Full Report for Tixel by Martijn Althuizen

Full Report for Tixel 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 30/10/2020, 01:00 from 103852 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 2014,Tix

Mechanism(s): Stalemate

BGG Stats

BGG EntryTixel
BGG Rating7.125
BGG Weight2.6667

BGG Ratings and Comments

mrraow6For some reason, I find the strategy of this game; and forerunner Tix; eludes me. I probably need to be beaten by an expert a few times before I get it!
MartinusN/ASix 2x3 modular board tiles
HilkMAN8Very tentative rating - after one play, against the designer who wiped me out, I would say that I am very fascinated, though it lacks the great balance between simple play and deep thinking of Tix, being much more complicated. But that might be because I played Tix more than 100 times and Tixel only once so far. It will be hard to find more opponents for this, but I will keep my eyes open for an online version. .
Yuki Shimizu3
fogus5.5The game is stunningly simplistic and for that I give it a point outright. That said, I found the play repetitive though some nice patterns emerged naturally during play. I'd play again.
glanfamN/APlus Extra Tix pieces. Having trouble with the rules.
mroy9This game is really awesome. It has just a small set of rules, but endless possible strategies. What I especially like about this game is the extremely delicate balance between being in the lead of the game and having to react to your opponent's actions. A balance between being the hunter at one moment and becoming the prey just one or a few turns later. Or the other way around. YOU HAVE TO STAY FOCUSED!!! From start to finish. Because right at the moment when you think you can't lose a particular game, you'll make a very tiny little (and probably at a first glance insignificant) mistake and it's "bye bye victory" or you have to come up with some ingenious mastermind solution to fix it. And trust me, you will definitely make such a crucial mistake when you start getting overconfident. It's even very likely that you won't notice it immediately that you have made a wrong move. I've said multiple times to myself:"WTH!??? I've made a mistake somewhere in the game, but where and when??? I should have won this game, not him!!!" In short: an obviously trivial move, will turn out to be not that trivial at all. Another very interesting aspect of the game is this: The dilemma of reducing the space on the board to limit your opponents options, or make more space on the board to ensure you have enough room for yourself. Every single one of your decisions can work in favor or terribly against you. Tip: make smart use of the chaining rule as it might help you in turning a game in your favor. However the rules are fairly simple, it's a very deep game and I'm sure this game has a lot of undiscovered secrets in it. This game is a very nice example of how an already good game (Tix) can evolve, by just some minor changes, to a perfect game. I own the Nestorgames version of this game, which looks very nice. Thanks to the cotton carrying case, you can easily take it with you on a travel. Martijn, you hit it again. Thanks, man!!!
zefquaavius9Another marvel from Martijn! It's [thing=63339][/thing], but with the square shapes taking a perfect arc of concavity on one side, with the rules tweaked just enough to accommodate that. This adds just enough extra mind-warping to enhance the experience that bit more.

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 second8027.46 (124.57µs/playout)
Reference Size1991635.13 (0.50µs/playout)
Ratio (low is good)248.10

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 playout8,04349226,7241,1312812

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 %53.06±0.30Includes draws = 50%
2: Black win %46.94±0.30Includes draws = 50%
Draw %4.88Percentage of games where all players draw.
Decisive %95.12Percentage of games with a single winner.
Samples103852Quantity 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)63102538840.6831 <= 0.7138 <= 0.742652.830.0047.1729.62
7UCT (its=8)63103609910.6063 <= 0.6367 <= 0.666151.360.0048.6433.05
22UCT (its=23)62943449770.6153 <= 0.6459 <= 0.675250.870.4148.7242.67
UCT (its=56)
0.5789 <= 0.6095 <= 0.6393
UCT (its=56)
0.4671 <= 0.4980 <= 0.5289

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 length70.22 
Branching factor98.41 
Complexity10^104.26Based on game length and branching factor
Computational Complexity10^9.19Sample quality (100 best): 16.96
Samples103852Quantity 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 actions930588Number of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves3294A 'killer' move is selected by the AI more than 50% of the time
Too many killers to list.
Good moves71800A good move is selected by the AI more than the average
Bad moves858788A bad move is selected by the AI less than the average
Terrible moves827660A terrible move is never selected by the AI
Too many terrible moves to list.
Response distance4.30Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples103852Quantity of logged games played

Board Coverage

A mean of 68.52% 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 5% of the game turns. Ai Ai found 1 critical turn (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 moves78.8272.6585.35
Mean no. of effective moves63.9365.6162.15
Effective game space10^107.6210^55.5710^52.05
Mean % of good moves39.8759.6618.93
Mean no. of good moves26.8139.8912.97
Good move game space10^73.3710^52.3410^21.03

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 turns38.57%A hot turn is one where making a move is better than doing nothing.
Momentum7.14%% of turns where a player improved their score.
Correction28.57%% of turns where the score headed back towards equality.
Depth8.31%Difference in evaluation between a short and long search.
Drama11.57%How much the winner was behind before their final victory.
Foulup Factor65.71%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 change97.14%Distance through game when the lead changed for the last time.
Decisiveness40.00%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)


69216 solutions found at depth 3.



Black to win in 8 moves

White to win in 5 moves

Weak puzzle selection criteria are in place; the first move may not be unique.