Full Report for King's Colour by Christian Freeling
Full Report for King's Colour by Christian Freeling
Generated at 26/07/2021, 15:28 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!
Movement
The king is confined to his 3x3 castle. He can move one step in any cardinal direction, one step diagonally, or one step using the knight's move (which is from a sharp corner to an opposite side).
The rook moves any unobstructed distance in any cardinal direction, unhindered by cells of the walls.
The bishop moves any unobstructed distance in any diagonal direction, unhindered by cells of the walls. It always is bound to the checkered sub-grid it moves on.
The queen moves any unobstructed distance in any cardinal or diagonal direction, unhindered by cells of the walls. A piece becomes a queen the very moment it ends its move inside the opponent's castle.
Check and capture
White moves first, after which turns alternate. Pieces may give check from any distance. However, mutual capture between pieces is restricted to a specific situation. In all other situations pieces simply block each other.
The right to mutual capture exists, and only exists, between an attacking piece on the opponent's wall and a defending piece inside the castle.
The rest is all chess, really. The king must evade check by moving or interposing a piece or capturing the attacking piece, whatever is possible or applicable. But there is one rule left, one that defines the game. The board is checkered in three differen shades, the sub-grids that the bishops are bound to. You will notice in the diagram that the king and the rooks are on the same sub-grid. That is not accidentally so.
The great switcheroo
Queens are permanent but unpromoted pieces that are on the same sub-grid as the king are always rooks, all other unpromoted pieces are always bishops. If the king moves to a different sub-grid, all rooks instantly become bishops and the bishops that were on the sub-grid that the king has moved to, now are rooks. If a rook moves to a different sub-grid it instantly becomes a bishop. The great switcheroo!
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
262.18 (3814.18µs/playout)
Reference Size
318238.23 (3.14µs/playout)
Ratio (low is good)
1213.82
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
249
17
13,557
775
55
26
search.UCT
242
57
36
18
search.AlphaBeta
5,545
573
7
1
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.
Heuristic Values
This chart shows the heuristic values thoughout a single representative* game. The orange line shows the difference between player scores. (* Representative, in the sense that it is close to the mean game length.)
Win % By Player (Bias)
1: White win %
57.90±3.08
Includes draws = 50%
2: Black win %
42.10±3.02
Includes draws = 50%
Draw %
6.20
Percentage of games where all players draw.
Decisive %
93.80
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)
521
220
194
935
0.6442 <= 0.6749 <= 0.7041
37.86
23.53
38.61
48.40
6
UCT (its=7)
538
92
370
1000
0.5532 <= 0.5840 <= 0.6142
45.60
9.20
45.20
42.06
7
UCT (its=7)
472
61
467
1000
0.4716 <= 0.5025 <= 0.5334
49.80
6.10
44.10
40.79
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
23.83
Branching factor
70.37
Complexity
10^39.71
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
Distinct actions
7732
Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
144
A 'killer' move is selected by the AI more than 50% of the time Too many killers to list.
Good moves
1758
A good move is selected by the AI more than the average
Bad moves
5936
A bad move is selected by the AI less than the average
Terrible moves
5323
A terrible move is never selected by the AI Too many terrible moves to list.
Response distance
1.95
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 19.32% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
23.83
Mode
[13]
Median
19.0
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 50% of the game turns. Ai Ai found 0 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
63.45
83.26
43.65
Mean no. of effective moves
44.04
57.08
31.00
Effective game space
10^34.15
10^18.87
10^15.28
Mean % of good moves
45.28
57.18
33.38
Mean no. of good moves
33.21
41.67
24.75
Good move game space
10^29.78
10^17.13
10^12.65
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
50.00%
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
20.83%
% of turns where the score headed back towards equality.
Depth
16.91%
Difference in evaluation between a short and long search.
Drama
2.91%
How much the winner was behind before their final victory.
Foulup Factor
75.00%
Moves that looked better than the best move after a short search.
Surprising turns
37.50%
Turns that looked bad after a short search, but good after a long one.
Last lead change
83.33%
Distance through game when the lead changed for the last time.
Decisiveness
16.67%
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.)
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
1
84
6986
595394
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 3.
Puzzles
Puzzle
Solution
White to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
White to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Black to win in 3 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
