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
8414.40 (118.84µs/playout)
Reference Size
1808645.32 (0.55µs/playout)
Ratio (low is good)
214.95
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
9,845
196
889,654
17,647
90
7
search.UCT
172,752
4,740
63
11
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 (Cross) win %
67.21±2.99
Includes draws = 50%
2: Player 2 (Parallel) win %
32.79±2.86
Includes draws = 50%
Draw %
0.00
Percentage of games where all players draw.
Decisive %
100.00
Percentage of games with a single winner.
Samples
988
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
238
869
0.6955 <= 0.7261 <= 0.7547
58.00
0.00
42.00
90.64
6
UCT (its=7)
631
0
363
994
0.6044 <= 0.6348 <= 0.6642
59.36
0.00
40.64
91.31
12
UCT (its=13)
631
0
333
964
0.6240 <= 0.6546 <= 0.6839
57.78
0.00
42.22
90.51
19
UCT (its=20)
631
0
349
980
0.6134 <= 0.6439 <= 0.6732
58.47
0.00
41.53
89.46
29
UCT (its=30)
631
0
295
926
0.6507 <= 0.6814 <= 0.7106
57.88
0.00
42.12
87.99
41
UCT (its=42)
631
0
366
997
0.6025 <= 0.6329 <= 0.6623
57.17
0.00
42.83
86.98
58
UCT (its=59)
631
0
336
967
0.6220 <= 0.6525 <= 0.6819
57.39
0.00
42.61
85.90
80
UCT (its=81)
631
0
364
995
0.6038 <= 0.6342 <= 0.6635
59.60
0.00
40.40
84.13
114
UCT (its=115)
631
0
350
981
0.6127 <= 0.6432 <= 0.6726
60.96
0.00
39.04
82.79
131
UCT (its=132)
525
0
475
1000
0.4940 <= 0.5250 <= 0.5558
62.50
0.00
37.50
81.94
132
UCT (its=132)
522
0
478
1000
0.4910 <= 0.5220 <= 0.5528
61.40
0.00
38.60
81.46
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
63.69
Branching factor
47.92
Complexity
10^104.19
Based on game length and branching factor
Computational Complexity
10^7.14
Sample quality (100 best): 11.44
Samples
988
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
199
Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
115
A good move is selected by the AI more than the average
Bad moves
84
A bad move is selected by the AI less than the average
Terrible moves
1
A terrible move is never selected by the AI Terrible moves: Swap
Response distance
4.67
Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples
988
Quantity of logged games played
Board Coverage
A mean of 64.33% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
63.69
Mode
[63]
Median
63.0
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 14% 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
28.06
30.69
25.42
Mean no. of effective moves
14.52
16.06
12.97
Effective game space
10^52.46
10^27.40
10^25.06
Mean % of good moves
29.38
43.65
15.12
Mean no. of good moves
14.20
24.25
4.16
Good move game space
10^35.37
10^27.92
10^7.45
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
93.75%
A hot turn is one where making a move is better than doing nothing.
Momentum
25.00%
% of turns where a player improved their score.
Correction
48.44%
% of turns where the score headed back towards equality.
Depth
2.35%
Difference in evaluation between a short and long search.
Drama
3.79%
How much the winner was behind before their final victory.
Foulup Factor
20.31%
Moves that looked better than the best move after a short search.
Surprising turns
4.69%
Turns that looked bad after a short search, but good after a long one.
Last lead change
75.00%
Distance through game when the lead changed for the last time.
Decisiveness
4.69%
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.
Openings
Moves
Animation
White g6,White b2,Black b9
White b10,White i6,White g8
Black b3,Black i11,Black g10
Black f7,Black d3,Black c9
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
4
1
198
13464
314028
14540724
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 2 (Parallel) to win in 5 moves
Player 1 (Parallel) to win in 5 moves
Player 2 (Parallel) to win in 5 moves
Player 2 (Parallel) to win in 5 moves
Player 2 (Parallel) to win in 7 moves
Player 1 (Cross) to win in 3 moves
Player 1 (Cross) to win in 7 moves
Player 1 (Cross) to win in 7 moves
Player 2 (Parallel) to win in 7 moves
Player 1 (Cross) to win in 7 moves
Player 1 (Cross) to win in 3 moves
Player 1 (Cross) to win in 5 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
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