Full Report for SQU by Néstor Romeral Andrés

Full Report for SQU by Néstor Romeral Andrés

Form the largest square.



Definition: a Squ is an arrangement of 4 discs of the same colour on the corners of a square with the sides parallel to the sides of the board (this is, the square must not be rotated).

Each player has an allocated colour (Red or Black).

The board starts empty. Decide the size of the board (8x8 or 10x10).

Red places one disc onto an empty cell of the board. Then, starting with Black, players alternate turns placing 2 discs of their colour onto empty spaces until either one of the players resigns or all cells are occupied.

If, at the end of a player’s turn (after placing both stones) a squ bigger than any previous squ of any colour has been created, the player claims that squ. Notice that the discs covered by pyramids still count for future squs.


When the game ends, the player with the largest squ wins the game.


General comments:

Play: Combinatorial

Mechanism(s): Pattern

Components: Board

Level: Standard

BGG Stats

BGG Rating7.6
BGG Weight0

BGG Ratings and Comments

mrraow7Elegantly simple game, which can be lost in the first few moves but still takes a long time before it's clear who has won; quite challenging to get the AI playing well on this one!

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0055.56100.00
Grand Unified UCT(U1-T,rSel=s, secs=0.03)36084481.8247.73100.00
Grand Unified UCT(U1-T,rSel=s, secs=0.07)360114776.6051.06100.00
Grand Unified UCT(U1-T,rSel=s, secs=0.55)360145072.0060.00100.00

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)29510
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 second154492.65 (6.47µs/playout)
Reference Size1710863.99 (0.58µs/playout)
Ratio (low is good)11.07

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: Red win %50.41±0.81Includes draws = 50%
2: Black win %49.59±0.81Includes draws = 50%
Draw %0.00Percentage of games where all players draw.
Decisive %100.00Percentage of games with a single winner.
Samples14758Quantity 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

LabelIts/sSDNodes/sSDGame lengthSD
Random playout194,0235,47519,402,254547,4601000

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.


Game length97.56 
Branching factor51.72 
Complexity10^155.15Based on game length and branching factor
Computational Complexity10^8.77Sample quality (100 best): 0.09
Samples14758Quantity of logged games played

Move Classification

Distinct actions100Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves36A good move is selected by the AI more than the average
Bad moves64A bad move is selected by the AI less than the average
Samples14758Quantity 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.


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 11% of the game turns. Ai Ai found 1 critical turn (turns with only one good option).

Overall, this playout was 48.00% hot.

Position Heatmap

This chart shows the relative temperature of all moves each turn. Colour range: black (worst), red, orange(even), yellow, white(best).


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


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 4.