A unification game on a square grid.

Generated at 20/05/2020, 03:32 from 1000 logged games.

Start Position

If possible: place a single piece of your colour on an empty space, so it is not next to another friendly piece.

If it is not possible to place a piece, move one of your pieces to an adjacent space.

You win if you unite all your pieces, or surround an opponent, so they can no longer unite their pieces.

Two repetitions is a draw.

General comments:

Play: Combinatorial

Family: Combinatorial 2019

Mechanism(s): Connection

Components: Board

Level: Standard

BGG Entry | Make Muster |
---|---|

BGG Rating | null |

#Voters | null |

SD | null |

BGG Weight | null |

#Voters | null |

Year | null |

Size (bytes) | 25411 |
---|---|

Reference Size | 10293 |

Ratio | 2.47 |

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 | 9385.04 (106.55µs/playout) |
---|---|

Reference Size | 577067.34 (1.73µs/playout) |

Ratio (low is good) | 61.49 |

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.

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

Random playout | 11,567 | 76 | 1,068,286 | 5,082 | 92 | 35 |

search.UCB | 11,500 | 247 | 31 | 7 | ||

search.UCT | 11,385 | 442 | 34 | 9 |

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.

1: Blue win % | 55.20±3.10 | Includes draws = 50% |
---|---|---|

2: Pink win % | 44.80±3.06 | Includes draws = 50% |

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

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

Samples | 1000 | 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.

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 | 47.22 | 41.69 |

Grand Unified UCT(U1-T,rSel=s, secs=0.07) | 36 | 0 | 3 | 39 | 92.31 | 48.72 | 32.38 |

Grand Unified UCT(U1-T,rSel=s, secs=0.55) | 36 | 0 | 4 | 40 | 90.00 | 50.00 | 34.15 |

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 length | 36.93 | |
---|---|---|

Branching factor | 22.04 | |

Complexity | 10^40.84 | Based on game length and branching factor |

Computational Complexity | 10^5.84 | Saturation reached - accuracy very high. |

Samples | 1000 | Quantity 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.

Distinct actions | 325 | Number of distinct moves (e.g. "e4") regardless of position in game tree |
---|---|---|

Good moves | 108 | A good move is selected by the AI more than the average |

Bad moves | 217 | A bad move is selected by the AI less than the average |

Samples | 1000 | Quantity of logged games played |

A mean of 71.26% of board locations were used per game.

Colour shows the frequency of visits.

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.

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 20% of the game turns. Ai Ai found 0 critical turns (turns with only one good option).

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

Measure | All players | Player 1 | Player 2 |
---|---|---|---|

Mean % of effective moves | 46.32 | 46.35 | 46.28 |

Mean no. of effective moves | 5.72 | 6.60 | 4.79 |

Effective game space | 10^-∞ | 10^-∞ | 10^-∞ |

Mean % of good moves | 15.83 | 30.49 | 0.39 |

Mean no. of good moves | 2.85 | 5.40 | 0.16 |

Good move game space | 10^11.93 | 10^11.45 | 10^0.48 |

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.

Measure | Value | Description |
---|---|---|

Hot turns | 94.87% | A hot turn is one where making a move is better than doing nothing. |

Momentum | 28.21% | % of turns where a player improved their score. |

Correction | 35.90% | % of turns where the score headed back towards equality. |

Depth | 4.59% | Difference in evaluation between a short and long search. |

Drama | 0.00% | How much the winner was behind before their final victory. |

Foulup Factor | 20.51% | Moves that looked better than the best move after a short search. |

Surprising turns | 0.00% | Turns that looked bad after a short search, but good after a long one. |

Last lead change | 74.36% | Distance through game when the lead changed for the last time. |

Decisiveness | 12.82% | 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).

0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

1 | 45 | 2025 | 38575 | 697565 | 7236347 |

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 5.