Comune is a placement game using rectangular pieces. In this game, there are three different angles for placing the pieces, and you can place up to two pieces at different angles on your turn. However, you cannot place a piece adjacent to an opponent's piece at a different angle. Take advantage of the rules to create larger settlements as possible with your pieces.
Generated at 2024-10-30, 02:43 from 1000 logged games.
Rules
Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!
PLACEMENT RULES
Players place their pieces orientated along the lines of the grid.
Adjacent pieces matching both color and angle are considered to be a group.
The group size is the number of pieces in the group.
During the game, two pieces that differ in both color and angle cannot be adjacent to each other.
GAME PLAY
White plays first, then turns alternate.
White's first turn they place one piece. On subsequent turns, players place up to two pieces per turn; if two, the pieces cannot have the same orientation. Passing is allowed
GAME END
The game ends when neither player can place any more pieces, or when both players pass in succession.
Player score by finding the largest group of that orientation, and multiplying the three sizes together.
Largest score wins. In the case of a tie, the game is a draw.
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
13467.81 (74.25µs/playout)
Reference Size
547285.16 (1.83µs/playout)
Ratio (low is good)
40.64
Tavener complexity: the heat generated by playing every possible instance of a game with a perfectly efficient programme. Since this is not possible to calculate, Ai Ai calculates the number of random playouts per second and compares it to the fastest non-trivial Ai Ai game (Connect 4). This ratio gives a practical indication of how complex the game is. Combine this with the computational state space, and you can get an idea of how strong the default (MCTS-based) AI will be.
State Space Complexity
% new positions/bucket
State Space Complexity
174256614
State Space Complexity bounds
65589497 < 174256614 < ∞
State Space Complexity (log 10)
8.24
State Space Complexity bounds (log 10)
7.82 <= 8.24 <= ∞
Samples
1089201
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
16,471
293
992,156
17,606
60
6
search.UCT
17,100
789
60
4
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 %
49.20±3.09
Includes draws = 50%
2: Black win %
50.80±3.10
Includes draws = 50%
Draw %
3.40
Percentage of games where all players draw.
Decisive %
96.60
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
1
UCT (its=2)
619
23
323
965
0.6228 <= 0.6534 <= 0.6827
50.57
2.38
47.05
60.14
5
UCT (its=6)
620
21
339
980
0.6129 <= 0.6434 <= 0.6727
51.73
2.14
46.12
60.90
17
UCT (its=18)
621
20
336
977
0.6153 <= 0.6459 <= 0.6752
49.03
2.05
48.93
60.45
34
UCT (its=35)
619
24
350
993
0.6050 <= 0.6354 <= 0.6648
47.43
2.42
50.15
60.22
60
UCT (its=61)
624
13
340
977
0.6148 <= 0.6453 <= 0.6747
48.41
1.33
50.26
59.95
76
UCT (its=77)
550
14
436
1000
0.5261 <= 0.5570 <= 0.5875
50.00
1.40
48.60
59.83
77
UCT (its=77)
489
28
483
1000
0.4721 <= 0.5030 <= 0.5339
50.10
2.80
47.10
59.73
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
60.58
Branching factor
46.56
Complexity
10^81.60
Based on game length and branching factor
Computational Complexity
10^7.22
Sample quality (100 best): 11.74
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
61
Quantity of distinct board cells
Distinct actions
184
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
62
A good move is selected by the AI more than the average
Bad moves
122
A bad move is selected by the AI less than the average
Response distance%
53.37%
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 85.99% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
60.58
Mode
[62]
Median
60.0
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.)
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 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
43.92
46.13
41.78
Mean no. of effective moves
19.56
19.60
19.52
Effective game space
10^40.13
10^21.14
10^18.99
Mean % of good moves
35.66
17.19
53.53
Mean no. of good moves
16.67
17.90
15.48
Good move game space
10^38.32
10^14.64
10^23.68
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
72.13%
A hot turn is one where making a move is better than doing nothing.
Momentum
24.59%
% of turns where a player improved their score.
Correction
27.87%
% of turns where the score headed back towards equality.
Depth
3.73%
Difference in evaluation between a short and long search.
Drama
0.86%
How much the winner was behind before their final victory.
Foulup Factor
39.34%
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
37.70%
Distance through game when the lead changed for the last time.
Decisiveness
24.59%
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
183
31251
1757901
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.
