Generated at 10/01/2021, 21:58 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!
Equipment
A sufficient number of hexagonal tiles in two colours - 20 per side should be sufficient.
Play
On the first turn, play a hexagon of your colour.
On each subsequent turn, play two hexagon according to the following rules:
Place a pieces so it shares at least one edge with an existing hexagon
Perform all necessary hops.
Hopping
After placing a hexagon, if there is a line of pieces to one side of it and no piece on the other side, the farthest piece in line jumps to the empty space.Note that a move can produce up to three hops, each in a different direction,/p>
Example. A player places a piece at B. There is an empty space to the right, and a row of pieces marked a to the left:
. . . a a a a B .
The leftmost piece in the line is moved to the empty space:
. . . . a a a B a
Goal
Make a line of 5 to win. If the moving player simultaneously makes lines for themselves and the opponent, the moving player is the winner.
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
10775.12 (92.81µs/playout)
Reference Size
324559.41 (3.08µs/playout)
Ratio (low is good)
30.12
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
12,253
252
805,131
16,119
66
28
search.UCB
12,465
494
18
5
search.UCT
12,497
446
18
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 %
50.80±3.10
Includes draws = 50%
2: Black win %
49.20±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
359
990
0.6069 <= 0.6374 <= 0.6667
47.27
0.00
52.73
61.84
8
UCT (its=121)
631
0
117
748
0.8158 <= 0.8436 <= 0.8679
50.94
0.00
49.06
35.41
9
UCT (its=328)
631
0
290
921
0.6544 <= 0.6851 <= 0.7143
46.91
0.00
53.09
23.46
10
UCT (its=890)
631
0
272
903
0.6681 <= 0.6988 <= 0.7278
50.61
0.00
49.39
20.02
11
UCT (its=2421)
631
0
188
819
0.7404 <= 0.7705 <= 0.7980
47.25
0.00
52.75
16.37
12
UCT (its=2421)
485
0
515
1000
0.4541 <= 0.4850 <= 0.5160
50.90
0.00
49.10
15.09
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
16.72
Branching factor
24.30
Complexity
10^22.35
Based on game length and branching factor
Computational Complexity
10^5.87
Sample quality (100 best): 30.99
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
331
Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
40
A good move is selected by the AI more than the average
Bad moves
291
A bad move is selected by the AI less than the average
Terrible moves
54
A terrible move is never selected by the AI Terrible moves: b10,b18,r14,s1,b21,b20,j21,j20,c9,t1,t2,t3,a11,a13,a12,a14,a16,a19,a18,d8,u1,u2,u3,a20,u4,u6,a21,u8,u9,i21,e7,f6,p16,h5,i3,j2,n18,f21,k1,l1,l2,m19,u11,u10,n1,t12,o1,d21,l20,s13,q1,c21,k21,r1
Response distance
2.81
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 4.35% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
16.72
Mode
[16]
Median
16.0
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 37% of the game turns. Ai Ai found 2 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
60.36
69.69
51.03
Mean no. of effective moves
9.88
10.75
9.00
Effective game space
10^13.34
10^7.02
10^6.32
Mean % of good moves
49.47
50.68
48.26
Mean no. of good moves
9.75
8.50
11.00
Good move game space
10^10.29
10^4.59
10^5.70
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
100.00%
A hot turn is one where making a move is better than doing nothing.
Momentum
37.50%
% of turns where a player improved their score.
Correction
37.50%
% of turns where the score headed back towards equality.
Depth
3.45%
Difference in evaluation between a short and long search.
Drama
0.00%
How much the winner was behind before their final victory.
Foulup Factor
50.00%
Moves that looked better than the best move after a short search.
Surprising turns
0.00%
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
12.50%
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
l10,k11,l11,n10,p8
j11,h12,i12,i13,i15
j11,i12,j13,l13,i14
j12,k11,m10,i12,h13
j12,k11,i12,m10,h13
l10,n8,m10,o8,n8
k10,j10,i12,h14
k10,l10,m9,k8
k10,k11,l10,k11
l10,m8,m6,k10
l10,k10,n9,i10
l10,k10,i10,n9
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
6
1
6
54
564
6912
112038
1730574
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 6.
Puzzles
Puzzle
Solution
White to win in 2 moves
Black to win in 2 moves
White to win in 2 moves
Black to win in 2 moves
White to win in 2 moves
Black to win in 2 moves
White to win in 2 moves
Black to win in 2 moves
White to win in 2 moves
White to win in 2 moves
White to win in 2 moves
White to win in 2 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
