Full Report for Pinch by Craig Duncan

Full Report for Pinch by Craig Duncan

An orthogonal connection game.



On each turn, a player must place a single own-stone on any empty point. If as a direct result of the placement, a player has two own-stones that are orthogonally adjacent to an enemy stone at a right angle, then that enemy stone is converted to an own-stone.

If the newly converted stone creates conditions for a similar capture, then that capture takes place immediately, and so on in a chain reaction. A capturing pair (i.e. the two own-stones that bring about a capture of an enemy stone) must contain at least one newly placed or newly converted stone, otherwise no capture takes place.


A player's goal is to connect his/her two same-coloured board sides with a group of orthogonally-connected stones of his/her colour.

Capture variant

In the variant of Pinch in which captured stones are removed (rather than flipped to the opposite colour), on the next turn, a player cannot play a stone into the cell just vacated by a captured stone.


General comments:

Play: Combinatorial

Family: Combinatorial 2019

Mechanism(s): Connection

Components: Board

BGG Stats

BGG EntryPinch
BGG Rating0
BGG Weight0

Levels of Play

AIStrong WinsDrawsStrong Losses#GamesStrong Win%p1 Win%Game Length
Grand Unified UCT(U1-T,rSel=s, secs=0.01)360036100.0044.44104.72
Grand Unified UCT(U1-T,rSel=s, secs=0.03)36023894.7450.0093.61
Grand Unified UCT(U1-T,rSel=s, secs=0.07)360114776.6057.4581.13
Grand Unified UCT(U1-T,rSel=s, secs=0.20)36044090.0045.0067.55
Grand Unified UCT(U1-T,rSel=s, secs=0.55)36094580.0037.7861.71

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)27256
Reference Size10293

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 second17301.34 (57.80µs/playout)
Reference Size363081.84 (2.75µs/playout)
Ratio (low is good)20.99

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 (Black) win %48.70±3.09Includes draws = 50%
2: Player 2 (White) win %51.30±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.

Playout/Search Speed

LabelIts/sSDNodes/sSDGame lengthSD
Random playout23,6451593,409,18922,88514414

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.


Game length84.29 
Branching factor127.37 
Complexity10^176.07Based on game length and branching factor
Computational Complexity10^7.35Sample quality (100 best): 33.04
Samples1000Quantity of logged games played

Move Classification

Distinct actions170Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves83A good move is selected by the AI more than the average
Bad moves87A 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 33% of the game turns. Ai Ai found 0 critical turns (turns with only one good option).

Overall, this playout was 54.55% 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)

No solutions found to depth 3.