Full Report for HexSymple(19x19, group penalty=12) by Christian Freeling

Full Report for HexSymple(19x19, group penalty=12) by Christian Freeling

Have the highest score at the end of the game.

Generated at 20/02/2021, 01:13 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!


Each turn, either:


When the board is full, you score as follows:
{Stones placed} - k x {number of groups}
Where k is a multiple of 4 chosen at the start of the game.


General comments:

Play: Combinatorial

Mechanism(s): Connection,Pattern

Components: Board

BGG Stats

BGG EntryHexSymple(19x19, group penalty=12)
BGG Rating7.97
BGG Weight0

BGG Ratings and Comments

mrraow8Clever territory game; the branching factor is brutal, so don't expect a strong AI!
RichardV8.5Great abstract game that distils something of the essence of Go and Hex with very simple rules. There are several distinct phases to the game, from early proliferation, to later block expansion, and then a final push to consolidate groups. The java ai on ai ai is pretty good to get started.
milomilo122N/AA beautiful idea that doesn't quite work as a game for me, because too many stones need to be placed on a single turn. When I have to place 8 stones on a turn in a deep game like this, it's a recipe for titanic analysis paralysis.
orangeblood8This is a very interesting design with mechanics that I've not seen before. You could call it a Go variant, but I think it’s less like Go than Blooms, for example (where territory and captures matter). As concisely as I can explain, on your turn you either place a single stone to start a new group, or add one stone to each of your existing groups. When the board is filled you score one point per stone, minus a predetermined number (e.g., 6 points) for every group you have. If you’re somewhat dense like me it will take you a few of plays to begin to understand the delicate early-game balance between starting new groups, vs. switching gears and adding to existing ones. The math tells you that the more groups you have the more stones you’ll eventually be able to add… and yet the higher group penalty points at the end. That brings up the entire strategy of positioning your stones — where Go-like play is generally rewarded. For instance, it’s nice if you could join up groups toward the end to avoid penalty points, or deny your opponent the same…. and to have staked out some territory to give your groups room to grow. Co-designed by Christian Freeling and Benedikt Rosenau, Christian says it’s one of only six games of his that he considers relevant. Or, as he also says, in as much as abstract games matter, this one matters.
Zapawa8This game should have been created thousands of years ago and been played as a classic ever since. It's versatile, simple, sharp and very original. Sadly, it's only 10 years old and quite obscure at this point, but I hope it's time of glory comes within my lifetime. For all my admiration for the idea, I enjoyed the reality of it far less than I thought I would -- I'm just too dumb to appreciate the strategies here. Might increase the rating if I ever learn to play it properly.

Kolomogorov Complexity Analysis

Size (bytes)33297
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 second1853.14 (539.62µs/playout)
Reference Size372286.96 (2.69µs/playout)
Ratio (low is good)200.90

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

LabelIts/sSDNodes/sSDGame lengthSD
Random playout1,93916525,5364,4572710

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)

1: White win %48.10±3.08Includes draws = 50%
2: Black win %51.90±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.

UCT Skill Chains

MatchAIStrong WinsDrawsStrong Losses#GamesStrong Scorep1 Win%Draw%p2 Win%Game Length
1UCT (its=2)63103459760.6160 <= 0.6465 <= 0.675951.740.0048.26271.00
6UCT (its=7)63103389690.6206 <= 0.6512 <= 0.680550.150.0049.85271.00
UCT (its=11)
0.5441 <= 0.5750 <= 0.6053
UCT (its=11)
0.4731 <= 0.5040 <= 0.5349

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.


Game length271.01 
Branching factor59.02 
Complexity10^394.63Based on game length and branching factor
Samples1000Quantity 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.

Move Classification

Distinct actions272Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves82A good move is selected by the AI more than the average
Bad moves190A bad move is selected by the AI less than the average
Response distance9.08Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples1000Quantity of logged games played

Board Coverage

A mean of 100.00% 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.)


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.

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 2.