Nice connection game with some non-obvious strategy. The board as presented seems a bit small for a connection game, even with the stacking; I'm not sure the swap rule is sufficient to find balance.
hiimjosh
8
I really like this! You are playing a game of Y except that there is a capturing element related to stacking. Very elegant idea which adds significant tension to your typical connection game. I particularly like how every capture is a tradeoff: do I give up my position now to take that stronger position? You are almost forced to do so because your opponent will likely capture you if you don't, and being down a piece is a huge disadvantage. This creates a richer second layer game where you are playing chicken around the board until you inevitably have to start making trades. Great!
Zargasheth
7
WickedVegan
8
schwarzspecht
8
Kolomogorov Complexity Analysis
Size (bytes)
28103
Reference Size
10915
Ratio
2.57
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
43044.63 (23.23µs/playout)
Reference Size
512925.73 (1.95µs/playout)
Ratio (low is good)
11.92
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
82495710
State Space Complexity bounds
63587421 < 82495710 < ∞
State Space Complexity (log 10)
7.92
State Space Complexity bounds (log 10)
7.80 <= 7.92 <= ∞
Samples
1113565
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
44,438
144
2,726,545
7,250
61
16
search.UCT
44,302
521
80
20
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 win %
51.20±3.10
Includes draws = 50%
2: Player 1 win %
48.80±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
340
971
0.6193 <= 0.6498 <= 0.6792
51.18
0.00
48.82
59.72
4
UCT (its=5)
631
0
336
967
0.6220 <= 0.6525 <= 0.6819
50.36
0.00
49.64
59.68
9
UCT (its=10)
631
0
356
987
0.6089 <= 0.6393 <= 0.6687
45.90
0.00
54.10
63.78
17
UCT (its=18)
631
0
336
967
0.6220 <= 0.6525 <= 0.6819
49.74
0.00
50.26
66.50
22
UCT (its=23)
631
0
367
998
0.6019 <= 0.6323 <= 0.6616
48.70
0.00
51.30
65.83
33
UCT (its=34)
631
0
369
1000
0.6006 <= 0.6310 <= 0.6604
49.10
0.00
50.90
63.90
36
UCT (its=98)
631
0
135
766
0.7952 <= 0.8238 <= 0.8491
49.09
0.00
50.91
57.10
37
UCT (its=266)
631
0
166
797
0.7622 <= 0.7917 <= 0.8185
47.68
0.00
52.32
58.08
38
UCT (its=723)
631
0
216
847
0.7146 <= 0.7450 <= 0.7732
44.98
0.00
55.02
58.08
39
UCT (its=1966)
631
0
171
802
0.7571 <= 0.7868 <= 0.8137
45.14
0.00
54.86
61.10
40
UCT (its=5343)
443
0
140
583
0.7236 <= 0.7599 <= 0.7928
45.45
0.00
54.55
66.05
41
UCT (its=5343)
518
0
482
1000
0.4870 <= 0.5180 <= 0.5488
42.80
0.00
57.20
71.48
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
83.24
Branching factor
22.41
Complexity
10^108.90
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
36
Quantity of distinct board cells
Distinct actions
206
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
1
A 'killer' move is selected by the AI more than 50% of the time Killers: Choose Blue
Good moves
180
A good move is selected by the AI more than the average
Bad moves
26
A bad move is selected by the AI less than the average
Response distance%
31.18%
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 88.59% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
83.24
Mode
[79]
Median
82.0
Change in Material Per Turn
Mean change in material/round
0.36
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 4% 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
35.24
31.91
38.49
Mean no. of effective moves
8.34
7.98
8.69
Effective game space
10^61.70
10^30.04
10^31.67
Mean % of good moves
36.35
71.69
1.85
Mean no. of good moves
8.90
17.80
0.21
Good move game space
10^47.42
10^46.25
10^1.18
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
54.22%
A hot turn is one where making a move is better than doing nothing.
Momentum
24.10%
% of turns where a player improved their score.
Correction
38.55%
% of turns where the score headed back towards equality.
Depth
2.27%
Difference in evaluation between a short and long search.
Drama
0.05%
How much the winner was behind before their final victory.
Foulup Factor
16.87%
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
24.10%
Distance through game when the lead changed for the last time.
Decisiveness
10.84%
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
b2,Choose Blue,a2,a6
d2,Choose Blue,a3,c1
b5,Choose Blue,g2,d1
b1,Choose Blue,b6,a3
c1,Choose Yellow,b4,e2
c2,Choose Yellow,c6,c1
f2,Choose Blue,e1,c3
a3,Choose Blue,b6,b1
c3,Choose Blue,e1,f2
b4,Choose Yellow,d5,b7
e4,Choose Yellow,a5,c6
b1,Choose Yellow,d1
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
36
72
1332
22788
378738
4212918
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
Player 2(Yellow) to win in 34 moves
Player 1(Yellow) to win in 28 moves
Player 2(Yellow) to win in 18 moves
Player 1(Blue) to win in 18 moves
Player 1(Blue) to win in 18 moves
Player 1(Blue) to win in 26 moves
Player 1(Blue) to win in 22 moves
Player 2(Yellow) to win in 16 moves
Player 1(Yellow) to win in 12 moves
Player 1(Blue) to win in 14 moves
Player 2(Yellow) to win in 12 moves
Player 2(Yellow) to win in 10 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
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