Generated at 2024-08-25, 10:24 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!
The first player places 1 stone at their discretion on the empty board.
The second player places 2 stones according to a protocol in 2 moves: 1 Drop 1 Free. Drop move: the player places their stone in place of an opponent's stone, moving that opponent's stone to a free adjacent square that is diagonally or orthogonally adjacent. Free move: the player then places their own stone in a free square that has no stones adjacent diagonally or orthogonally.
Players take turns placing their 2 stones according to the 1Drop - 1Free protocol on the board until it is no longer possible to place Free moves. At that point, players proceed only with Drop moves.
When placement possibilities are exhausted, the groups sizes for each player are counted. The player with the largest group wins, in the event of a tie, the size of the second largest group is counted and so on.
'Groups' refer to a single stone or a set of stones of the same color adjacent orthogonally.
Interesting biggest group game. Loses a few points because I've seen all the elements before so feels more like a remix than a new game.
RichardIngram
7
Kolomogorov Complexity Analysis
Size (bytes)
27566
Reference Size
10915
Ratio
2,53
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
10316,11 (96,94µs/playout)
Reference Size
589900,90 (1,70µs/playout)
Ratio (low is good)
57,18
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
327882429
State Space Complexity bounds
98094292 < 327882429 < ∞
State Space Complexity (log 10)
8,52
State Space Complexity bounds (log 10)
7,99 <= 8,52 <= ∞
Samples
642453
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
11.702
49
1.169.932
4.911
100
0
search.UCT
NaN
NaN
0
0
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 %
51,60±3,10
Includes draws = 50%
2: Black win %
48,40±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
1
UCT (its=2)
631
0
324
955
0,6301 <= 0,6607 <= 0,6901
52,46
0,00
47,54
99,99
4
UCT (its=5)
631
0
360
991
0,6063 <= 0,6367 <= 0,6661
47,73
0,00
52,27
99,97
14
UCT (its=15)
631
0
369
1000
0,6006 <= 0,6310 <= 0,6604
46,70
0,00
53,30
99,97
28
UCT (its=29)
631
0
363
994
0,6044 <= 0,6348 <= 0,6642
48,49
0,00
51,51
99,97
37
UCT (its=38)
544
0
456
1000
0,5130 <= 0,5440 <= 0,5746
48,60
0,00
51,40
99,97
38
UCT (its=38)
510
0
490
1000
0,4790 <= 0,5100 <= 0,5409
48,60
0,00
51,40
99,97
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
99,84
Branching factor
48,76
Complexity
10^157,07
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
100
Quantity of distinct board cells
Distinct actions
784
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
321
A good move is selected by the AI more than the average
Bad moves
463
A bad move is selected by the AI less than the average
Response distance%
45,61%
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 99,84% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
99,84
Mode
[100]
Median
100.0
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.)
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
100
784
61264
560346
39372746
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
White to win in 5 moves
Black to win in 5 moves
White to win in 5 moves
White to win in 6 moves
White to win in 5 moves
White to win in 5 moves
Black to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
Black to win in 7 moves
Black to win in 7 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
