Players alternate placing pieces until the board is full or both pass. The player with the group that connects most colors is the winner.
Generated at 31/07/2021, 05:04 from 1000 logged games.
Rules
Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!
On each turn, a player plays a single stone of his/her color to any empty cell; once placed, stones do not move. Play continues until the board is full or until both players pass in succession. The pie rule applies (that is, once the first stone is played, the second player can opt to switch colors with his/her opponent).
A group of same-color stones has a value equal to the number of border colors it touches. (Note that a stone in the cell where two colors meet touches both of those colors). At the end of the game, each player identifies his/her highest-valued group. The player whose highest-valued group is highest is the winner. In case of tie, each player identifies his/her highest-valued group among the groups other than the two tied groups that were just compared; highest value wins. This process is repeated until the tie is broken. Draws are not possible.
A worthy attempt to generalize the Hex-board connection genre.
russ
6
Hex grid connection game -- experience with Hex, Havannah, Cross, etc seems very helpful for basic tactics. For me, the scoring didn't add enough interest -- I'd rather play Havannah or Hex. cf. Starweb, which uses different scoring but also encourages you to make a big group connecting to multiple parts of the edge.
mrraow
7
Good connection game, most hex strategies still apply.
cackleton2
N/A
A connection game where the goal is to create the group that connects the most sides of the board, if there is a tie, compare the next most-side-connecting groups until a winner emerges. The scoring is done when the board is full or when a player resigns. I would play on a hexhex board using its 6 sides as the sides used for scoring.
TumbleSteak
N/A
Also try the Sivannah variant. You can also win by forming a loop.
pezpimp
8
You play one pieces each turn in an attempt to link link as many sides as you can game with a continuous set of pieces. We also played a variant where you can win by creating a loop. The strategy to ensure your links don't break is fairly straightforward but as you both have the same goal it is a give and take which I tend to give more than I take. We played a variant where you play three pieces and based on a die roll you get two of them and your opponent gets one, sure it adds luck but I found in a game where the mechanics are so straight forward this add a nice playful element and quite enjoyed it with that varient rather than simply playing a pieces with a back and forth reactive mechanic.
ThorSilver
9
A top-notch connection game with a characteristic that's rather rare in this genre: a pop of colour! I've written about it here: https://drericsilverman.wordpress.com/2020/03/12/connection-games-v-side-stitch/
cdunc123
8
(Full disclosure: I am the designer. I consider it part of my "Outer Rim Trilogy" along with Iris and Exo-Hex. ) A simple game that I find brain burny (in a good way). Slight worry that skilled play might eventually reveal that most opening placements are swap-worthy, so that the range of balanced initial placements is smaller than I'd like. But that's a hypothetical issue as of yet, and in any case I'm confident that there will be enough balanced initial placements to permit an interesting variety of play, even among experts.
Kolomogorov Complexity Analysis
Size (bytes)
34477
Reference Size
10293
Ratio
3.35
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 second
60532.32 (16.52µs/playout)
Reference Size
492077.55 (2.03µs/playout)
Ratio (low is good)
8.13
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
Label
Its/s
SD
Nodes/s
SD
Game length
SD
Random playout
107,053
794
18,199,039
134,978
170
12
search.UCT
46,073
1,041
166
24
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 %
56.80±3.09
Includes draws = 50%
2: Black win %
43.20±3.04
Includes draws = 50%
Draw %
0.00
Percentage of games where all players draw.
Decisive %
100.00
Percentage of games with a single winner.
Samples
1000
Quantity 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
Match
AI
Strong Wins
Draws
Strong Losses
#Games
Strong Score
p1 Win%
Draw%
p2 Win%
Game Length
0
Random
1
UCT (its=2)
631
0
366
997
0.6025 <= 0.6329 <= 0.6623
53.16
0.00
46.84
169.95
6
UCT (its=7)
631
0
366
997
0.6025 <= 0.6329 <= 0.6623
52.16
0.00
47.84
169.56
17
UCT (its=18)
631
0
306
937
0.6427 <= 0.6734 <= 0.7027
49.31
0.00
50.69
169.97
23
UCT (its=24)
631
0
357
988
0.6082 <= 0.6387 <= 0.6680
50.10
0.00
49.90
170.40
31
UCT (its=32)
631
0
352
983
0.6114 <= 0.6419 <= 0.6713
56.26
0.00
43.74
170.95
39
UCT (its=40)
631
0
327
958
0.6281 <= 0.6587 <= 0.6880
50.94
0.00
49.06
170.09
48
UCT (its=49)
631
0
354
985
0.6102 <= 0.6406 <= 0.6700
51.57
0.00
48.43
168.94
55
UCT (its=56)
631
0
332
963
0.6247 <= 0.6552 <= 0.6846
51.40
0.00
48.60
169.17
56
UCT (its=56)
515
0
485
1000
0.4840 <= 0.5150 <= 0.5459
48.50
0.00
51.50
169.00
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.
Complexity
Game length
173.08
Branching factor
84.45
Complexity
10^311.23
Based on game length and branching factor
Samples
1000
Quantity 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 actions
171
Number of distinct moves (e.g. "e4") regardless of position in game tree
Good moves
91
A good move is selected by the AI more than the average
Bad moves
80
A bad move is selected by the AI less than the average
Response distance
5.50
Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples
1000
Quantity of logged games played
Board Coverage
A mean of 99.64% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
173.08
Mode
[173]
Median
173.0
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.)
Actions/turn
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.)
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 11% of the game turns. Ai Ai found 7 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
Measure
All players
Player 1
Player 2
Mean % of effective moves
35.45
34.22
36.69
Mean no. of effective moves
10.46
9.64
11.29
Effective game space
10^90.97
10^43.88
10^47.08
Mean % of good moves
26.22
47.61
4.59
Mean no. of good moves
12.40
18.97
5.76
Good move game space
10^89.35
10^72.72
10^16.63
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
Measure
Value
Description
Hot turns
73.99%
A hot turn is one where making a move is better than doing nothing.
Momentum
21.39%
% of turns where a player improved their score.
Correction
31.79%
% of turns where the score headed back towards equality.
Depth
2.27%
Difference in evaluation between a short and long search.
Drama
1.81%
How much the winner was behind before their final victory.
Foulup Factor
11.56%
Moves that looked better than the best move after a short search.
Surprising turns
0.00%
Turns that looked bad after a short search, but good after a long one.
Last lead change
35.26%
Distance through game when the lead changed for the last time.
Decisiveness
5.20%
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.)
Swap Heatmap (Full Scan)
Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.
Based on 100 trials/move at 0.1s thinking time each.
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.
Swap Heatmap (Historic)
Colour shows the frequency of swaps on turn 2 if this move is played on turn 1; black < red < yellow < white.
Size shows the frequency this move is played.
Unique Positions Reachable at Depth
0
1
2
3
1
169
28730
2427854
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.
