AlmaTafl is an abstract strategy game influenced by the Tafl family of games, where one player controls the invaders(Black) and one player controls the defenders (White and Red).
Generated at 2024-12-09, 04:38 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!
Special Spaces
Throne
The central space is the throne, where the king starts. Only the king can occupy the throne (unless the invaders can capture the king there).
Escape space
The marked spaces at the edge of the board are escape spaces; only the king can land there, and will win by doing so.
Stacking
Pieces can stack, to a maximum height of 3.
Only the top piece in a stack may move.
If the king(red) or all defending pieces(white) are covered, the attackers win.
Moving
On your turn, make one move with an active piece of your colour. A piece moves:
In a straight line,
A distance equal to its height,
Ignoring any obstacles between its start and end spaces,
Landing on top of any pieces in the destination space.
Restrictions:
A piece may not move so as to make a stack higher than three
Only the king (red) can move to an escape space
Only the king (red) can move to the throne. Exception: an invading piece (black) may move to the throne to cover the king(red), thereby winning the game
Bouncing
After the king moves, it may make a follow-on move so long as each move ends on an invading(black) piece.
Goal
The invading player (black pieces) wins if they cover the king (red), or all defenders (white)
The defending player (white/red pieces) wins if the king (red) reaches one of the escape spaces at the edge of the board.
Advanced Game
The defending player only wins if the king is in an escape space at the start of their turn.
Seems like a good game. With bounce moves and stacking, it has come a long way from its Tafl roots; you need a completely different set of strategies to win.
raphaell7
9
schwarzspecht
8
JamieRufe
8
Rating: Enthusiastic Impressions after first play I really enjoyed my first play! First of all, I love the asymmetry between the two players. I played as the King in this game and it was so much bouncing the King around the board. It was especially fun to win this game off of a king bounce! I think Almatafl is the type of abstract design that modern board gamers would really enjoy.
anastasiou1987
10
alekerickson
8
thenexusgame
8
hiimjosh
8
Super fun abstract. I already liked Tafl style games, and this amps it up quite a lot. The hex board is nice, but it's really the addition of stacking that makes this cool. The king bounce is the final cherry on it all. Fantastic.
nestorgames
8
Looks interesting.
Kolomogorov Complexity Analysis
Size (bytes)
32051
Reference Size
10915
Ratio
2.94
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
10166.73 (98.36µs/playout)
Reference Size
504641.18 (1.98µs/playout)
Ratio (low is good)
49.64
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
Samples
1608001
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
11,803
93
1,435,106
7,149
122
83
search.UCT
10,879
13,573
26
14
search.AlphaBeta
197,750
55,875
49
49
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: Invaders win %
15.40±2.10
Includes draws = 50%
2: Defenders win %
84.60±2.37
Includes draws = 50%
Draw %
5.40
Percentage of games where all players draw.
Decisive %
94.60
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
339
970
0.6200 <= 0.6505 <= 0.6799
62.47
0.00
37.53
99.94
44
UCT (its=45)
631
0
319
950
0.6336 <= 0.6642 <= 0.6935
49.05
0.00
50.95
81.14
45
UCT (its=46)
305
0
302
607
0.4628 <= 0.5025 <= 0.5421
39.37
0.00
60.63
70.82
46
UCT (its=46)
504
0
496
1000
0.4731 <= 0.5040 <= 0.5349
38.00
0.00
62.00
69.10
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
76.82
Branching factor
62.53
Complexity
10^126.87
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
73
Quantity of distinct board cells
Distinct actions
835
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
53
A 'killer' move is selected by the AI more than 50% of the time Too many killers to list.
Good moves
475
A good move is selected by the AI more than the average
Bad moves
360
A bad move is selected by the AI less than the average
Terrible moves
9
A terrible move is never selected by the AI Terrible moves: g2-j2,c5-f2,f9-f6,g9-j6,i7-f10,e10-h7,f3-f6,e10-b10,i3-f6
Response distance%
27.21%
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 56.05% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
76.82
Mode
[500]
Median
44.0
Change in Material Per Turn
Mean change in material/round
-0.19
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 first player never had the advantage. The lead changed on 0% of the game turns. Ai Ai found 3 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
95.13
99.69
91.53
Mean no. of effective moves
48.35
77.79
25.07
Effective game space
10^116.41
10^64.19
10^52.21
Mean % of good moves
63.38
24.35
94.23
Mean no. of good moves
21.78
17.18
25.42
Good move game space
10^74.73
10^21.63
10^53.10
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
40.26%
A hot turn is one where making a move is better than doing nothing.
Momentum
14.29%
% of turns where a player improved their score.
Correction
57.14%
% of turns where the score headed back towards equality.
Depth
2.99%
Difference in evaluation between a short and long search.
Drama
0.00%
How much the winner was behind before their final victory.
Foulup Factor
96.10%
Moves that looked better than the best move after a short search.
Surprising turns
2.60%
Turns that looked bad after a short search, but good after a long one.
Last lead change
-1.30%
Distance through game when the lead changed for the last time.
Decisiveness
6.49%
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
4
5
1
90
6570
298314
8159633
13751066
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)
3932 solutions found at depth 5.
Puzzles
Puzzle
Solution
Defenders to win in 4 moves
Defenders to win in 5 moves
Defenders to win in 6 moves
Defenders to win in 5 moves
Defenders to win in 5 moves
Defenders to win in 4 moves
Defenders to win in 4 moves
Defenders to win in 4 moves
Defenders to win in 3 moves
Defenders to win in 3 moves
Defenders to win in 4 moves
Defenders to win in 4 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
