Players take turns placing stones, until the board is full or until all players pass consecutively. Groups of like-coloured stones are *chunks* if they contain two or more stones; single stones are merely *crumbs*.

On his/her turn, a player is allotted a number of stones equal to his/her current number of chunks. A player may play any number of stones from 0 (a pass) up to his/her allotted number. A player may play any colour of stone (even an opponent's colour); multiple stones can be any colour or colour mix.

The winner is the player with the fewest CHUNKS in his/her colour of stones.In the case of a tie in the number of chunks, the tied player with the *fewest smallest* groups wins. That is, tied players compare their number of CRUMBS; the player with the fewest crumbs wins. If the number of crumbs is also tied, then players compare their number of groups consisting of just two stones; the player with the smallest number of size-2 groups wins - and so on up through the various sizes (size-3, size-4, ...) until the tie is broken.

(In the two player game, an *all the way up* tie is mathematically impossible so long as the players did not prematurely pass; eventually the tie will necessarily be broken as players compare larger and larger groups. In the multi-player game, an *all the way up* tie is theoretically possible but non-existent in practice.)

In the two player game, in order to offset the first player advantage, the PIE rule applies: After Player 1 plays his/her stone, Player 2 decides whether to play a stone to the board or switch colours with Player 1. (If *switch colours* is chosen, then the player who was formerly Player 1 is now Player 2, and immediately plays a stone as his/her turn #1 move.)

General comments:

- Requires αβ search to play well.

Play: Combinatorial

Family: Connection,Scoring,Strict PLacement,Combinatorial 2019

Mechanism(s): Scoring

Components: Board

Level: Standard

BGG Entry | Wunchunk |
---|---|

BGG Rating | 0 |

#Voters | 0 |

SD | 0 |

BGG Weight | 0 |

#Voters | 0 |

Year | 2019 |

AI | Strong Wins | Draws | Strong Losses | #Games | Strong Win% | p1 Win% | Game Length |
---|---|---|---|---|---|---|---|

Random | |||||||

Rαβ + ocqBKs (t=0.01s) | 36 | 0 | 4 | 40 | 90.00 | 47.50 | 148.15 |

Rαβ + ocqBKs (t=0.07s) | 36 | 0 | 10 | 46 | 78.26 | 52.17 | 155.37 |

Rαβ + ocqBKs (t=0.20s) | 36 | 0 | 1 | 37 | 97.30 | 48.65 | 165.92 |

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) | 30205 |
---|---|

Reference Size | 10293 |

Ratio | 2.93 |

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 | 12613.27 (79.28µs/playout) |
---|---|

Reference Size | 1503759.40 (0.67µs/playout) |

Ratio (low is good) | 119.22 |

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: Player 1 (Black) win % | 47.30±3.08 | Includes draws = 50% |
---|---|---|

2: Player 2 (White) win % | 52.70±3.10 | 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.

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

Random playout | 13,355 | 63 | 2,224,269 | 10,454 | 167 | 6 |

search.UCB | 13,401 | 159 | 151 | 38 | ||

search.UCT | 13,220 | 153 | 152 | 38 | ||

search.Minimax | 876,818 | 100,787 | 112 | 66 | ||

search.AlphaBeta | 130,417 | 12,833 | 167 | 1 |

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 | 163.61 | |
---|---|---|

Branching factor | 168.47 | |

Complexity | 10^343.11 | Based on game length and branching factor |

Computational Complexity | 10^7.43 | Saturation reached - accuracy very high. |

Samples | 1000 | Quantity of logged games played |

Distinct actions | 332 | Number of distinct moves (e.g. "e4") regardless of position in game tree |
---|---|---|

Good moves | 199 | A good move is selected by the AI more than the average |

Bad moves | 133 | A bad move is selected by the AI less than the average |

Samples | 1000 | 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).

First player's position continued to deteriorate throughout the game. The lead changed on 50% of the game turns. Ai Ai found 0 critical turns (turns with only one good option).

Overall, this playout was 50.00% 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 |
---|---|---|---|

1 | 331 | 55443 | 6233281 |

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.

1 solutions found at depth 2.

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

Wh11,Wi11,Wh10 | |

Wi11,Wh11,Wh10 | |

Bm4,Wj5 | |

Bj7,Wg4 | |

Wg4,Bj7 | |

Wj5,Bm4 | |

Bf6,Wi5 | |

Bb15,Wo8 | |

Wk4,Wj5 | |

Wi5,Bf6 | |

Wj5,Wk4 | |

Wo8,Bb15 | |

Bj2,Wo5 | |

Wo5,Bj2 | |

Wh11,Wi11 | |

Wi11,Wh11 | |

Wg14,Wf15 | |

Wf15,Wg14 | |

Bi2 | |

Bk2 |