Full Report for Starweb by Christian Freeling

Full Report for Starweb by Christian Freeling

Players alternate placing pieces until board is full or both pass. Points are scored for connecting the most corners.

Rules

Starweb is a placement game without movement or capture. Players take turns to place one stone. The starshaped board has 18 corners, 12 outward and 6 inward ones. Groups containing corners have a value of 1 point for one corner, 2 points for the second corner, 3 for the third and so on. A group containing 4 corners thus has a value of 1+2+3+4=10 points. This 'triangular' score makes connecting groups very advantageous.The game starts with the pie rule and ends when both players pass on successive turns. The player with the highest score wins. In case of an equal score the player who placed the second stone on the board wins.

The main challenge here is that the designer prefers large boards, which is troublesome for the AI in two ways. More board spaces make for a larger branching factor at each move AND longer games. To some extent, I compensate for this with a transposition table (i.e. recognising that you can reach the same position through different move sequences), but I also had to make the random playouts smarter (recognising and enforcing solid connections). That plus a little magic in the opening leads to a passable AI, but you might want to choose a smaller board size if you want a strong game. One other finding; the games are really over when the last connection has been made, which is significantly before the board is full. To short-circuit a boring endgame, I added code to the GUI to end the game early in a won/lost situation. (Why the GUI? Well, whether a game CAN be ended early or not is a feature of the game; whether a game should be ended early is down to player preference to some extent. The AIs provide the information, the game and the player settings guide the decision.)

Miscellaneous

General comments:

Play: Combinatorial

Family: Combinatorial 2017

Mechanism(s): Connection,Scoring

Components: Board

BGG Stats

BGG Entry Starweb
BGG Rating 6.625
#Voters 4
SD 1.47373
BGG Weight 0
#Voters 0
Year 2017

BGG Ratings and Comments

User Rating Comment
hojoh N/A http://mindsports.nl/index.php/arena/starweb/
russ 6 Hex grid connection game -- experience with Hex, Havannah, Cross, etc seems very helpful for basic tactics. For me, the triangular scoring didn't add enough interest -- I'd rather play Havannah or Hex. cf. Side Stitch, which uses different scoring but also encourages you to make a big group connecting to multiple parts of the edge.
mrraow 9 A simple, original intuitive connection game. Don't be put off by the maths-y victory conditions. You just need to aim for as few groups as possible, connecting to as many corners as possible. Playable in Ai Ai. The main challenge here is that the designer prefers large boards, which is troublesome for the AI in two ways. More board spaces make for a larger branching factor at each move AND longer games. To some extent, I compensate for this with a transposition table (i.e. recognising that you can reach the same position through different move sequences), but I also had to make the random playouts smarter (recognising and enforcing solid connections). That plus a little magic in the opening leads to a passable AI, but you might want to choose a smaller board size if you want a strong game. One other finding; the games are really over when the last connection has been made, which is significantly before the board is full. To short-circuit a boring endgame, I added code to the GUI to end the game early in a won/lost situation. (Why the GUI? Well, whether a game CAN be ended early or not is a feature of the game; whether a game should be ended early is down to player preference to some extent. The AIs provide the information, the game and the player settings guide the decision.)
Kaffedrake 5 Feels like Hex with additional wrinkles, or what might have impelled someone to invent Hex saying, "Let's trim this down to the essential mechanism." The multidirectional connection and triangular scoring seem like they should add strategic considerations, yet I can't make up my mind that they make for a much better game.
fogus 6.5

Levels of Play

AI Strong Wins Draws Strong Losses #Games Strong Win% p1 Win% Game Length
Random              
Grand Unified UCT(U1-T,rSel=s, secs=0.01) 36 0 0 36 100.00 47.22 134.67
Grand Unified UCT(U1-T,rSel=s, secs=0.03) 36 0 0 36 100.00 47.22 171.75
Grand Unified UCT(U1-T,rSel=s, secs=0.07) 36 0 0 36 100.00 58.33 182.69
Grand Unified UCT(U1-T,rSel=s, secs=0.20) 36 0 0 36 100.00 47.22 194.92

Level of Play: Strong beats Weak 60% of the time (lower bound with 90% confidence).

Draw%, p1 win% and game length may give some indication of trends as AI strength increases; but be aware that the AI can introduce bias due to horizon effects, poor heuristics, etc.

Kolomogorov Complexity Estimate

Size (bytes) 33738
Reference Size 10293
Ratio 3.28

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 77011.35 (12.99µs/playout)
Reference Size 402592.86 (2.48µs/playout)
Ratio (low is good) 5.23

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.

Win % By Player (Bias)

1: White win % 60.30±3.07 Includes draws = 50%
2: Black win % 39.70±2.99 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.

Playout/Search Speed

Label Its/s SD Nodes/s SD Game length SD
Random playout 91,371 464 19,918,772 101,490 218 14
search.UCB 62,366 724 217 21
search.UCT 60,980 585 205 46

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.

Complexity

Game length 211.62  
Branching factor 113.09  
Complexity 10^404.97 Based on game length and branching factor
Samples 1000 Quantity of logged games played

Move Classification

Distinct actions 219 Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves 68 A good move is selected by the AI more than the average
Bad moves 151 A bad move is selected by the AI less than the average
Samples 1000 Quantity of logged games played

Change in Material Per Turn

This chart is based on a single playout, and gives a feel for the change in material over the course of a game.

Actions/turn

Table: branching factor per turn.

Action Types per Turn

This chart is based on a single playout, and gives a feel for the types of moves available over the course of a game.

Red: removal, Black: move, Blue: Add, Grey: pass, Purple: swap sides, Brown: other.

Unique Positions Reachable at Depth

0 1 2 3
1 217 47306 5180007

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)

                       

1448 solutions found at depth -1.

Openings

Moves Animation
d13,d10,d16,j16,j4,p10,p4
d13,d10,d16,j16,j4,p10
d13,d10,d16,j16,j4
d13,d10,d16,j16
d13,d10,d16
n7,o1
l15,l16
f19,l7
m5,j16
q5,d16
i7,p10
g12,o1