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.
Make a row of 4, with knight's moves.
Start with a single stack. Move part of a stack like a knight, leaving at least one piece behind. If you make a row of four (orthogonally or diagonally), you win. All pieces must remain connected to all other pieces after each move.
General comments:
Play: Combinatorial,Multiplayer
Family: Combinatorial 2013
Mechanism(s): Line,Stacking,Movement
| BGG Entry | Knight Line |
|---|---|
| BGG Rating | 7.61538 |
| #Voters | 13 |
| SD | 1.07692 |
| BGG Weight | 1.5 |
| #Voters | 2 |
| Year | 2013 |
| User | Rating | Comment |
|---|---|---|
| Pionek | 8 | |
| plays for keeps | 7 | Aha! I had found a bag full of thick-cut plastic squares while thrifting a while back. Now I know what to do with them! Can't wait to give this a try. |
| rseater | 7 | A surprisingly subtle N-in-a-row abstract. Choosing how much of a stack to leave behind can be reasoned about heuristically without doing the full computation, making the game amenable to quick play without ruining its depth. |
| mrraow | 10 | My game. Inspired by the "grail games" thread http://boardgamegeek.com/thread/1017068/grail-games in the abstract forums here on BGG, this is my take on a minimalist n-in-a-row game. All that is required are two sets of stackable pieces; no board so, about as minimal as I can make it in terms of material while still being a good strategic game. This is actually my best tested game. I designed it just before a beach holiday with the family, and spent part of the holiday coding an AI, then used self-play to test the fairness of the game under various parameters. It turns out, according to the AI at least, that allowing the first player to move only a single pieces is the best balancing mechanism; a line of length 4 works best; and the actual starting number of pieces in the stacks isn't too important. Anywhere between 16 and 24 seems viable. I haven't tested beyond that point. The AI is now available - you can download it from http://mrraow.com/index.php/aiai-home/ (warning: java 8 required) |
| 1974vertigo2009 | N/A | PnP - 1396 |
| schwarzspecht | 8 | |
| at010 | 7 | |
| Thesse1955 | 7 | |
| Helmi68 | 8 | |
| ludopath | N/A | Could, at least theoretically, fall prey to fixed opening routines. Also, forcing the 1st move seems a less than elegant way of compensating 1st player advantage. The vaguely similar "Splits" has none of these issues. |
| russ | 6 | The splitting & moving stack paradigm of Splits meets n-in-a row, with chess knight moves. Playing with face-down regular and special tiles from the game [gameid=27173] looks very pretty! |
| Butsudoka | 8 | Please see [url=https://www.boardgamegeek.com/thread/1594753/clever-little-game-which-deserves-more-attention]my review[/url]. |
| Arcanio | 6 | |
| jmastill | 8 | |
| nestorgames | 9 |
| AI | Wins vs prev level | Draws | Losses | #Games | Win% |
|---|---|---|---|---|---|
| Random | |||||
| R?? + ocqBKs (t=v0.01s) | 27 | 19 | 0 | 46 | 79.35 |
Level of Play: strong beats weak 60% of the time (lower bound with 90% confidence).
| Size (bytes) | 31714 |
|---|---|
| Reference Size | 10328 |
| Ratio | 3.07 |
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 | 33330.89 (30.00µs/playout) |
|---|---|
| Reference Size | 1041992.29 (0.96µs/playout) |
| Ratio (low is good) | 31.26 |
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: White win % | 42.02±1.79 | Includes draws = 50% |
|---|---|---|
| 2: Black win % | 61.10±1.79 | Includes draws = 50% |
| Draw % | 0.00 | Percentage of games where all players draw. |
| Decisive % | 100.00 | Percentage of games with a single winner. |
| Samples | 2887 | 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.
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 | 16.11 | |
|---|---|---|
| Branching factor | 46.31 | |
| Complexity | 10^25.41 | Based on game length and branching factor |
| Computational Complexity | 10^6.14 | Saturation reached - accuracy very high. |
| Samples | 2887 | Quantity of logged games played |
| Distinct actions | 6263 | Number of distinct moves (e.g. "e4") regardless of position in game tree |
|---|---|---|
| Killer moves | 51 | A 'killer' move is selected by the AI more than 50% of the time Killers: c6-d8x5,c10-d12x4,d11-e13x6,j11-i13x8,d8-c10x4,h3-j4x4,f2-h3x1,c8-d10x4,d13-b12x2,c10-a9x4,d12-c10x2,g4-e5x14,h12-j11x11,a6-b4x3,j6-l5x8,d5-f6x1,b5-a3x1,f13-e11x3,e6-f8x14,l5-j4x7,k4-j6x9,j10-i8x13,d3-f4x6,g3-h5x2,h11-i9x12,h8-g10x12,l8-j9x4,h13-j12x5,l6-k4x6,a9-b11x3,m9-k10x3,e4-g5x12,l7-m9x5,f12-d11x7,c6-e5x1,g4-i5x11,g4-i5x12,e10-f8x11,i10-h12x13,l9-m7x4,c5-e6x2,g3-f5x3,g11-i10x14,h13-i11x2,h6-j7x16,h5-f6x16,l7-m5x2,b12-d11x1,d4-e2x3,b8-c10x5,k4-m5x3 |
| Good moves | 1462 | A good move is selected by the AI more than the average |
| Bad moves | 4800 | A bad move is selected by the AI less than the average |
| Terrible moves | 3750 | A terrible move is never selected by the AI Terrible moves: e10-c9x9,j5-k7x2,j5-k7x5,j5-k7x4,j5-k7x7,j5-k7x6,e10-c9x1,e10-c9x2,b4-d5x2,e10-c9x3,b4-d5x1,e10-c9x4,e10-c9x5,e10-c9x6,e10-c9x7,e10-c9x8,g4-f6x11,g4-f6x12,g4-f6x10,b8-a10x1,b8-a10x2,i11-k10x4,i3-k4x1,i11-k10x7,i11-k10x6,i11-k10x9,i11-k10x8,c6-d8x4,c6-d8x3,c6-d8x2,l10-m12x1,d10-c12x3,d10-c12x6,d10-c12x7,f3-d4x3,f3-d4x5,f3-d4x4,i5-g4x13,h6-i8x16,h6-i8x15,h6-i8x14,h6-i8x13,h6-i8x12,h6-i8x11,i5-g4x10,h6-i8x10,i5-g4x11,i5-g4x12,e11-g12x5,e11-g12x4,k4-i5x1,k4-i5x3,k4-i5x2,c9-d7x2,c9-d7x5,c9-d7x7,c9-d7x6,c9-d7x9,c9-d7x8,h6-g4x16,h6-g4x15,h6-g4x12,h6-g4x11,k7-l5x11,k7-l5x12,k7-l5x10,i9-g10x14,i9-g10x12,i9-g10x18,i9-g10x16,i9-g10x17,i6-k7x11,i6-k7x10,i8-j6x15,i8-j6x16,i8-j6x13,i8-j6x14,j9-i11x11,i8-j6x17,j9-i11x13,j9-i11x14,i8-j6x11,i8-j6x12,i8-j6x10,d9-c7x10,d9-c7x11,e8-c7x6,e8-c7x9,l7-k9x3,l7-k9x2,e12-g11x8,e5-d7x10,h12-f13x2,h12-f13x3,e5-d7x13,e5-d7x12,e5-d7x11,e13-d11x3,e13-d11x2,h11-i13x4,h11-i13x7,h11-i13x8,h11-i13x9,e13-d11x1,d6-e4x10,j10-i12x11,j10-i12x12,j10-i12x10,i4-h6x2,j10-i12x13,i4-h6x3,k6-m5x6,k6-m5x2,k6-m5x3,k6-m5x4,k6-m5x5,k6-m5x1,g10-i9x12,g10-i9x13,g10-i9x10,g10-i9x16,g10-i9x17,g10-i9x14,g10-i9x15,d5-b6x4,d5-b6x3,d5-b6x2,d5-b6x1,h12-f13x4,h12-f13x5,h12-f13x6,h12-f13x7,e12-g11x5,e12-g11x7,e12-g11x6,d7-f6x1,d7-f6x5,d7-f6x4,d7-f6x3,d7-f6x2,d7-f6x9,d7-f6x8,d7-f6x7,d7-f6x6,f7-h6x10,f7-h6x11,j8-k6x8,j8-k6x7,j8-k6x6,j8-k6x5,j8-k6x4,j6-h7x10,f7-h6x13,g5-h3x6,g5-h3x7,g5-h3x8,g5-h3x9,g5-h3x3,g5-h3x5,l11-j12x2,l11-j12x3,l11-j12x4,l11-j12x6,l11-j12x7,f8-d9x14,f8-d9x13,m9-l11x1,f8-d9x12,f8-d9x11,f8-d9x16,f8-d9x15,c8-b6x2,c8-b6x1,f8-d9x10,i12-h10x1,b5-a7x2,b5-a7x1,g5-i6x7,g5-i6x6,g5-i6x3,e11-d13x7,e11-d13x6,e11-d13x9,e11-d13x8,e11-d13x5,j8-l9x3,j8-l9x4,j8-l9x5,j8-l9x6,j8-l9x7,j8-l9x8,g9-f7x9,h7-i9x3,i8-j10x17,i8-j10x16,i8-j10x15,i8-j10x14,d6-c4x4,i8-j10x13,d6-c4x1,i8-j10x12,i8-j10x11,d6-c4x3,i9-j7x14,i9-j7x13,e8-g9x13,i9-j7x16,i9-j7x18,i9-j7x17,e8-f10x9,e3-c4x4,e3-c4x6,e3-c4x7,e3-c4x1,e3-c4x2,e3-c4x3,h12-g10x12,h12-g10x11,h12-g10x10,k8-l6x4,k8-l6x5,k8-l6x2,k8-l6x6,k8-l6x7,f9-e11x8,f9-e11x7,f9-e11x6,f9-e11x9,g10-i9x5,g10-i9x8,e5-g4x9,e5-g4x8,e5-g4x7,e5-g4x6,e5-g4x5,e5-g4x4,f12-h13x2,f11-e9x9,f11-e9x8,f11-e9x7,f11-e9x6,f11-e9x4,i10-h12x4,i10-h12x5,i10-h12x8,i10-h12x9,h13-f12x2,h13-f12x3,h13-f12x1,j8-i10x11,j8-i10x10,d9-e7x6,d9-e7x7,d9-e7x8,d9-e7x9,d9-e7x5,k5-j3x2,k5-j3x3,k5-j3x1,k5-j3x4,c10-d12x3,c10-d12x2,c10-d12x1,j12-l11x2,h13-f12x6,h13-f12x7,h13-f12x4,h13-f12x5,h13-f12x8,h13-f12x9,h12-f11x6,h12-f11x7,h12-f11x8,h12-f11x9,g4-f2x3,g4-f2x1,h10-i8x9,h10-i8x7,g4-f2x9,h10-i8x8,g4-f2x8,h10-i8x5,g4-f2x7,h10-i8x6,g4-f2x6,g4-f2x5,g4-f2x4,h10-i8x2,h6-f5x7,h6-f5x5,e8-f10x16,k10-i11x8,k10-i11x7,k10-i11x6,e8-f10x15,k10-i11x5,j4-h5x2,j4-h5x1,f10-h11x13,f10-h11x12,f10-h11x11,f10-h11x10,e6-d8x12,e6-d8x11,e6-d8x14,e6-d8x13,l7-j6x8,l7-j6x9,e6-d8x10,l7-j6x6,l7-j6x7,l7-j6x4,l7-j6x5,l7-j6x2,l7-j6x3,g10-e11x7,g10-e11x9,g10-e11x8,g10-e11x5,f7-g9x15,f7-g9x14,f7-g9x13,f7-g9x12,l5-k3x5,f7-g9x11,l5-k3x4,f7-g9x10,l5-k3x7,l5-k3x6,l5-k3x1,l5-k3x3,l5-k3x2,b10-a8x1,b10-a8x2,b10-a8x3,b10-a8x4,g12-e11x10,h11-j10x10,b9-d8x4,b9-d8x3,b9-d8x2,h11-i13x10,i6-g5x12,f5-g3x2,f5-g3x3,i6-g5x14,i6-g5x13,h5-i7x10,h5-i7x11,h5-i7x12,f5-g3x8,h5-i7x13,f5-g3x9,h5-i7x14,f5-g3x6,h5-i7x15,f5-g3x7,h5-i7x16,f7-e5x10,f7-e5x12,f7-e5x11,f7-e5x14,f7-e5x13,f9-h10x7,f5-h6x8,f9-h10x9,f5-h6x6,f9-h10x4,g11-e10x9,g5-e4x11,g11-e10x8,f5-h6x4,f9-h10x6,g11-e10x7,g11-e10x6,g5-e4x10,b8-a6x5,b8-a6x4,b8-a6x1,b8-a6x3,b8-a6x2,i5-k6x12,i5-k6x11,i5-k6x13,f4-g6x1,f4-g6x2,f4-g6x5,f4-g6x4,h8-f9x4,f4-g6x7,f4-g6x6,h8-f9x7,h8-f9x8,h8-f9x9,d3-c5x1,h5-g3x15,h5-g3x16,h5-g3x10,h5-g3x13,h5-g3x14,h5-g3x11,h5-g3x12,j6-k8x10,i13-j11x4,i13-j11x3,i13-j11x2,i13-j11x1,d10-f11x8,d10-f11x9,d10-f11x5,h6-j5x10,h6-j5x11,h6-j5x12,h6-j5x13,h6-j5x14,h6-j5x15,h6-j5x16,h12-i10x3,h7-f8x14,i7-h5x6,h12-i10x2,h7-f8x13,h7-f8x12,h7-f8x11,i7-h5x9,h7-f8x16,h7-f8x15,e6-d4x3,h12-i10x7,h12-i10x5,h12-i10x4,e6-d4x7,e6-d4x6,e6-d4x5,e6-d4x4,e6-d4x9,e6-d4x8,f8-d7x5,f8-d7x4,f8-d7x8,f8-d7x7,f8-d7x6,e7-g6x6,e7-g6x9,i8-h10x4,e7-g6x5,d10-b9x6,d10-b9x4,d10-b9x3,d10-b9x2,d10-b9x1,l11-m9x5,l11-m9x6,l11-m9x3,l11-m9x4,l11-m9x7,l11-m9x1,i8-k7x9,k8-m9x3,k8-m9x1,d10-b9x8,d10-b9x7,k8-m9x4,d11-e13x1,d11-e13x4,d11-e13x5,d11-e13x2,d11-e13x3,i11-k12x3,f9-e7x6,i11-k12x5,f9-e7x8,i11-k12x4,f9-e7x9,i11-k12x7,i11-k12x6,i11-k12x9,i11-k12x8,f9-h10x11,f9-h10x10,f9-h10x13,f9-h10x12,f9-h10x15,f9-h10x16,f7-d8x10,f7-d8x12,f7-d8x11,f7-d8x14,f7-d8x13,d8-c6x3,d8-c6x8,d8-c6x7,d8-c6x4,f9-e7x14,f9-e7x13,f9-e7x12,f9-e7x11,e12-d10x3,f9-e7x10,i9-k8x12,e12-d10x7,i9-k8x11,e12-d10x6,e12-d10x5,e12-d10x4,e12-d10x8,f9-e7x17,f9-e7x16,f9-e7x15,i11-k12x10,g8-h6x19,c6-b4x2,c6-b4x3,c6-b4x1,e6-c5x11,g12-e11x7,g12-e11x5,e6-c5x10,i11-k12x11,h10-i12x8,c6-b4x4,h10-i12x9,g12-e11x8,g12-e11x9,g6-i7x10,e7-d9x10,e7-d9x11,e7-d9x12,d5-f4x7,f8-h7x16,d5-f4x6,f8-h7x14,d5-f4x8,f8-h7x13,h11-g9x8,h11-g9x6,h11-g9x9,d5-f4x2,d5-f4x5,d5-f4x4,j5-i3x3,j5-i3x4,f8-h7x12,f8-h7x11,f8-h7x10,f3-e5x3,f3-e5x1,g9-h11x8,d9-b10x11,d9-b10x10,m5-l7x1,m5-l7x2,j6-i4x10,m5-k4x1,k7-j5x5,k7-j5x6,j11-i13x9,d8-c10x5,d8-c10x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|
| Samples | 2887 | 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 5% of the game turns. Ai Ai found 1 critical turn (turns with only one good option).
Overall, this playout was 63.16% 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 | 5 |
|---|---|---|---|---|---|
| 1 | 2 | 154 | 8324 | 448307 | 20032766 |
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.
| Moves | Animation |
|---|---|
| g7-f9x1,g8-f10x13,g7-e8x13,f10-d9x8,e8-f6x7,d9-f8x4,g7-f5x3,g8-h6x4,f6-d7x4,h6-f7x2 |  |
| g7-f9x1,g8-f10x14,g7-e8x12,f10-d9x9,e8-g9x8,d9-f8x4,g7-h9x3,f8-h7x2,g9-f7x4,g8-e9x4 |  |
| g7-f9x1,g8-e9x10,g7-h9x4,e9-g10x5,g7-e8x12,g8-f10x5,e8-g9x9,g10-f8x2,g9-h7x3,e9-f7x2 |  |
| g7-f9x1,g8-e9x10,g7-h9x4,e9-g10x5,g7-e8x12,g8-f10x5,e8-g9x9,g10-f8x2,g9-h7x3,e9-f7x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x4,e9-g10x5,g7-e8x12,g8-f10x5,e8-g9x9,g10-f8x3,g9-h7x3,e9-f7x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x5,e9-g10x5,g7-e8x10,g8-f10x5,e8-g9x6,g10-f8x2,g9-h7x2,g8-i9x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x5,e9-g10x5,g7-e8x10,g8-f10x5,e8-g9x7,g10-f8x2,g9-h7x3,g8-i9x2 |  |
| g7-f9x1,g8-e9x10,g7-h9x5,e9-g10x5,g7-e8x10,g8-f10x5,e8-g9x7,g10-f8x2,g9-h7x3,e9-f11x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x6,e9-g10x5,g7-i8x8,g8-f10x5,h9-f8x3,e9-f11x4,i8-h6x4,f10-h11x2 |  |
| g7-f9x1,g8-e9x10,g7-h9x6,e9-g10x5,g7-i8x8,g8-f10x5,h9-f8x3,e9-f11x4,i8-h6x4,f10-h11x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x6,e9-g10x5,g7-i8x9,g8-f10x5,h9-f8x3,e9-f11x4,i8-g9x3,f10-h11x3 |  |
| g7-f9x1,g8-e9x10,g7-h9x7,e9-g10x5,g7-i8x8,g8-f10x5,h9-f8x3,e9-f11x4,i8-g9x2,f10-h11x2 |  |
| Puzzle | Solution |
|---|---|
 White to win in 3 moves | |
 White to win in 3 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.
