Generated at 6/14/23, 6:04 PM 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!
Definitions
A stack is a set of one or more pieces piled onto each other on the same point. The color of a stack is the color of its topmost piece, which denotes its owner. A stack's height is the number of pieces in it.
A crosscut is a 2x2 set of pieces consisting of two diagonally adjacent black pieces and two diagonally adjacent white pieces.
Two like-colored stacks are considered connected in the following cases:
They are orthogonally or diagonally adjacent to each other and not part of the same crosscut.
They are both part of the same crosscut and higher than the lower enemy stack in it.
They are both part of the same crosscut, the lower of them is the same height as the lower enemy stack in the crosscut and the higher of them is higher than the higher enemy stack in the crosscut.
Play
Black plays first, then turns alternate. On your turn, you must perform exactly one of the following actions:
Place a piece of your color on an empty point.
Move the topmost piece of a stack of your color onto an orthogonally adjacent enemy stack, provided that, before the move, the heights of both stacks are the same. Then, place a piece of your opponent's color onto the stack from which you just moved your piece.
If, at the start of a player's turn, there's a chain of connected stacks of their color touching the two opposite board edges of their color, that player wins. Failing that, a player loses if they have no moves available on their turn, in which case the opponent will necessarily have a winning chain of the type just described. Draws are not possible.
It's clever, it works, but I find it totally opaque; even with the new rules.
Kolomogorov Complexity Analysis
Size (bytes)
28478
Reference Size
10673
Ratio
2.67
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 second
47423.26 (21.09µs/playout)
Reference Size
2816901.41 (0.35µs/playout)
Ratio (low is good)
59.40
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
692171493
State Space Complexity bounds
51994887 < 692171493 < ∞
State Space Complexity (log 10)
8.84
State Space Complexity bounds (log 10)
7.72 <= 8.84 <= ∞
Samples
771560
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
39,980
757
1,812,475
33,980
45
11
search.UCT
40,773
5,126
46
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: White win %
42.30±3.03
Includes draws = 50%
2: Black win %
57.70±3.09
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
2
UCT (its=3)
631
0
322
953
0.6315 <= 0.6621 <= 0.6914
46.59
0.00
53.41
43.73
7
UCT (its=8)
631
0
360
991
0.6063 <= 0.6367 <= 0.6661
46.92
0.00
53.08
44.97
15
UCT (its=16)
631
0
360
991
0.6063 <= 0.6367 <= 0.6661
47.12
0.00
52.88
47.83
26
UCT (its=27)
631
0
354
985
0.6102 <= 0.6406 <= 0.6700
48.73
0.00
51.27
51.58
36
UCT (its=37)
631
0
353
984
0.6108 <= 0.6413 <= 0.6706
49.09
0.00
50.91
51.50
48
UCT (its=49)
631
0
366
997
0.6025 <= 0.6329 <= 0.6623
51.35
0.00
48.65
50.40
49
UCT (its=133)
631
0
144
775
0.7853 <= 0.8142 <= 0.8400
50.45
0.00
49.55
40.91
50
UCT (its=362)
631
0
194
825
0.7347 <= 0.7648 <= 0.7925
46.79
0.00
53.21
37.87
51
UCT (its=984)
631
0
218
849
0.7128 <= 0.7432 <= 0.7715
47.11
0.00
52.89
35.82
52
UCT (its=2675)
631
0
254
885
0.6823 <= 0.7130 <= 0.7418
43.84
0.00
56.16
36.06
53
UCT (its=7272)
468
0
162
630
0.7073 <= 0.7429 <= 0.7754
45.24
0.00
54.76
39.46
54
UCT (its=7272)
515
0
485
1000
0.4840 <= 0.5150 <= 0.5459
41.50
0.00
58.50
42.62
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
52.02
Branching factor
35.17
Complexity
10^79.11
Based on game length and branching factor
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
49
Quantity of distinct board cells
Distinct actions
217
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
185
A good move is selected by the AI more than the average
Bad moves
32
A bad move is selected by the AI less than the average
Response distance%
37.82%
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 69.09% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
52.02
Mode
[42, 50]
Median
51.0
Change in Material Per Turn
Mean change in material/round
0.67
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.)
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 19% of the game turns. Ai Ai found 11 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
23.78
33.09
14.48
Mean no. of effective moves
7.69
10.27
5.12
Effective game space
10^34.71
10^21.21
10^13.51
Mean % of good moves
10.90
14.17
7.64
Mean no. of good moves
3.56
4.00
3.12
Good move game space
10^15.39
10^9.04
10^6.35
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
92.31%
A hot turn is one where making a move is better than doing nothing.
Momentum
17.31%
% of turns where a player improved their score.
Correction
42.31%
% of turns where the score headed back towards equality.
Depth
2.81%
Difference in evaluation between a short and long search.
Drama
2.32%
How much the winner was behind before their final victory.
Foulup Factor
32.69%
Moves that looked better than the best move after a short search.
Surprising turns
1.92%
Turns that looked bad after a short search, but good after a long one.
Last lead change
92.31%
Distance through game when the lead changed for the last time.
Decisiveness
9.62%
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
d6,f2,f3
a5,c5,f4
d6,a3,g1
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
49
2401
57841
1344461
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
Black to win in 18 moves
White to win in 12 moves
White to win in 10 moves
Black to win in 12 moves
White to win in 10 moves
White to win in 14 moves
White to win in 12 moves
Black to win in 12 moves
Black to win in 8 moves
Black to win in 12 moves
White to win in 6 moves
Black to win in 8 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
