Full Report for Throngs by Dale Walton

Full Report for Throngs by Dale Walton

Objective: Have a majority of pieces when the board is full and no captures are left to be made.

Generated at 11/03/2021, 16:57 from 1000 logged games.


Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!


The structure of the game

Before play begins, one player places a Black stone and two White stones on three different intersections. Then the other player decides to play either as Black or as White. After this the players alternate turns taking two moves each, beginning with Black.

A move begins on an intersection that has sufficient action-potential (calculated as described above). Before movement, the following deductions must be made from the potential, based on the intersection's contents:

If you have any leftover actions, you MAY now move the piece in the intersection; in a sequence of steps and jumps, spending one action for each space moved during the sequence.

The distance along the path traveled may not exceed the number of actions that remain.

Voluntary passing and partial passing are allowed, with the following exception:

Ending the game:

Play continues until no moves are left, and the player with the most pieces on the board wins.

Resigning in advance is a courtesy.


General comments:

Play: Combinatorial

Family: Combinatorial 2020

Mechanism(s): Connection,Movement,Scoring

Components: Board

BGG Stats

BGG EntryThrongs
BGG Ratingnull
BGG Weightnull

Kolomogorov Complexity Analysis

Size (bytes)31545
Reference Size10293

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 second7621.42 (131.21µs/playout)
Reference Size1735207.36 (0.58µs/playout)
Ratio (low is good)227.67

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.

Playout/Search Speed

LabelIts/sSDNodes/sSDGame lengthSD
Random playout7,76054837,3923,60910853

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: Player 1 win %48.90±3.09Includes draws = 50%
2: Player 2 win %51.10±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
1UCT (its=2)5731153009880.6077 <= 0.6382 <= 0.667540.2811.6448.08106.52
3UCT (its=4)597683339980.6019 <= 0.6323 <= 0.661636.876.8156.31113.84
9UCT (its=10)607473019550.6296 <= 0.6602 <= 0.689640.004.9255.08133.15
21UCT (its=22)621193509900.6064 <= 0.6369 <= 0.666241.921.9256.16152.31
UCT (its=28)
0.5060 <= 0.5370 <= 0.5677
UCT (its=28)
0.4616 <= 0.4925 <= 0.5235

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.


Game length194.40 
Branching factor25.69 
Complexity10^228.26Based on game length and branching factor
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

Distinct actions5579Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves336A 'killer' move is selected by the AI more than 50% of the time
Too many killers to list.
Good moves4252A good move is selected by the AI more than the average
Bad moves1327A bad move is selected by the AI less than the average
Terrible moves1081A terrible move is never selected by the AI
Too many terrible moves to list.
Response distance3.56Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples1000Quantity of logged games played

Board Coverage

A mean of 98.11% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.


Change in Material Per Turn

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.)


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.


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 2% of the game turns. Ai Ai found 7 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 moves69.1065.1672.88
Mean no. of effective moves16.5917.6215.61
Effective game space10^181.5310^91.4210^90.11
Mean % of good moves45.9290.453.18
Mean no. of good moves12.9426.050.35
Good move game space10^114.2710^110.4410^3.83

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

Hot turns51.55%A hot turn is one where making a move is better than doing nothing.
Momentum22.68%% of turns where a player improved their score.
Correction41.75%% of turns where the score headed back towards equality.
Depth2.99%Difference in evaluation between a short and long search.
Drama0.08%How much the winner was behind before their final victory.
Foulup Factor70.10%Moves that looked better than the best move after a short search.
Surprising turns0.52%Turns that looked bad after a short search, but good after a long one.
Last lead change7.73%Distance through game when the lead changed for the last time.
Decisiveness3.09%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.)


Add g7,Add f10,Add k6,Play white,Add f8,Add h6
Add g7,Add f10,Add k6,Play white,Add f8
Add h1,Add a11,Add c11,Play black
Add k1,Add f3,Add l7,Play black
Add l2,Add a12,Add i4,Play black
Add k3,Add j6,Add j7,Play black
Add i4,Add h6,Add g4,Play black
Add i4,Add h6,Add d11,Play black
Add g5,Add e8,Add e10,Play black
Add b6,Add f5,Add k4,Play black
Add l6,Add b9,Add g11,Play black
Add c7,Add b10,Add h1,Play black

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


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 6.