moves	3.10	3.10	3.10
Effective game space	10^5.49	10^2.84	10^2.66
Mean % of good moves	25.04	0.00	50.08
Mean no. of good moves	32.99	0.00	65.97
Good move game space	10^44.40	10^0.00	10^44.40

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	97.44%	A hot turn is one where making a move is better than doing nothing.
Momentum	34.62%	% of turns where a player improved their score.
Correction	35.90%	% of turns where the score headed back towards equality.
Depth	3.82%	Difference in evaluation between a short and long search.
Drama	0.00%	How much the winner was behind before their final victory.
Foulup Factor	1.28%	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	38.46%	Distance through game when the lead changed for the last time.
Decisiveness	2.56%	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.)

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.

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

0	1	2	3
1	190	36290	2286650

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.

Puzzles

Puzzle	Solution
White to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
White to win in 3 moves
White to win in 3 moves

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