Full Report for Unlur by Jorge Gomez Arrausi

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!

Contract Phase

Because White's goal is easier to achieve than Black's, we start with a chicken ballot; players take turns to either place a black piece, or claim the black pieces. Once someone chooses black the game proceeds normally; with white taking the next move. During this phase, pieces may not be played on the edge (too weak).

Play

The two players take turns placing a piece of their colour in any space.

Goal

White wins by making a line (connecting any two opposite sides); black Wins by making a Y (connecting three non-adjacent sides). Corners count as both sides.

To avoid ties, if a player achieves their opponent's goal without winning at the same time, they lose.

Miscellaneous

General comments:

Play: Combinatorial

Mechanism(s): Connection

BGG Stats

BGG Entry	Unlur
BGG Rating	7.77432
#Voters	37
SD	1.39969
BGG Weight	3
#Voters	8
Year	2002

BGG Ratings and Comments

User	Rating	Comment
lyman	8	My favorite of the connection games. The contract phase is a unique aspect as is the rule that you can "lose" by fulfilling the other person's victory conditions.
seandavidross	6
Tony van der Valk	8
Matt1990	6
paradroid	10	the best connection game?
Aiken Drum	9	I have this unique game as a self made board.
dooz	6
molnar	8.75	Spawn of Hex and [gameid=5242], two of my favorite games. An interesting variation, probably more room for distinct strategies. Easy to play on the Yinsh board. Glad to see games from Abstract Games Magazine listed on this site.
Pensator	8	2 players. Abstract strategy.
Nap16	6	Free Print & Play. Awards: Unequal Forces Game Design Competition 2002(sponsored by About Board Games, Abstract Games Magazine, and the Strategy Gaming Society).
zefquaavius	6.5	Not the type of game that gets my juices flowing, but a brilliantly tricky, evenly unbalanced, pure strategy and tactics game.
Pionek	8
rayzg	5	I really wanted to like this game as the contract phase is very unique. However, after the contract phase, the game is basically Hex, and I find that game too tactically austere and dry.
JESSONSO	8
orangeblood	8	The contract phase (where both players play the same color) makes this unique among abstracts I'm familiar with. Meanwhile, the rule that you lose if your pieces fulfill your opponent's win condition (without simultaneously reaching your goal) adds a very interesting layer that can be used to rescue an otherwise losing position.
Valenox	6.5	Игра столь же абстрактна и рафинирована как Hex. Но с интересным началом - "торговлей". Другой родственник - Havannah. Там больше victory conditions, и это мне нравится больше. Становится не так сухо и узко в смысле приемов. Игра Punct делалась, несомненно не без знаний об этих играх.
upike	N/A	In or around Vilnius and want to play? Send me a PM!
schwarzspecht	8
_mrq_	N/A	Printed board
seneca29	N/A	Fare la linea o la Y. Havannah set. Still to play
evanvariano	N/A	I'm interested in the "famous" and "revolutionary" bidding method in which black keeps playing until white is ready to swap or accept their position.
XMJA	9
gmoralesor	8	tablero de Celtis
unic	4.5
aSoso	8.5
drunkenKOALA	8	Just play hex.
twerkface	N/A	On Ludii
wizhyun	8
clark94	9	Perhaps one of the most creative connections games EVER. A connection game with unequal goals is unheard of. Unlurs initial phase for balancing play is a brilliant way to make two unequal goals fair for both sides.
Hexer	9
cdunc123	8.5	Brilliant idea for a connection game on a hexhex board. And the opening phase -- sometimes called a "chicken ballot" or "chicken option" -- is a stroke of genius. (I borrowed the idea in two of my own games, Looper and Pippinzip.)
alekerickson	10
CDRodeffer	8	Great press-your-luck connection game! I made a set for myself.
Roughblade	N/A	Asy
n3k0	9
scih	7
camisdad	N/A	make my own project
Zickzack	7	The rules are ingenious and innovative. Game designers should take notice. This refers mainly to the "contract" which allows to create self balancing games. However, the rule that achieving your opponent's winning condition while not achieving your own means losing is equally important. For one, it prevents draws. For another, it redefines game play. In most other connection games, additional stones of one's own colour do not harm. Unlur is different. For strategy, the article in the Abstract Games Magazine is a good starting point.
echdareez	N/A	[Using my Havannah board]
trioker	6.4
mickwood	N/A	2 Players. Can be played on an Ingenious board.
escueladejuegos	N/A	Pendiente y buscar tablet.
glaurent	N/A	Homemade using printed board, Go stones.
slimy_asparagus	10	An almost perfect abstract. Haven't found a human who gets the rules yet. I haven't found a computer who can beat me (once I got the rules).
janus	N/A	I have an Havannah board. So I have an Unlur board, too. 8-D
terKo	7
minismurf	10	Excellently balanced and unique.
UanarchyK	N/A	DIY, Hex Grid and stones in two colours.
pezpimp	6	Based on one play: Connection games all tend to feel the same, as the strategy is similar between them. This one has an interesting start as you both play the same side until someone claims that side. The goal is different for each team hence the better starting position for one side. But then it becomes a fairly standard connection game, so when to take over the starting color is a major choice and where to play those tokens as you may be helping your opponent.
aprolepsis	9	The essence of asymmetricality (is that a contradiction...?)
JugamosTodos	N/A	Consorci de Biblioteques Universitàries de Catalunya

Kolomogorov Complexity Analysis

Size (bytes)	28794
Reference Size	10673
Ratio	2.70

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 second	8704.93 (114.88µs/playout)
Reference Size	505535.61 (1.98µs/playout)
Ratio (low is good)	58.07

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

Samples	551449
Confidence	0.00	0: totally unreliable, 100: perfect

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

Label	Its/s	SD	Nodes/s	SD	Game length	SD
Random playout	8,884	240	1,055,801	28,772	119	21
search.UCT	9,506	380			85	16

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 win %	57.60±3.09	Includes draws = 50%
2: Player 2 win %	42.40±3.03	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
48	UCT (its=49)	435	0	565	1000	0.4046 <= 0.4350 <= 0.4659	53.10	0.00	46.90	116.94
49	UCT (its=49)	486	0	514	1000	0.4551 <= 0.4860 <= 0.5170	50.80	0.00	49.20	118.54

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	84.39
Branching factor	123.19
Complexity	10^175.15	Based on game length and branching factor
Computational Complexity	10^7.77	Sample quality (100 best): 3.98
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

Board Size	169	Quantity of distinct board cells
Distinct actions	170	Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves	87	A good move is selected by the AI more than the average
Bad moves	83	A bad move is selected by the AI less than the average
Response distance%	30.89%	Distance from move to response / maximum board distance; a low value suggests a game is tactical rather than strategic.
Samples	1000	Quantity of logged games played

Board Coverage

A mean of 49.34% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean	84.39
Mode	[79]
Median	83.0

Change in Material Per Turn

Mean change in material/round	0.97	Complete 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 8% of the game turns. Ai Ai found 1 critical turn (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	10.31	15.08	5.55
Mean no. of effective moves	9.74	14.21	5.26
Effective game space	10^26.97	10^15.05	10^11.92
Mean % of good moves	41.33	0.02	82.64
Mean no. of good moves	50.00	0.02	99.98
Good move game space	10^74.87	10^0.00	10^74.87

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	98.81%	A hot turn is one where making a move is better than doing nothing.
Momentum	41.67%	% of turns where a player improved their score.
Correction	27.38%	% of turns where the score headed back towards equality.
Depth	2.77%	Difference in evaluation between a short and long search.
Drama	0.00%	How much the winner was behind before their final victory.
Foulup Factor	4.76%	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	9.52%	Distance through game when the lead changed for the last time.
Decisiveness	2.38%	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

Moves	Animation
j6,b10,f6
b10,j6,f6

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	4
1	128	8425	399529	17001373

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 4.

Puzzles

Puzzle	Solution
Player 1 (White) to win in 5 moves
Player 2 (Black) to win in 3 moves
Player 2 (Black) to win in 3 moves
Player 2 (Black) to win in 3 moves
Player 1 (Black) to win in 3 moves
Player 1 (Black) to win in 3 moves
Player 1 (Black) to win in 3 moves
Player 1 (Black) to win in 3 moves
Player 2 (Black) to win in 3 moves
Player 1 (White) to win in 3 moves
Player 2 (White) to win in 3 moves
Player 1 (Black) to win in 3 moves

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