Full Report for Carteso by Luis Bolaños Mures,Corey L. Clark

Full Report for Carteso by Luis Bolaños Mures,Corey L. Clark

Carteso is a finite territory game for two players: Vertical and Horizontal.



A group is a maximal set of like-colored, orthogonally connected stones.

A group, regardless of color, is owned by Vertical if it spans more rows than columns, and by Horizontal if it spans more columns than rows. Groups that span exactly as many rows as columns are owned by the opponent of the player who most recently placed a stone on the board.

To claim a group is to place a marker of yours on top of one of its stones.

A group is finished if its vertical and horizontal dimensions can't grow larger by means of any series of placements on empty points.


Vertical plays first, then turns alternate. On their turn, a player must either pass or place one stone of any color on an empty point. After a placement, every unclaimed finished group is claimed by its current owner.

The game ends when both players pass consecutively. A player's score is the total number of stones on the board in groups that they have claimed, plus a komi in the case of Horizontal. The player with the highest score wins.


The komi is the number of points which is added to Horizontal's score at the end of the game as a compensation for playing second. Before the game starts, the first player chooses the value of komi, and then the second player chooses sides. To avoid ties, it is suggested that komi be of the form n + 0.5, where n is a whole number.


General comments:

Play: Combinatorial

Family: Combinatorial 2016

Mechanism(s): Territory

Components: Board

BGG Stats

BGG EntryCarteso
BGG Rating6.75
BGG Weight0

BGG Ratings and Comments

luigi879My and Corey Clark's game.
mrraow7Interesting, but I found myself frustrated with this game. I _really_ wanted to own a colour.

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0050.0076.53
Grand Unified UCT(U1-T,rSel=s, secs=0.03)36033992.3135.9071.51
Grand Unified UCT(U1-T,rSel=s, secs=0.07)36054187.8048.7870.63
Grand Unified UCT(U1-T,rSel=s, secs=0.20)36023894.7450.0083.76
Grand Unified UCT(U1-T,rSel=s, secs=0.55)360036100.0061.1182.39

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.

Kolomogorov Complexity Estimate

Size (bytes)27145
Reference Size10577

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 second5581.80 (179.15µs/playout)
Reference Size676681.55 (1.48µs/playout)
Ratio (low is good)121.23

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: Player 1 win %46.30±3.07Includes draws = 50%
2: Player 2 win %53.70±3.10Includes draws = 50%
Draw %0.00Percentage of games where all players draw.
Decisive %100.00Percentage 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 length79.64 
Branching factor83.91 
Complexity10^139.32Based on game length and branching factor
Samples1000Quantity of logged games played

Move Classification

Distinct actions176Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves1A 'killer' move is selected by the AI more than 50% of the time
Killers: Play Vertical
Good moves93A good move is selected by the AI more than the average
Bad moves83A 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 37% of the game turns. Ai Ai found 4 critical turns (turns with only one good option).

Overall, this playout was 89.41% 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.

Positions Reachable at Depth (Includes Transpositions)


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.
Zobrist hashes are not available for this game, so transpositions are included in the counts.

Shortest Game(s)


22 solutions found at depth 4.



Vertical (p1) 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.