Full Report for Las Médulas(size=7,advanced) by Drew Edwards

Full Report for Las Médulas(size=7,advanced) by Drew Edwards

Las Médulas is an ancient Roman gold mine in Spain. Think of your stones as miners digging corridors through the rock. If they dig too closely together, the mine will collapse. To win, trap your opponent so that you have space to mine safely and they do not.

Generated at 2/17/21, 6:43 AM 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!

Play

On your turn, Mine and then Move one of your miners (i.e. stones).

Mining:

Movement:

Removal:

Winning

The first player who cannot Mine (place a tile) loses.

Miscellaneous

General comments:

Play: Combinatorial

Family: Combinatorial 2020

Mechanism(s): Connection,Movement,Capture,Stalemate

Components: Board

BGG Stats

BGG EntryLas Médulas(size=7,advanced)
BGG Rating8.5
#Voters2
SD0.5
BGG Weight3
#Voters1
Year2020

BGG Ratings and Comments

UserRatingComment
PSchulman8
rsb762gm9Fun, moderately strategic, fast moving game with simple rules.

Kolomogorov Complexity Analysis

Size (bytes)27431
Reference Size10293
Ratio2.67

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 second886.18 (1128.43µs/playout)
Reference Size844523.27 (1.18µs/playout)
Ratio (low is good)952.99

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 playout1,00435137,0244,7891368
search.UCB1,0414513211
search.UCT1,0375113112

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 %50.30±3.09Includes draws = 50%
2: Black win %49.70±3.09Includes 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.

UCT Skill Chains

MatchAIStrong WinsDrawsStrong Losses#GamesStrong Scorep1 Win%Draw%p2 Win%Game Length
0Random         
1UCT (its=2)63103539840.6108 <= 0.6413 <= 0.670648.070.0051.93136.31
2
UCT (its=3)
545
0
455
1000
0.5140 <= 0.5450 <= 0.5756
49.90
0.00
50.10
135.98
3
UCT (its=4)
606
0
394
1000
0.5754 <= 0.6060 <= 0.6358
50.00
0.00
50.00
135.86
4
UCT (its=5)
593
0
407
1000
0.5623 <= 0.5930 <= 0.6230
50.70
0.00
49.30
135.75
5
UCT (its=6)
616
0
384
1000
0.5855 <= 0.6160 <= 0.6456
48.40
0.00
51.60
136.17
6UCT (its=7)63103119420.6392 <= 0.6699 <= 0.699151.590.0048.41136.09
7
UCT (its=8)
510
0
490
1000
0.4790 <= 0.5100 <= 0.5409
47.20
0.00
52.80
135.92
8
UCT (its=9)
542
0
458
1000
0.5110 <= 0.5420 <= 0.5727
51.00
0.00
49.00
135.72
9
UCT (its=10)
560
0
440
1000
0.5291 <= 0.5600 <= 0.5905
50.80
0.00
49.20
135.15
10
UCT (its=11)
534
0
466
1000
0.5030 <= 0.5340 <= 0.5647
47.60
0.00
52.40
135.93
11
UCT (its=12)
553
0
447
1000
0.5220 <= 0.5530 <= 0.5836
47.50
0.00
52.50
135.63
12
UCT (its=13)
570
0
430
1000
0.5391 <= 0.5700 <= 0.6004
51.60
0.00
48.40
135.02
13
UCT (its=14)
585
0
415
1000
0.5542 <= 0.5850 <= 0.6152
50.70
0.00
49.30
135.79
14
UCT (its=15)
580
0
420
1000
0.5492 <= 0.5800 <= 0.6102
52.20
0.00
47.80
135.61
15
UCT (its=16)
537
0
463
1000
0.5060 <= 0.5370 <= 0.5677
51.30
0.00
48.70
135.70
16
UCT (its=17)
588
0
412
1000
0.5572 <= 0.5880 <= 0.6181
51.40
0.00
48.60
135.58
17
UCT (its=18)
603
0
397
1000
0.5723 <= 0.6030 <= 0.6329
51.10
0.00
48.90
136.03
18
UCT (its=19)
589
0
411
1000
0.5582 <= 0.5890 <= 0.6191
52.70
0.00
47.30
135.78
19
UCT (its=20)
593
0
407
1000
0.5623 <= 0.5930 <= 0.6230
50.30
0.00
49.70
135.93
20
UCT (its=21)
574
0
426
1000
0.5431 <= 0.5740 <= 0.6043
51.00
0.00
49.00
135.21
21
UCT (its=22)
599
0
401
1000
0.5683 <= 0.5990 <= 0.6289
47.70
0.00
52.30
135.60
22
UCT (its=23)
600
0
400
1000
0.5693 <= 0.6000 <= 0.6299
47.00
0.00
53.00
135.44
23
UCT (its=24)
594
0
406
1000
0.5633 <= 0.5940 <= 0.6240
49.60
0.00
50.40
135.53
24
UCT (its=25)
623
0
377
1000
0.5925 <= 0.6230 <= 0.6525
50.30
0.00
49.70
135.69
25
UCT (its=26)
612
0
388
1000
0.5814 <= 0.6120 <= 0.6417
51.20
0.00
48.80
135.82
26
UCT (its=27)
604
0
396
1000
0.5733 <= 0.6040 <= 0.6339
52.60
0.00
47.40
136.15
27
UCT (its=28)
613
0
387
1000
0.5824 <= 0.6130 <= 0.6427
48.90
0.00
51.10
135.48
28
UCT (its=29)
611
0
389
1000
0.5804 <= 0.6110 <= 0.6407
48.10
0.00
51.90
135.78
29
UCT (its=30)
585
0
415
1000
0.5542 <= 0.5850 <= 0.6152
51.10
0.00
48.90
136.08
30UCT (its=31)63103379680.6213 <= 0.6519 <= 0.681247.830.0052.17135.66
31
UCT (its=32)
494
0
506
1000
0.4631 <= 0.4940 <= 0.5250
48.20
0.00
51.80
135.30
32
UCT (its=32)
489
0
511
1000
0.4581 <= 0.4890 <= 0.5200
50.90
0.00
49.10
136.13

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 length130.84 
Branching factor53.34 
Complexity10^184.81Based on game length and branching factor
Computational Complexity10^7.39Sample quality (100 best): 4.83
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 actions16130Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves1877A good move is selected by the AI more than the average
Bad moves14253A bad move is selected by the AI less than the average
Terrible moves3666A terrible move is never selected by the AI
Too many terrible moves to list.
Response distance5.55Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples1000Quantity of logged games played

Board Coverage

A mean of 55.84% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean130.84
Mode[133]
Median133.0

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.)

Red: removal, Black: move, Blue: Add, Grey: pass, Purple: swap sides, Brown: other.

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

0123
112715445891361

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

PuzzleSolution

White to win in 3 moves

Black to win in 3 moves

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