Full Report for Pippinzip(zipline) by Craig Duncan,João Pedro Neto,Bill Taylor

Rules

Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!

THE BASIC IDEA

The game begins with an auction phase -- a sort of mini-game of chicken (reminiscent of the game Unlur), in which the board is gradually seeded with a growing number of initial stones. The auction phase determines who will play the role of "Pip" (using black stones) and who plays the role of "Zip" (using white stones).

After the auction phase ends and the roles are thereby determined, the players take turns playing stones of their color to the board. Play continues until a winning condition is reached. (Draws are impossible.) Pip wins by connecting any TWO opposite sides of the board via a chain of orthogonally-adjacent black stones. Zip wins connecting all FOUR sides of the board via a chain of 8-way-adjacent white stones. ("8-way-adjacent" = either orthogonally or diagonally adjacent.)

IN MORE DETAIL

Pipline

Immediately after "take" is announced, the non-taker (i.e. Zip) has his/her turn and places a single white stone, followed by a single black stone from Pip, then a single white stone from Zip, etc. Turns alternate in this fashion until one player achieves his/her win condition (or until one player resigns). Zip wins by connecting all FOUR sides of the board with a chain of white stones that are orthogonally and/or diagonally adjacent; Pip wins by connecting any TWO opposite sides with a chain of black stones that are orthogonally adjacent.

Zipline

This is an alternative version of the game. To start the game, on each turn a player places 1-3 WHITE stones in the auction phase. (Each player has a free choice of whether to place 1 white stone, or 2 white stones, or 3 white stones on his/her turn.) Players alternate turns, playing white stones exclusively in this phase of the game, until one player on his/her turn says "take" instead of placing any stones. This taker is henceforth known as "Zip" and on future turns Zip will play a SINGLE white stone per turn. The opponent is known as "Pip." On future turns, Pip will play TWO black stones per turn, with the following restriction: Pip's second black stone of a given turn is NOT allowed to be placed orthogonally adjacent to the first black stone of the turn. (Placing two diagonally adjacent black stones in the same turn IS allowed. Also, note that in the extremely rare case where ALL remaining empty cells are orthogonally adjacent to first black stone, the second black stone is forfeited.)

Immediately after "take" is announced, the non-taker (i.e. Pip) has his/her turn and plays two black stones, followed by a single white stone played by Zip, then two black stones from Pip, then a single white stone from Zip, etc. Turns alternate in this fashion until one player achieves his/her win condition (or until one player resigns). Zip wins by connecting all FOUR sides of the board with a chain of white stones that are orthogonally and/or diagonally adjacent; Pip wins by connecting any TWO opposite sides with a chain of black stones that are orthogonally adjacent.

NOTE: In either version of the game (Pipline or Zipline), if during the auction phase a player creates the win condition for the color being used in the auction, then that player wins the game. (However, this won't happen if both player play competently!)

Not implemented in Ai Ai: Zipline can also be played as a 3 player game. In 3 player Zipline, the taker plays as Zip and the two non-takers play as a single Pip team. Each non-taker plays a single black stone on his/her turn, for a total of two black stones for Pip for every one white stone for Zip. Roles are determined in the auction phase using the same process described for 3 player Unlur in this thread.

"Freestyle" Zipline Variant: For variety you can play with free placement for Pip's two black stones, that is, with no ban on orthogonally adjacent placements.

Miscellaneous

General comments:

Play: Combinatorial

Family: Combinatorial 2020

Mechanism(s): Connection

BGG Stats

BGG Ratings and Comments

Kolomogorov Complexity Analysis

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.

Playout Complexity Estimate

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.

Playout/Search Speed

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.

Mirroring Strategies

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.

Win % By Player (Bias)

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.

UCT Skill Chains

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.

1st Player Win Ratios by Playing Strength

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.

Complexity

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.

Move Classification

Board Coverage

A mean of 37.69% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Change in Material Per Turn

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.)

Actions/turn

Table: branching factor per turn, based on a single representative* game. (* Representative in the sense that it is close to the mean game length.)

Action Types per Turn

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.

Trajectory

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 18% of the game turns. Ai Ai found 1 critical turn (turns with only one good option).

Position Heatmap

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

Good/Effective moves

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.

Quality Measures

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.)

Opening Heatmap

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

Size shows the frequency this move is played.

Unique Positions Reachable at Depth

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.

Shortest Game(s)

No solutions found to depth 3.