Full Report for Regatta by Martijn Althuizen

Full Report for Regatta by Martijn Althuizen

The Tix family of games have common rules, but different piece mixes. The objective is to deprive your opponent of moves by deactivating their active pieces.

Generated at 29/10/2020, 19:37 from 22807 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!


The full rules are long and complex. I suggest reading the rules at the Nestorgames web site if you are not fully familiar with them.


  • An active piece can move.
  • If you have at least one active piece on the board, you can add pieces.
  • After your first move, if you have no active pieces at the start of your turn, you lose.
  • Visually, an active piece is rotated diagonally so its corners are outside the board squares.
  • An inactive piece cannot move.
  • Visually, an inactive piece is aligned with the board squares.


The following actions are available at the start of a turn:

Add a piece to the board; after your first move you can only do this if you already have at least one active piece. The piece must physically fit on the board without overlapping another piece.
Slide an active piece orthogonally; it may inactivate pieces that it passes, and may end in an inactive state. If the sliding piece ends in an inactive state, you get a bonus move.

Bonus moves:

Add a piece to the board.
Remove a piece from the board.
As above. This can trigger another bonus action, and so on.
Rotate an inactive piece so it is active.
Re-orient a Tixel or Regatta piece so it is visually different.


Bounded/Unbounded board
In Tix and Tixel (but not Regatta), the edge of the board is unbounded by default, meaning that pieces can protrude beyond the edge of the board. There is an option to play with the board bounded, making the edgesmore deadly; this is recommended only for board sizes 8 or larger.
In Poka Yoke, the first two pieces you remove from the board are promoted from Tixel pieces to Regatta pieces.


Played only with Tix pieces (simple squares).


Played only with Tixel pieces (one hollow edge).


Played only with Regatta pieces (one hollow edge, one rounded corner). The board edge is bounded.

Poka Yoke

Played only with Tixel pieces (one hollow edge). Promotions are allowed.

Game End

If you cannot move on your turn, you lose.


General comments:

Play: Combinatorial

Family: Combinatorial 2015,Tix

Mechanism(s): Stalemate

Components: Board

BGG Stats

BGG EntryRegatta
BGG Rating8.66667
BGG Weight4

BGG Ratings and Comments

Sokpuppet9A fascinating design.
mrraow7I would enjoy this more, but I have a great deal of trouble visualising the moves :(
FiveStars10What I really like of his games is that you can start with Tix, then go on to Tixel then to Regatta increasing the challenge step by step.

Kolomogorov Complexity Analysis

Size (bytes)39329
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 second773.64 (1292.59µs/playout)
Reference Size2070393.37 (0.48µs/playout)
Ratio (low is good)2676.17

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 playout7841837,2343274827

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.

Heuristic Values

This chart shows the heuristic values thoughout a single representative* game. The orange line shows the difference between player scores. (* Representative, in the sense that it is close to the mean game length.)

Win % By Player (Bias)

1: White win %51.38±0.65Includes draws = 50%
2: Black win %48.62±0.65Includes draws = 50%
Draw %0.02Percentage of games where all players draw.
Decisive %99.98Percentage of games with a single winner.
Samples22807Quantity 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
2UCT (its=3)63102448750.6905 <= 0.7211 <= 0.749849.710.0050.2952.84
5UCT (its=6)631036910000.6006 <= 0.6310 <= 0.660451.100.0048.9062.21
UCT (its=12)
0.5915 <= 0.6220 <= 0.6515
UCT (its=12)
0.4880 <= 0.5190 <= 0.5498

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 length63.59 
Branching factor227.05 
Complexity10^139.49Based on game length and branching factor
Samples22807Quantity 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 actions3451654Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves8117A 'killer' move is selected by the AI more than 50% of the time
Too many killers to list.
Good moves113873A good move is selected by the AI more than the average
Bad moves3337781A bad move is selected by the AI less than the average
Terrible moves3324319A terrible move is never selected by the AI
Too many terrible moves to list.
Response distance5.20Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples22807Quantity of logged games played

Board Coverage

A mean of 75.22% 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.


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 1% of the game turns. Ai Ai found 6 critical turns (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

MeasureAll playersPlayer 1Player 2
Mean % of effective moves90.4686.7394.68
Mean no. of effective moves211.56212.09210.97
Effective game space10^142.2610^74.0210^68.24
Mean % of good moves37.7347.4926.66
Mean no. of good moves98.75146.2644.90
Good move game space10^83.4510^56.3110^27.14

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

Hot turns62.50%A hot turn is one where making a move is better than doing nothing.
Momentum15.62%% of turns where a player improved their score.
Correction34.38%% of turns where the score headed back towards equality.
Depth0.52%Difference in evaluation between a short and long search.
Drama1.51%How much the winner was behind before their final victory.
Foulup Factor73.44%Moves that looked better than the best move after a short search.
Surprising turns0.00%Turns that looked bad after a short search, but good after a long one.
Last lead change-1.56%Distance through game when the lead changed for the last time.
Decisiveness93.75%Distance from the result being known to the end of the game.

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)


11808 solutions found at depth 2.