Xerz is a two-player abstract strategy game, in which players move pawns in order to trap a pawn. The twist is, players share all the pawns, so trying to trap a pawn willy-nilly can backfire!
Generated at 2023-06-25, 02:40 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!
How to Win
The last player to complete a turn wins. In other words, you win if you move a pawn so that your opponent wouldn’t be able to move the pawn to an empty space (you win before they get the next turn).
Play
Starting with White, players take alternate turns.
On your turn, build a pillar, and then move the pawn of the active color to an empty space. The color of that space is the next active color (= the color of the pawn your opponent must move on the next turn).
Building a Pillar
At the beginning of your turn, the space the active pawn is on becomes a pillar. This pillar is of your color (white or black) with a symbol of the active color (blue, green, violet, or red).
Once placed on the board, pillars can never be moved or removed.
Moving a Pawn
On your turn, after placing a pillar, you must move the pawn of the active color, following the these rules:
A pawn moves in one straight line (orthogonally or diagonally), just like a queen in Chess.
It can only move through empty spaces.
It can only stop on an empty space or a space with a sunken pillar.
It can’t stop on a like-colored space, even if it’s empty. E.g. the blue pawn can’t stop on a blue space.
Interesting abstract that reminds me of a mix between LYNGK and Kamisado. You are trying to be the last player with a move. You create passages which only you can move pieces through. The game uses colored spaces which you move pieces to to determine which piece your opponent must move. It's weird. The rulebook is a mess, but it was fun. Would play again. Label: Good But Not Great
onoborisan
9
Early game strategy is unclear, but I love that it's non-loopy.
Kolomogorov Complexity Analysis
Size (bytes)
17247
Reference Size
10673
Ratio
1.62
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
51160.84 (19.55µs/playout)
Reference Size
576535.02 (1.73µs/playout)
Ratio (low is good)
11.27
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
66560091
State Space Complexity bounds
63919838 < 66560091 < ∞
State Space Complexity (log 10)
7.82
State Space Complexity bounds (log 10)
7.81 <= 7.82 <= ∞
Samples
1931866
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
51,687
199
1,936,882
7,116
37
8
search.UCT
53,008
1,946
40
8
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
1
UCT (its=2)
631
0
323
954
0.6308 <= 0.6614 <= 0.6908
49.69
0.00
50.31
37.18
5
UCT (its=6)
631
0
361
992
0.6057 <= 0.6361 <= 0.6655
53.53
0.00
46.47
37.20
13
UCT (its=14)
631
0
366
997
0.6025 <= 0.6329 <= 0.6623
50.55
0.00
49.45
36.44
17
UCT (its=46)
631
0
195
826
0.7338 <= 0.7639 <= 0.7916
52.30
0.00
47.70
34.91
18
UCT (its=126)
631
0
265
896
0.6735 <= 0.7042 <= 0.7332
45.65
0.00
54.35
35.09
19
UCT (its=341)
631
0
285
916
0.6581 <= 0.6889 <= 0.7180
49.89
0.00
50.11
34.83
20
UCT (its=928)
631
0
299
930
0.6478 <= 0.6785 <= 0.7077
50.11
0.00
49.89
35.55
21
UCT (its=2523)
631
0
253
884
0.6831 <= 0.7138 <= 0.7426
52.38
0.00
47.62
35.99
22
UCT (its=6858)
631
0
262
893
0.6759 <= 0.7066 <= 0.7355
52.41
0.00
47.59
36.73
23
UCT (its=6858)
510
0
490
1000
0.4790 <= 0.5100 <= 0.5409
48.40
0.00
51.60
37.78
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
40.40
Branching factor
13.33
Complexity
10^40.06
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
64
Quantity of distinct board cells
Distinct actions
136245
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
6054
A 'killer' move is selected by the AI more than 50% of the time Too many killers to list.
Good moves
12893
A good move is selected by the AI more than the average
Bad moves
123194
A bad move is selected by the AI less than the average
Terrible moves
121883
A terrible move is never selected by the AI Too many terrible moves to list.
Response distance%
50.90%
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 69.38% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
40.40
Mode
[44]
Median
42.0
Change in Material Per Turn
Mean change in material/round
0.38
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 52% of the game turns. Ai Ai found 11 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
73.27
81.55
64.99
Mean no. of effective moves
9.88
11.70
8.05
Effective game space
10^33.12
10^19.44
10^13.67
Mean % of good moves
16.46
13.95
18.96
Mean no. of good moves
1.57
1.95
1.20
Good move game space
10^6.82
10^4.18
10^2.64
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
72.50%
A hot turn is one where making a move is better than doing nothing.
Momentum
27.50%
% of turns where a player improved their score.
Correction
40.00%
% of turns where the score headed back towards equality.
Depth
2.66%
Difference in evaluation between a short and long search.
Drama
0.42%
How much the winner was behind before their final victory.
Foulup Factor
35.00%
Moves that looked better than the best move after a short search.
Surprising turns
5.00%
Turns that looked bad after a short search, but good after a long one.
Last lead change
72.50%
Distance through game when the lead changed for the last time.
Decisiveness
25.00%
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
f1-f7,h6-h4,c8-e8,a3-h3,h4-e4
f1-f7,h6-h4,c8-e8,a3-h3
f1-h1,h6-c6,a3-e3,h1-h5
f1-c4,a3-c1,c4-g8
f1-c4,a3-a1,c4-e4
f1-b5,h6-h8,c8-a8
f1-b5,h6-d2,c8-c5
f1-b5,h6-e6,a3-c5
f1-f3,h6-d2,c8-f5
f1-f3,h6-c1,f3-b3
f1-f4,c8-f5,h6-a6
f1-f5,h6-c1,f5-h3
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
17
303
5728
105337
1944717
34002746
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)
96 solutions found at depth 5.
Puzzles
Puzzle
Solution
Black to win in 23 moves
White to win in 23 moves
Black to win in 21 moves
White to win in 23 moves
White to win in 19 moves
White to win in 21 moves
White to win in 19 moves
White to win in 21 moves
White to win in 19 moves
Black to win in 19 moves
White to win in 17 moves
Black to win in 13 moves
Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.
