Generated at 28/07/2021, 14:42 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!
MOVE TYPES
There are two types of moves in Zola: non-capturing and capturing.
NON-CAPTURING MOVES
The non-capturing move is a king-like move to an adjacent (horizontally, vertically, or diagonally), unoccupied square. A non-capturing move must increase the straight line distance to the center point of the board.
CAPTURING MOVES
The capturing move is a queen-like move along a straight (horizontal, vertical or diagonal) sequence of zero or more unoccupied squares terminating with an enemy occupied square. The enemy checker is removed and replaced with the capturing checker. A capturing move must maintain or decrease the straight line distance to the center point of the board.
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
10832.78 (92.31µs/playout)
Reference Size
578737.20 (1.73µs/playout)
Ratio (low is good)
53.42
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
11,124
212
616,180
11,815
55
4
search.UCT
11,130
647
49
5
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 %
66.90±2.98
Includes draws = 50%
2: Black win %
33.10±2.85
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
1
UCT (its=2)
631
0
317
948
0.6350 <= 0.6656 <= 0.6949
54.11
0.00
45.89
55.26
6
UCT (its=7)
631
0
314
945
0.6371 <= 0.6677 <= 0.6970
51.43
0.00
48.57
54.59
14
UCT (its=15)
631
0
352
983
0.6114 <= 0.6419 <= 0.6713
54.83
0.00
45.17
53.84
22
UCT (its=23)
631
0
369
1000
0.6006 <= 0.6310 <= 0.6604
51.90
0.00
48.10
53.77
32
UCT (its=33)
631
0
362
993
0.6050 <= 0.6354 <= 0.6648
54.18
0.00
45.82
53.28
36
UCT (its=98)
631
0
132
763
0.7985 <= 0.8270 <= 0.8522
53.34
0.00
46.66
51.89
37
UCT (its=266)
631
0
118
749
0.8146 <= 0.8425 <= 0.8668
51.27
0.00
48.73
50.24
38
UCT (its=723)
631
0
93
724
0.8452 <= 0.8715 <= 0.8940
52.07
0.00
47.93
48.45
39
UCT (its=1966)
625
0
65
690
0.8817 <= 0.9058 <= 0.9254
53.04
0.00
46.96
46.95
40
UCT (its=1966)
499
0
501
1000
0.4681 <= 0.4990 <= 0.5299
61.50
0.00
38.50
47.48
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
47.77
Branching factor
19.75
Complexity
10^54.81
Based on game length and branching factor
Computational Complexity
10^6.86
Sample quality (100 best): 5.07
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
445
Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
31
A 'killer' move is selected by the AI more than 50% of the time Killers: a6-f1,a6-f6,f4-a4,f5-a5,f1-f6,e1-b1,f2-f5,a5-a2,f2-b6,f2-a2,b6-f2,b6-e6,a6-a1,f1-a6,f1-a1,a2-b1,a2-a5,b1-f5,e6-f5,a1-f6,a1-f1,f5-f2,e6-b6,f6-f1,b1-e1,a1-a6,f5-b1,f5-e6,f6-a6,b1-b6,f6-a1
Good moves
203
A good move is selected by the AI more than the average
Bad moves
241
A bad move is selected by the AI less than the average
Response distance
2.48
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 99.82% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
47.77
Mode
[47]
Median
48.0
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.)
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 27% of the game turns. Ai Ai found 7 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
36.03
39.55
32.50
Mean no. of effective moves
3.48
4.08
2.88
Effective game space
10^20.25
10^11.84
10^8.42
Mean % of good moves
17.45
3.83
31.06
Mean no. of good moves
1.71
0.83
2.58
Good move game space
10^9.68
10^2.32
10^7.35
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
79.17%
A hot turn is one where making a move is better than doing nothing.
Momentum
20.83%
% of turns where a player improved their score.
Correction
35.42%
% of turns where the score headed back towards equality.
Depth
3.03%
Difference in evaluation between a short and long search.
Drama
0.04%
How much the winner was behind before their final victory.
Foulup Factor
20.83%
Moves that looked better than the best move after a short search.
Surprising turns
2.08%
Turns that looked bad after a short search, but good after a long one.
Last lead change
70.83%
Distance through game when the lead changed for the last time.
Decisiveness
27.08%
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
d1-d2,c5-d5,a4-b4,b2-b3
f1-f2,c3-c4,d5-d4
c2-c3,b2-c3,a4-b4
c2-d2,b2-d2,a4-b4
e2-e3,f6-f5,c6-d6
b3-b4,d2-d3,a2-a3
b3-b4,d2-c2,d3-c3
a4-a3,c5-d5,e4-d5
c4-c3,c1-d1,b3-b4
e4-e3,b6-b5,c6-b5
a6-b6,d2-c2,d3-d4
c6-d6,b6-d6,e4-e3
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
5
1
36
1308
27068
530601
7329780
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 5.
Puzzles
Puzzle
Solution
Black to win in 21 moves
Black to win in 17 moves
Black to win in 17 moves
White to win in 13 moves
White to win in 15 moves
White to win in 11 moves
Black to win in 9 moves
White to win in 9 moves
White to win in 15 moves
Black to win in 5 moves
White to win in 13 moves
White to win in 5 moves
Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.
