Full Report for Linear Pursuit by Stuart Ralph

Full Report for Linear Pursuit by Stuart Ralph

A chesslike game, played on the perimeter of a circle.



Capture your opponent's Masterpiece to win.

You also win if your opponent has no legal moves.


Each turn, either:

Bringing a piece into play

Move one of your pieces from the outer ring, to the space immediately in front iof it, in the inner ring. The inner space must be empty.


There are three types of piece:

Pieces may end in either an empty space or one occupied by an enemy piece. If the space is occupied, the enemy piece is captured.


General comments:

Play: Combinatorial

Family: Chess

Mechanism(s): Movement,Capture

BGG Stats

BGG EntryLinear Pursuit
BGG Rating8.75
BGG Weight0

BGG Ratings and Comments

thenexusgame9Travel set. Really slick little abstract. Seems simple on the face of it, but is really challenging to play. Only complaint is there should be three sizes of pieces, not four (to make it easier to distinguish them from each other).
mrraow8Attractive chesslike game with simple components. The topology is surprisingly complex for such a small board, so it takes a few games to get your head around the movement to the point where you're not making silly mistakes..
GeekenN/A3KS 2022
HastingsGameStudios9An abstract concept that's easy to pick up but hard to master. Plenty of strategy and richness to the game very much like chess.

Levels of Play

AIWins vs prev levelDrawsLosses#GamesWin%
Rαβ + ocqBKs (t=v0.01s)360036100.00
Rαβ + ocqBKs (t=v0.07s)33603992.31

Level of Play: strong beats weak 60% of the time (lower bound with 90% confidence).

Kolomogorov Complexity Estimate

Size (bytes)24200
Reference Size10328

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

Playouts per second95237.19 (10.50µs/playout)
Reference Size1645819.62 (0.61µs/playout)
Ratio (low is good)17.28

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.

Win % By Player (Bias)

1: White win %65.55±3.00Includes draws = 50%
2: Black win %34.45±2.88Includes draws = 50%
Draw %18.10Percentage of games where all players draw.
Decisive %81.90Percentage of games with a single winner.
Samples1000Quantity 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.

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.


Game length49.04 
Branching factor9.16 
Complexity10^45.46Based on game length and branching factor
Samples1000Quantity of logged games played

Move Classification

Distinct actions137Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves58A good move is selected by the AI more than the average
Bad moves78A bad move is selected by the AI less than the average
Samples1000Quantity of logged games played

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.


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 66% of the game turns. Ai Ai found 1 critical turn (turns with only one good option).

Overall, this playout was 100.00% hot.

Position Heatmap

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.

Action Types 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.

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)


2 solutions found at depth 3.