Full Report for Tumbleweed by Mike Zapawa

Full Report for Tumbleweed by Mike Zapawa

Settle the most spaces to win.

Generated at 21/02/2021, 03:07 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!

A stack is said to be seen from a hex, when they are connected by a straight line, with no stacks in between.The players take turns settling hexes by placing a stack of their tokens on a hex of their choice. The stack height is equal to the number of your stacks in sight of the settled hex.

Only hexes that see at least one of your stacks may be settled. Removing a stack occupying a hex and re-settling it with a new stack is possible, as long as the new stack is taller than the previous one. This works with opponent stacks (to capture), or your own stacks (to reinforce).

Before the game, the host sets up the board and the guest decides which side he wants to play. The recommended way of setting up the board is to put a stack of two neutral tokens in the center, and then give each player a single starting token in a cell of the host's choosing

The game ends when no more moves can be made by either player, or after two successive passes. The player who occupies over half the board wins.


General comments:

Play: Combinatorial

Family: Combinatorial 2020

Mechanism(s): Capture,Territory

BGG Stats

BGG EntryTumbleweed
BGG Rating9.11111
BGG Weight0

BGG Ratings and Comments

alekerickson10A drawless, stacking territorial game with elegant, simple rules and extraordinary depth. Many recent attempts have been made to apply the "line of sight" mechanic to a territorial game; this game somehow feels like the essential implementation of this goal. Best played on big boards, larger than hex 8. Physical play is not easy -- many stacking checkers are needed, which is a slight drawback. Still, the sleek architecture of this game being built around a single rule -- "settling" cells based on lines of sight to friendly pieces -- is reminiscent of great designs from the recent past, like Amazons, or Oust. Gameplay can be sharp, tactical, and deeply strategic. I can see this game developing a dedicated player community if it would be implemented on iggamecenter, little golem, or a similar site.
nconoan9Great game, with very simple logic but extremely complex meta game.
coldsalmon9A simple yet compelling game. Each piece has the potential to affect the entire board, so you will quickly find yourself concocting grand strategies. It's just a lot of fun.
michamund10My favorite abstract game design. Highly original and enticing. It feels like a giant world of intricate structures to discover all packed into an elegant gem that fits inside one's head – like it's tiny (and beautiful) on the outside and big (but gentle) on the inside. It lets you know that it is full of wonderful things to discover while still remaining approachable (not scary). This might be partly due to it's being quite suggestive – much more so than Go. I think it is much more pleasant to find one's way into the riches of this game than with other games of comparable depth.
le_4TC9Very elegant rules, and easy to learn for a beginner (especially online with automatic calculation of lines of sight). The elements of territory and life/death are reminiscent of Go, while the tactical implications of lines of sight have more in common with Amazons.
clark949A little confusing at first but wow did i enjoy this game.
Zapawa9I might well be biased, but it seems like Tumbleweed has robust strategies and tactics, very simple rules and a more than decent narrative potential. A rare combination indeed! It's one flaw is that it's very hard to play with a physical set, at least in the originally intended form (with stacks of tokens). However, playing with dice (number of pips indicates the height of a stack) is an acceptable alternative, plus it can be played online for free on multiple platforms

Kolomogorov Complexity Analysis

Size (bytes)29580
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 second2466.93 (405.36µs/playout)
Reference Size2141327.62 (0.47µs/playout)
Ratio (low is good)868.01

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 playout2,56318984,2287,04038460

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: Host win %50.65±3.10Includes draws = 50%
2: Guest win %49.35±3.09Includes draws = 50%
Draw %0.50Percentage of games where all players draw.
Decisive %99.50Percentage 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
2UCT (its=3)622182949340.6449 <= 0.6756 <= 0.704848.181.9349.89386.43
12UCT (its=13)621203529930.6050 <= 0.6354 <= 0.664850.252.0147.73380.23
UCT (its=14)
0.5085 <= 0.5395 <= 0.5702
UCT (its=14)
0.4775 <= 0.5085 <= 0.5394

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 length333.95 
Branching factor75.85 
Complexity10^591.05Based 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 actions172Number 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 Black (second)
Good moves124A good move is selected by the AI more than the average
Bad moves48A bad move is selected by the AI less than the average
Response distance6.81Mean 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 92.54% 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 30% of the game turns. Ai Ai found 3 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 moves35.0736.3133.82
Mean no. of effective moves11.0711.3410.80
Effective game space10^167.2110^83.1010^84.11
Mean % of good moves21.390.7042.34
Mean no. of good moves8.781.1716.49
Good move game space10^112.7410^3.6710^109.07

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 turns87.72%A hot turn is one where making a move is better than doing nothing.
Momentum27.25%% of turns where a player improved their score.
Correction39.52%% of turns where the score headed back towards equality.
Depth12.49%Difference in evaluation between a short and long search.
Drama0.98%How much the winner was behind before their final victory.
Foulup Factor3.29%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 change55.39%Distance through game when the lead changed for the last time.
Decisiveness2.69%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.)


i3,i2,Play White (first)
h6,k6,Play Black (second)
l6,k1,Play Black (second)
d12,l9,Play Black (second)
k12,i7,Play Black (second)
h14,d9,Play Black (second)
j2,h1,Play Black (second)
o5,d10,Play White (first)
c6,k9,Play Black (second)
g11,j2,Play Black (second)
b13,k2,Play White (first)

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 0.