Paintbucket is a flipping game of elimination for two players, White and Black.
Generated at 2023-06-18, 19:33 from 1000 logged games.
Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!
DEFINITION: A group is a maximal set of orthogonally adjacent like-colored pieces.
SETUP: Set up a chessboard using Reversi pieces in a checkered pattern.
GAMEPLAY: On your turn, flip an enemy group.
OBJECTIVE: Eliminate the enemy pieces.
General comments:
Play: Combinatorial
Family: Combinatorial 2022
Level: Standard
| BGG Entry | Paintbucket |
|---|---|
| BGG Rating | 7 |
| #Voters | 2 |
| SD | 0 |
| BGG Weight | 0 |
| #Voters | 0 |
| Year | 2022 |
| User | Rating | Comment |
|---|---|---|
| luigi87 | 7 | Opaque but impressively simple. |
| snth | N/A | Amazing game! Needs three reversi sets. Tedious to play in real life and works better as a video game. But still! Wow! |
| RichardIngram | 7 |
| Size (bytes) | 25372 |
|---|---|
| Reference Size | 10673 |
| Ratio | 2.38 |
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 | 283808.71 (3.52µs/playout) |
|---|---|
| Reference Size | 532282.96 (1.88µs/playout) |
| Ratio (low is good) | 1.88 |
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.
% new positions/bucket
| State Space Complexity | 49573303 | |
|---|---|---|
| State Space Complexity (log 10) | 7.70 | |
| Samples | 3653392 | |
| Confidence | 16.04 | 0: totally unreliable, 100: perfect |
State space complexity (where present) is an estimate of the number of distinct game tree reachable through actual play. Over a series of random games, Ai Ai checks each position to see if it is new, or a repeat of a previous position and keeps a total for each game. As the number of games increase, the quantity of new positions seen per game decreases. These games are then partitioned into a number of buckets, and if certain conditions are met, Ai Ai treats the number in each bucket as the start of a strictly decreasing geometric sequence and sums it to estimate the total state space. The accuracy is calculated as 1-[end bucket count]/[starting bucklet count]
| Label | Its/s | SD | Nodes/s | SD | Game length | SD |
|---|---|---|---|---|---|---|
| Random playout | 306,944 | 1,872 | 6,002,819 | 36,753 | 20 | 3 |
| search.UCT | 309,027 | 89,891 | 18 | 2 |
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 % | 50.20±3.09 | Includes draws = 50% |
|---|---|---|
| 2: Black win % | 49.80±3.09 | 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.
| Match | AI | Strong Wins | Draws | Strong Losses | #Games | Strong Score | p1 Win% | Draw% | p2 Win% | Game Length |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Random | |||||||||
| 1 | UCT (its=2) | 631 | 0 | 283 | 914 | 0.6597 <= 0.6904 <= 0.7195 | 47.70 | 0.00 | 52.30 | 19.88 |
| 15 | UCT (its=16) | 631 | 0 | 325 | 956 | 0.6294 <= 0.6600 <= 0.6894 | 49.90 | 0.00 | 50.10 | 20.96 |
| 34 | UCT (its=643) | 631 | 0 | 284 | 915 | 0.6589 <= 0.6896 <= 0.7188 | 49.51 | 0.00 | 50.49 | 21.76 |
| 36 | UCT (its=4749) | 631 | 0 | 317 | 948 | 0.6350 <= 0.6656 <= 0.6949 | 51.37 | 0.00 | 48.63 | 20.31 |
| 38 | UCT (its=35092) | 631 | 0 | 274 | 905 | 0.6665 <= 0.6972 <= 0.7263 | 48.40 | 0.00 | 51.60 | 17.81 |
| 39 | UCT (its=95391) | 599 | 0 | 401 | 1000 | 0.5683 <= 0.5990 <= 0.6289 | 54.90 | 0.00 | 45.10 | 17.56 |
| 40 | UCT (its=95391) | 490 | 0 | 510 | 1000 | 0.4591 <= 0.4900 <= 0.5210 | 49.00 | 0.00 | 51.00 | 17.75 |
Search for levels ended: time limit reached.
Level of Play: Strong beats Weak 60% of the time (lower bound with 95% confidence).
Draw%, p1 win% and game length may give some indication of trends as AI strength increases.
This chart shows the win(green)/draw(black)/loss(red) percentages, as UCT play strength increases. Note that for most games, the top playing strength show here will be distinctly below human standard.
| Game length | 22.38 | |
|---|---|---|
| Branching factor | 13.90 | |
| Complexity | 10^22.28 | Based on game length and branching factor |
| 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.
| Board Size | 64 | Quantity of distinct board cells |
|---|---|---|
| Distinct actions | 64 | Quantity of distinct moves (e.g. "e4") regardless of position in game tree |
| Good moves | 23 | A good move is selected by the AI more than the average |
| Bad moves | 41 | A bad move is selected by the AI less than the average |
| Response distance% | 40.21% | Distance from move to response / maximum board distance; a low value suggests a game is tactical rather than strategic. |
| Samples | 1000 | Quantity of logged games played |
A mean of 33.10% of board locations were used per game.
Colour and size show the frequency of visits.
Game length frequencies.
| Mean | 22.38 |
|---|---|
| Mode | [23] |
| Median | 23.0 |
| Mean change in material/round | 0.00 | Complete round of play (all players) |
|---|
This chart is based on a single representative* playout, and gives a feel for the change in material over the course of a game. (* Representative in the sense that it is close to the mean length.)
Table: branching factor per turn, based on a single representative* game. (* Representative in the sense that it is close to the mean game length.)
This chart is based on a single representative* game, and gives a feel for the types of moves available throughout that game. (* Representative in the sense that it is close to the mean game length.)
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 22% of the game turns. Ai Ai found 8 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 | 73.91 | 89.33 | 58.49 |
| Mean no. of effective moves | 11.41 | 12.82 | 10.00 |
| Effective game space | 10^17.08 | 10^9.84 | 10^7.25 |
| Mean % of good moves | 21.17 | 20.08 | 22.27 |
| Mean no. of good moves | 3.09 | 4.55 | 1.64 |
| Good move game space | 10^5.41 | 10^4.16 | 10^1.26 |
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 | 63.64% | A hot turn is one where making a move is better than doing nothing. |
| Momentum | 9.09% | % of turns where a player improved their score. |
| Correction | 18.18% | % of turns where the score headed back towards equality. |
| Depth | 5.81% | Difference in evaluation between a short and long search. |
| Drama | 0.69% | How much the winner was behind before their final victory. |
| Foulup Factor | 27.27% | Moves that looked better than the best move after a short search. |
| Surprising turns | 9.09% | Turns that looked bad after a short search, but good after a long one. |
| Last lead change | 50.00% | Distance through game when the lead changed for the last time. |
| Decisiveness | 54.55% | Distance from the result being known to the end of the game. |
These figures were calculated over a single representative* game, and based on the measures of quality described in "Automatic Generation and Evaluation of Recombination Games" (Cameron Browne, 2007). (* Representative, in the sense that it is close to the mean game length.)
| Moves | Animation |
|---|---|
| Flip b5,Flip e3,Flip e6,Flip e1 |  |
| Flip e6,Flip e3,Flip b5,Flip e1 |  |
| Flip e2,Flip c3,Flip g8,Flip b4 |  |
| Flip g8,Flip c3,Flip e2,Flip b4 |  |
| Flip d1,Flip h2,Flip h5 |  |
| Flip f1,Flip b8,Flip e6 |  |
| Flip c2,Flip b8,Flip d7 |  |
| Flip e2,Flip h2,Flip f5 |  |
| Flip e2,Flip c3,Flip g8 |  |
| Flip c4,Flip a7,Flip a2 |  |
| Flip f5,Flip f8,Flip g6 |  |
| Flip h5,Flip h2,Flip d1 |  |
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 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 32 | 976 | 15256 | 212578 | 1986596 | 16659559 |
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 6.
| Puzzle | Solution |
|---|---|
 White to win in 15 moves | |
 White to win in 13 moves | |
 White to win in 9 moves | |
 White to win in 9 moves | |
 White to win in 11 moves | |
 Black to win in 9 moves | |
 White to win in 11 moves | |
 Black to win in 9 moves | |
 Black to win in 9 moves | |
 White to win in 9 moves | |
 Black to win in 9 moves | |
 White to win in 7 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.
