Full Report for Alliances by Markus Hagenauer

Full Report for Alliances by Markus Hagenauer

This tricky game requires you to connect opposite sides of the board: purple to purple, orange to orange, green to green. To make those connections, you must use the colour matching the sides you are connecting… but your allied colour also works!

Generated at 12/05/2020, 01:53 from 1000 logged games.


Start Position


On your turn, take a disc from the supply and place it on any empty space.

If you just formed a connection between opposite sides, with an uninterrupted chain of tiles of the sides' colour and/or the allied colour, you win that colour, even if the disc you placed formed a connection for both of you.

When you win a colour, take a disc of that colour from the supply and place it on the corresponding cell of your chart, while your opponent places a silver disc on the same colour on their chart (they lost that colour). If you just won your second colour, you win the game.

Player 1
Player 2


General comments:

Play: Combinatorial

Family: Connection,Strict Placement,Combinatorial 2019

Mechanism(s): Majorities

Components: Board

Level: Standard

BGG Stats

BGG EntryAlliances
BGG Rating8.5
BGG Weight0

BGG Ratings and Comments

liquidus letum8
ed_in_playN/Aconnection game get 2 out of 3 connections. each connection can use 2 colors

Kolomogorov Complexity Estimate

Size (bytes)29652
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 second2745.44 (364.24µs/playout)
Reference Size390823.62 (2.56µs/playout)
Ratio (low is good)142.35

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 playout4,255184410,58717,708979

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 %50.90±3.10Includes draws = 50%
2: Player 2 win %49.10±3.09Includes 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.

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0047.2285.72
Grand Unified UCT(U1-T,rSel=s, secs=0.03)36064285.7159.5280.02
Grand Unified UCT(U1-T,rSel=s, secs=0.07)36054187.8053.6677.37
Grand Unified UCT(U1-T,rSel=s, secs=0.20)36013797.3067.5771.59
Grand Unified UCT(U1-T,rSel=s, secs=0.55)36013797.3043.2465.41

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.


Game length69.82 
Branching factor259.78 
Complexity10^167.41Based 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 actions363Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves176A good move is selected by the AI more than the average
Bad moves187A bad move is selected by the AI less than the average
Samples1000Quantity of logged games played

Board Coverage

A mean of 60.18% of board locations were used per game.

Colour shows the frequency of visits.

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.


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.


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 82% of the game turns. Ai Ai found 0 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 moves1.653.120.18
Mean no. of effective moves2.925.530.31
Effective game space10^-∞10^-∞10^-∞
Mean % of good moves3.410.006.82
Mean no. of good moves6.060.0012.12
Good move game space10^6.5910^0.0010^6.59

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 turns98.44%A hot turn is one where making a move is better than doing nothing.
Momentum48.44%% of turns where a player improved their score.
Correction39.06%% of turns where the score headed back towards equality.
Depth29.75%Difference in evaluation between a short and long search.
Drama0.00%How much the winner was behind before their final victory.
Foulup Factor0.00%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 change84.38%Distance through game when the lead changed for the last time.
Decisiveness4.69%Distance from the result being known to the end of the game.

These figures were calculated over a single game, and based on the measures of quality described in "Automatic Generation and Evaluation of Recombination Games" (Cameron Browne, 2007).

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 3.