Rosenkreuz (Rosy Cross in English) is an abstract strategy game for two players. It was designed based on Turkish checkers, also partially inspired from Oust by Mark Steere and Dameo by Christian Freeling.
Generated at 27/07/2021, 01:10 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
In this game, "adjacent" refers to adjacent in the orthogonal direction. Therefore, diagonals are not included in adjacencies.
A "group" is pieces of the same color that are adjacent to each other (any combination of symbols).
GAMEPLAY
The player with Rose symbol is the first to move, then alternate turns moving a piece with their own symbol.
All pieces move by "Step" or "Jump". Passing is not allowed.
Step:
All pieces can move toward adjacent empty squares in eight directions. However, it may only move sideways, straight backwards and diagonally backwards if its movement would allow it to capture an opponent's piece or pieces (may by any type of capturing).
Jump:
All pieces may jump over a friendly piece or an unbroken straight line of friendly pieces (any combination of colors) that is next to in any of eight directions and landing on the empty square immediately after. Any piece may never jump over opponent's pieces. Also, multiple jumps are not allowed. As with step, jump to the side, straight backward, and diagonally backward can only be made if the jump allows capture an opponent's piece or pieces (may by any type of capturing).
CAPTURING
There are three types of capturing: Major Capturing, Minor Capturing, and Attainment Capturing.
Major Capturing:
If your move results in a group that contains two type of symbols and in which the number of your symbols is greater than the number of opponent's symbols, then all opponent's pieces directly adjacent to your pieces in that group are captured and removed from the game.
Minor Capturing:
When an opponent's piece is on a square of the opposite color, you can capture it by moving your own piece of the same color as the square onto it and remove it from the game. This can be done either by Step or Jump (Thus, a piece can only be moved to a non-empty square when minor capturing is possible).
Attainment Capturing:
When one of your pieces arrives at the end of the row on the opponent's side, you can capture one opponent's piece (any color) of your choice and remove it from the game. The piece of yours that reaches the end is repositioned to any empty squares of the same color that is closest to your side (So if the four or five squares closest to your side are occupied by pieces, it is placed in one of the squares closest to the second).
SUICIDE MOVE
If your move causes the situation that a group contains two type of symbols and in which the number of your symbols is smaller than the number of opponent's symbols, then that move is considered a suicide move, and all your pieces adjacent to the opponent's in the group are captured by Major Capturing and removed from the game.
It is possible that after your piece captures an opponent's piece by Minor Capturing, then it is captured at the same time by Major Capturing as a suicide move.
If your piece is captured by your suicide move in the farthest row of the opponent's side, the piece cannot perform an Attainment Capturing.
GAME END
The player who removes all enemy pieces of either dark or light color wins the game immediately.
If a player cannot to move during the turn, the player loses the game.
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
1405.69 (711.40µs/playout)
Reference Size
434593.65 (2.30µs/playout)
Ratio (low is good)
309.17
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
1,583
16
128,700
1,370
81
19
search.UCT
1,572
80
61
10
search.AlphaBeta
40,050
6,658
66
14
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: Rose win %
52.80±3.10
Includes draws = 50%
2: Cross win %
47.20±3.08
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
294
925
0.6515 <= 0.6822 <= 0.7114
49.51
0.00
50.49
79.62
8
UCT (its=9)
630
1
350
981
0.6122 <= 0.6427 <= 0.6721
52.60
0.10
47.30
79.49
18
UCT (its=19)
631
0
304
935
0.6442 <= 0.6749 <= 0.7041
46.31
0.00
53.69
78.53
19
UCT (its=20)
440
1
429
870
0.4731 <= 0.5063 <= 0.5394
47.70
0.11
52.18
78.78
20
UCT (its=20)
509
0
491
1000
0.4780 <= 0.5090 <= 0.5399
44.70
0.00
55.30
77.89
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
64.09
Branching factor
21.21
Complexity
10^80.33
Based on game length and branching factor
Computational Complexity
10^7.01
Sample quality (100 best): 11.47
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
1052
Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
42
A 'killer' move is selected by the AI more than 50% of the time Killers: f4-b4,g6-a6,f4-c7,g4-d7,e2-a2,c7-f7,c7-a2,a5-c7,c7-b2,b7-a2,d7-g7,g1-a6,c4-g4,e3-c1,d1-e1,g3-g1,f3-b7,g3-e1,a4-d7,a4-d1,f1-b6,f1-e6,g1-f6,g3-a3,a4-a7,d5-f7,e7-d2,a1-d1,f7-e7,f7-e2,a3-a1,d5-d7,e7-b1,b1-a1,g7-g2,d3-f1,c3-c7,c1-b6,c1-c6,e3-g1,f5-d7,g5-g7
Good moves
693
A good move is selected by the AI more than the average
Bad moves
355
A bad move is selected by the AI less than the average
Terrible moves
106
A terrible move is never selected by the AI Too many terrible moves to list.
Response distance
2.43
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 92.94% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
64.09
Mode
[62]
Median
63.0
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 0% of the game turns. Ai Ai found 8 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
89.85
81.74
99.04
Mean no. of effective moves
20.20
18.44
22.20
Effective game space
10^77.94
10^38.44
10^39.50
Mean % of good moves
32.11
39.16
24.12
Mean no. of good moves
5.84
6.74
4.83
Good move game space
10^33.28
10^20.06
10^13.23
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
45.31%
A hot turn is one where making a move is better than doing nothing.
Momentum
7.81%
% of turns where a player improved their score.
Correction
9.38%
% of turns where the score headed back towards equality.
Depth
1.61%
Difference in evaluation between a short and long search.
Drama
0.13%
How much the winner was behind before their final victory.
Foulup Factor
57.81%
Moves that looked better than the best move after a short search.
Surprising turns
1.56%
Turns that looked bad after a short search, but good after a long one.
Last lead change
-1.56%
Distance through game when the lead changed for the last time.
Decisiveness
9.38%
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
a1-a3,a6-b5,b1-d3
b1-d3,a6-b5,a1-a3
c1-c3,b6-c5,g2-g3
d1-f3,b6-a5,d2-e3
a2-a3,e6-e5,c2-c3
b2-a3,e7-e5,a3-b4
d2-e3,b6-a5,d1-f3
e2-f3,c7-e5,b2-a3
f2-f3,e7-c5,g2-g3
a1-a3,d7-b5,f2-g3
e1-e3,b7-b5,g2-g3
e1-g3,d6-e5,d2-c3
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
36
1332
28296
583699
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
Rose to win in 20 moves
Rose to win in 6 moves
Cross to win in 8 moves
Cross to win in 6 moves
Cross to win in 6 moves
Rose to win in 6 moves
Rose to win in 6 moves
Rose to win in 6 moves
Rose to win in 4 moves
Rose to win in 4 moves
Rose to win in 4 moves
Cross to win in 4 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
