Sayū is an abstract strategy tile-laying, tile-flipping for two players. It is played with 49 unique two-sided octagonal wooden tiles and uses no board. The objective of the game is to have more tile of your color face up when all the tiles are placed.
Generated at 2023-06-19, 07:42 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!
Setup
Place the home tile at the center of the table. This tile has no arrows. From now on no tiles can be placed further than 3 spaces away from this tile (this creates a 7 by 7 grid when finished).
Play
Players take alternate turns. On your turn you must choose a tile that is still available and place it on an empty space - up, down, left or right of a tile already placed.
You must place it in any of the 8 possible orientations you wish. The orientation of a tile is indicated by the white arrow in the middle.
Once a tile is placed, check whether it can convert an opponent's tile over to your side - to do so you must fulfill three conditions;
your tile must have your color arrow pointing toward your opponent's tile
the target opponent tile must not have their color arrow pointing back
the two tiles must not share the same orientation
If multiple tiles can be converted at the same time you may only choose one.,/p>
The converted tile is flipped over to your side and rotated to the same orientation as one that converted it. You then treat that tile as though it just been placed and check if another conversion can be made. Repeat this process until no further conversion is possible.
Now it is your opponent's turn.
Players will take turn placing and converting tiles back and forth in this manner until all the tiles are placed and the game is over. Count up the total number of tiles for each player; whoever has the most of their color facing up is the winner.
What a fun 2 player game! Super thinky but luck of the draw too. Really enjoyed this one. Super compact to travel with, but does need a good size table for play. Great value for the price too. 8 out of 10.
improv321
6
MetalSlacker
7.5
aidolon
8
2 Players Board
Geeken
N/A
?.??-1KS 2025
dougwu
6
Thimsj
8
inkstainedpapers
7
I love spatial games and this was right up my alley. It reminds me of Neuroshima Hex, another game I love, but much faster and with less rules overhead.
aL3s5aNdRo
6.5
TwiznessAsUsual
N/A
cost range ($20 - $30???) for simple wooden chips & a cloth bag.... considering re-creating for my friend, Dex
sethamin1
9
OmegasSquared
6
Interesting abstract about trying to set up and deny chain reactions. The start of the game is overwhelming with the full pool of pieces available to both players. But in the mid to late game as that pool diminishes and there's some gamestate to work with, it collapses into a decision space I find more manageable but still very interesting. Reminds me a little bit of Fresh Fish. I could see this one going up for me as the early game becomes easier to play.
jthomas22a
6.5
DJCoulton
10
Mind4u2c
7
JudoSurfer94
9.5
nestorgames
8
Kolomogorov Complexity Analysis
Size (bytes)
29746
Reference Size
10673
Ratio
2.79
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
2683.12 (372.70µs/playout)
Reference Size
595131.82 (1.68µs/playout)
Ratio (low is good)
221.81
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
2290668762
State Space Complexity bounds
46598967 < 2290668762 < ∞
State Space Complexity (log 10)
9.36
State Space Complexity bounds (log 10)
7.67 <= 9.36 <= ∞
Samples
305365
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
2,685
12
195,308
990
73
6
search.UCT
2,660
61
112
12
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: Red win %
45.50±3.06
Includes draws = 50%
2: Black win %
54.50±3.10
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
277
908
0.6642 <= 0.6949 <= 0.7240
42.40
0.00
57.60
73.75
7
UCT (its=8)
631
0
350
981
0.6127 <= 0.6432 <= 0.6726
36.29
0.00
63.71
76.76
16
UCT (its=17)
547
0
453
1000
0.5160 <= 0.5470 <= 0.5776
32.10
0.00
67.90
79.41
17
UCT (its=17)
495
0
505
1000
0.4641 <= 0.4950 <= 0.5259
34.70
0.00
65.30
79.86
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
118.00
Branching factor
973.71
Complexity
10^155.79
Based on game length and branching factor
Computational Complexity
10^8.92
Sample quality (100 best): 1.71
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
169
Quantity of distinct board cells
Distinct actions
18530
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
32
A 'killer' move is selected by the AI more than 50% of the time Too many killers to list.
Good moves
1233
A good move is selected by the AI more than the average
Bad moves
17297
A bad move is selected by the AI less than the average
Terrible moves
1490
A terrible move is never selected by the AI Too many terrible moves to list.
Response distance%
14.62%
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 57.38% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
118.00
Mode
[116]
Median
117.0
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 27% of the game turns. Ai Ai found 5 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
46.64
46.20
47.08
Mean no. of effective moves
6.40
7.76
5.03
Effective game space
10^25.84
10^12.31
10^13.52
Mean % of good moves
37.67
13.50
61.83
Mean no. of good moves
160.26
55.25
265.27
Good move game space
10^92.83
10^31.33
10^61.50
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
72.88%
A hot turn is one where making a move is better than doing nothing.
Momentum
21.19%
% of turns where a player improved their score.
Correction
40.68%
% of turns where the score headed back towards equality.
Depth
7.91%
Difference in evaluation between a short and long search.
Drama
0.23%
How much the winner was behind before their final victory.
Foulup Factor
44.07%
Moves that looked better than the best move after a short search.
Surprising turns
0.85%
Turns that looked bad after a short search, but good after a long one.
Last lead change
56.78%
Distance through game when the lead changed for the last time.
Decisiveness
4.24%
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
1
1536
2330232
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.
