Full Report for Starweb (size 10) by Christian Freeling

Full Report for Starweb (size 10) by Christian Freeling

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

Generated at 03/08/2021, 12:20 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!

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.

Miscellaneous

General comments:

Play: Combinatorial

Family: Combinatorial 2017

Mechanism(s): Connection,Scoring

Components: Board

BGG Stats

BGG EntryStarweb (size 10)
BGG Rating6.32
#Voters5
SD1.45245
BGG Weight0
#Voters0
Year2017

BGG Ratings and Comments

UserRatingComment
hojohN/Ahttp://mindsports.nl/index.php/arena/starweb/
russ6Hex 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.
mrraow9A 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.)
twerkfaceN/AOn Ai Ai
Kaffedrake5Feels 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.
fogus6.5

Kolomogorov Complexity Analysis

Size (bytes)34819
Reference Size10293
Ratio3.38

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 second37932.67 (26.36µs/playout)
Reference Size297495.09 (3.36µs/playout)
Ratio (low is good)7.84

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 Complexity48925456 
State Space Complexity (log 10)7.69 
Confidence56.450: totally unreliable, 100: perfect
Samples225038 

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

LabelIts/sSDNodes/sSDGame lengthSD
Random playout90,2401,74519,671,867379,88721814
search.UCT40,1012,04921720

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 %46.00±3.07Includes draws = 50%
2: Black win %54.00±3.10Includes draws = 50%
Draw %0.00Percentage of games where all players draw.
Decisive %100.00Percentage of games with a single winner.
Samples1000Quantity 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

MatchAIStrong WinsDrawsStrong Losses#GamesStrong Scorep1 Win%Draw%p2 Win%Game Length
0Random         
2UCT (its=3)63102989290.6485 <= 0.6792 <= 0.708547.360.0052.64217.59
9UCT (its=10)63103639940.6044 <= 0.6348 <= 0.664251.510.0048.49218.32
19UCT (its=20)63103529830.6114 <= 0.6419 <= 0.671346.490.0053.51219.01
27UCT (its=28)63103619920.6057 <= 0.6361 <= 0.665548.490.0051.51218.52
37UCT (its=38)63103349650.6233 <= 0.6539 <= 0.683248.290.0051.71217.93
45
UCT (its=46)
628
0
372
1000
0.5976 <= 0.6280 <= 0.6574
49.00
0.00
51.00
218.42
46
UCT (its=46)
515
0
485
1000
0.4840 <= 0.5150 <= 0.5459
49.70
0.00
50.30
218.13

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 length220.63 
Branching factor108.58 
Complexity10^420.17Based on game length and branching factor
Computational Complexity10^9.09Sample quality (100 best): 0.01
Samples1000Quantity 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 Size217Quantity of distinct board cells
Distinct actions219Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves63A good move is selected by the AI more than the average
Bad moves156A bad move is selected by the AI less than the average
Response distance%36.79%Distance from move to response / maximum board distance; a low value suggests a game is tactical rather than strategic.
Samples1000Quantity of logged games played

Board Coverage

A mean of 99.50% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean220.63
Mode[222]
Median221.0

Change in Material Per Turn

Mean change in material/round0.97Complete 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.)

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

Trajectory

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 6% of the game turns. Ai Ai found 9 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

MeasureAll playersPlayer 1Player 2
Mean % of effective moves29.5429.2629.81
Mean no. of effective moves9.268.989.55
Effective game space10^99.1610^47.3810^51.78
Mean % of good moves24.1943.584.62
Mean no. of good moves15.1521.338.92
Good move game space10^120.0010^91.3910^28.62

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

MeasureValueDescription
Hot turns78.28%A hot turn is one where making a move is better than doing nothing.
Momentum21.72%% of turns where a player improved their score.
Correction30.32%% of turns where the score headed back towards equality.
Depth2.49%Difference in evaluation between a short and long search.
Drama1.41%How much the winner was behind before their final victory.
Foulup Factor6.79%Moves that looked better than the best move after a short search.
Surprising turns0.00%Turns that looked bad after a short search, but good after a long one.
Last lead change52.94%Distance through game when the lead changed for the last time.
Decisiveness4.07%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.)

Swap Heatmap (Full Scan)

Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.

Based on 100 trials/move at 0.1s thinking time each.

Openings

MovesAnimation
d15,j4,d10,p4,j16
d15,j4,d10,p4
h17,p4,j16,j4
f6,d10,j16
l8,p4,j16
d15,j4,d10
e16,p10,j16
m2,d16,j4
n3,d10,j4
n5,d16,j4
o7,d16,j16
j8,j4,p10

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.

Swap Heatmap (Historic)

Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.

Size shows the frequency this move is played.

Unique Positions Reachable at Depth

0123
1217473065132918

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 3.