Either furl up a row of your pieces, or unfurl a stack. If you have a piece in your end row at the *start of your turn, you win.*

Generated at 10/05/2020, 18:47 from 1235 logged games.

Start Position

Each turn, choose one of two types of moves:

- Furl
- Choose two or more of your pieces in an unbroken line, and stack them on the piece at the end of that line.
- Unfurl
- Choose a stack of at least two pieces and sow them one per space in a straight line starting in the space in front of your stack. Intermediate spaces must be empty, but the final space may be occupied by an enemy piece or stack. If so, you capture those pieces.

You win if you have a piece or stack on the row farthest from you at the start of your turn.

You lose if you have no legal moves.

General comments:

- Requires αβ search to play well.

Play: Combinatorial

BGG Entry | Furl (Square 8x8) |
---|---|

BGG Rating | null |

#Voters | null |

SD | null |

BGG Weight | null |

#Voters | null |

Year | null |

Size (bytes) | 26336 |
---|---|

Reference Size | 10293 |

Ratio | 2.56 |

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 | 5980.50 (167.21µs/playout) |
---|---|

Reference Size | 557693.38 (1.79µs/playout) |

Ratio (low is good) | 93.25 |

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 | 6,117 | 182 | 574,839 | 16,831 | 94 | 53 |

search.UCB | 9,222 | 12,378 | 16 | 12 | ||

search.UCT | 7,197 | 1,816 | 20 | 14 | ||

search.Minimax | 354,221 | 79,840 | 19 | 6 | ||

search.AlphaBeta | 47,140 | 73,588 | 14 | 3 |

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: White win % | 51.09±2.79 | Includes draws = 50% |
---|---|---|

2: Black win % | 48.91±2.78 | Includes draws = 50% |

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

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

Samples | 1235 | 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 | |||||||

Rαβ + ocqBKs (t=0.01s) | 36 | 0 | 0 | 36 | 100.00 | 55.56 | 19.94 |

Rαβ + ocqBKs (t=0.07s) | 36 | 0 | 8 | 44 | 81.82 | 54.55 | 14.50 |

Rαβ + ocqBKs (t=0.55s) | 36 | 0 | 5 | 41 | 87.80 | 41.46 | 13.22 |

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 | 18.22 | |
---|---|---|

Branching factor | 113.25 | |

Complexity | 10^33.90 | Based on game length and branching factor |

Samples | 1235 | 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 | 2282 | Number of distinct moves (e.g. "e4") regardless of position in game tree |
---|---|---|

Killer moves | 119 | A 'killer' move is selected by the AI more than 50% of the time Too many killers to list. |

Good moves | 1228 | A good move is selected by the AI more than the average |

Bad moves | 1053 | A bad move is selected by the AI less than the average |

Terrible moves | 433 | A terrible move is never selected by the AI Too many terrible moves to list. |

Samples | 1235 | Quantity of logged games played |

A mean of 38.94% 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 31% of the game turns. Ai Ai found 3 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 | 64.71 | 73.58 | 54.86 |

Mean no. of effective moves | 62.32 | 50.60 | 75.33 |

Effective game space | 10^-∞ | 10^15.37 | 10^-∞ |

Mean % of good moves | 39.34 | 33.86 | 45.42 |

Mean no. of good moves | 36.74 | 24.90 | 49.89 |

Good move game space | 10^21.20 | 10^8.95 | 10^12.25 |

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 | 73.68% | A hot turn is one where making a move is better than doing nothing. |

Momentum | 5.26% | % of turns where a player improved their score. |

Correction | 36.84% | % of turns where the score headed back towards equality. |

Depth | 8.07% | Difference in evaluation between a short and long search. |

Drama | 1.41% | How much the winner was behind before their final victory. |

Foulup Factor | 78.95% | Moves that looked better than the best move after a short search. |

Surprising turns | 10.53% | Turns that looked bad after a short search, but good after a long one. |

Last lead change | 57.89% | Distance through game when the lead changed for the last time. |

Decisiveness | 21.05% | 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).

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

Furl g1:a1,Furl a8:g8,Furl h1:f3,Furl h8:h6,Unfurl f3:f6,Unfurl h6:h3,Furl b3:d3,Furl f7:h5,Furl f5:f6,Unfurl h5:e8 | |

Furl h1:b1,Furl a8:g8,Furl h2:c2,Furl h7:c7,Furl a1:c3,Furl g6:e6,Unfurl c3:c6,Unfurl e6:e3,Furl c5:c6,Furl e3:e5 | |

Furl h1:b1,Furl b8:h8,Furl a1:a3,Furl a7:f7,Unfurl a3:d6,Furl h6:f6,Furl h2:c2,Unfurl f6:f3,Furl c5:d6,Furl f4:f3 | |

Furl b1:h1,Furl a8:g8,Furl a1:a3,Furl h8:h6,Unfurl a3:d6,Unfurl h6:e3,Furl h2:c2,Furl a7:f7,Furl c5:d6,Furl f4:e3 | |

Furl h1:b1,Furl a8:g8,Furl a1:a3,Furl h8:h6,Unfurl a3:d6,Unfurl h6:e3,Furl h3:f3,Furl g7:g5,Furl d2:h2,Unfurl g5:d5 | |

Furl a1:g1,Furl a8:g8,Furl a2:f2,Furl h8:h6,Furl h1:f3,Unfurl h6:e3,Unfurl f3:c6,Furl g5:f4,Furl a3:c3,Unfurl f4:f2 | |

Furl a1:g1,Furl b8:h8,Furl h1:f3,Furl a8:a6,Unfurl f3:c6,Unfurl a6:d3,Furl c2:f2,Furl c4:d3,Unfurl f2:f6,Unfurl d3:f1 | |

Furl a1:g1,Furl b8:h8,Furl h1:h3,Furl a8:a6,Unfurl h3:e6,Unfurl a6:d3,Furl a3:c3,Furl b7:b5,Furl f2:a2,Unfurl b5:e5 | |

Furl b1:h1,Furl a8:g8,Furl a1:a3,Furl h8:h6,Unfurl a3:d6,Unfurl h6:e3,Furl h2:c2,Furl a6:c6,Furl h3:g3,Furl g7:f6 | |

Furl b1:h1,Furl b8:h8,Furl h2:c2,Furl a8:a6,Furl a1:c3,Unfurl a6:d3,Unfurl c3:f6,Furl b5:c4,Furl h3:f3,Unfurl c4:c2 | |

Furl g1:a1,Furl h8:b8,Furl h1:h3,Furl a8:a6,Unfurl h3:e6,Unfurl a6:d3,Furl a3:c3,Furl b7:b5,Furl a2:f2 | |

Furl g1:a1,Furl a8:g8,Furl h1:f3,Furl h8:h6,Unfurl f3:f6,Unfurl h6:h3,Furl b3:d3,Furl f7:h5,Furl f5:f6 |

Colour shows the success ratio of this play over the first 10moves; black < red < yellow < white.

Size shows the frequency this move is played.

0 | 1 | 2 |
---|---|---|

1 | 296 | 87912 |

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 2.

Puzzle | Solution |
---|---|

Black to win in 10 moves | |

Black to win in 12 moves | |

Black to win in 6 moves | |

White to win in 6 moves | |

White to win in 4 moves | |

Black to win in 2 moves | |

Black to win in 2 moves | |

Black to win in 2 moves | |

Black to win in 2 moves | |

White to win in 2 moves | |

Black to win in 4 moves |

Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.