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 players 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 Entry | SQU |
---|---|

BGG Rating | 7.6 |

#Voters | 5 |

SD | 1.2 |

BGG Weight | 0 |

#Voters | 0 |

Year | 2019 |

User | Rating | Comment |
---|---|---|

at010 | 7 | |

pecan | 6 | |

mrraow | 7 | Elegantly 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! |

maruXV | 9 | |

jmastill | 9 |

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 | 55.56 | 100.00 |

Grand Unified UCT(U1-T,rSel=s, secs=0.03) | 36 | 0 | 8 | 44 | 81.82 | 47.73 | 100.00 |

Grand Unified UCT(U1-T,rSel=s, secs=0.07) | 36 | 0 | 11 | 47 | 76.60 | 51.06 | 100.00 |

Grand Unified UCT(U1-T,rSel=s, secs=0.55) | 36 | 0 | 14 | 50 | 72.00 | 60.00 | 100.00 |

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.

Size (bytes) | 29510 |
---|---|

Reference Size | 10293 |

Ratio | 2.87 |

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.

Playouts per second | 154492.65 (6.47µs/playout) |
---|---|

Reference Size | 1710863.99 (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.

1: Red win % | 50.41±0.81 | Includes draws = 50% |
---|---|---|

2: Black win % | 49.59±0.81 | Includes draws = 50% |

Draw % | 0.00 | Percentage of games where all players draw. |

Decisive % | 100.00 | Percentage of games with a single winner. |

Samples | 14758 | 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.

Label | Its/s | SD | Nodes/s | SD | Game length | SD |
---|---|---|---|---|---|---|

Random playout | 194,023 | 5,475 | 19,402,254 | 547,460 | 100 | 0 |

search.UCB | 220,019 | 8,463 | 100 | 0 | ||

search.UCT | 192,448 | 8,321 | 100 | 0 |

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.

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 length | 97.56 | |
---|---|---|

Branching factor | 51.72 | |

Complexity | 10^155.15 | Based on game length and branching factor |

Computational Complexity | 10^8.77 | Sample quality (100 best): 0.09 |

Samples | 14758 | Quantity of logged games played |

Distinct actions | 100 | Number of distinct moves (e.g. "e4") regardless of position in game tree |
---|---|---|

Good moves | 36 | A good move is selected by the AI more than the average |

Bad moves | 64 | A bad move is selected by the AI less than the average |

Samples | 14758 | Quantity of logged games played |

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.

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.

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.

0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|

1 | 100 | 10000 | 495100 | 24022450 |

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.

No solutions found to depth 4.

Moves | Animation |
---|---|

e8 | |

b4 | |

h9 | |

a8 | |

i3 | |

j3 | |

c10 | |

j8 | |

g3 | |

c4 | |

h5 | |

b1 |