Verge is a two-player strategy game played on an initially empty hexhex board.
Generated at 2024-10-27, 06:43 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!
The players take turns placing a stone of their color on an empty hex. The first player unable to place a stone has won.
A partitioning group is a group separating two hexes outside the group, in the sense that all paths between the two hexes go through the group.
You're not allowed to place adjacent to a friendly partitioning group.
When a group becomes partitioning, remove all nonpartitioning groups adjacent to it.
The game is balanced with the pie rule: One player decides what player 1's first placement will be, and the other player decides whether to play as player 1 or player 2.
This is a good game, but it's not really for me. I felt like there weren't a lot moments of action considering how many moves we made (~80).
CoreyClark
9
A game unfortunately very close to my own incomplete game, Maelstrom. Oh well, you snooze, you lose.
RichardIngram
8
Kolomogorov Complexity Analysis
Size (bytes)
26380
Reference Size
10915
Ratio
2.42
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
60087.13 (16.64µs/playout)
Reference Size
518860.58 (1.93µs/playout)
Ratio (low is good)
8.64
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.
State Space Complexity
% new positions/bucket
State Space Complexity
144555454
State Space Complexity bounds
64808262 < 144555454 < ∞
State Space Complexity (log 10)
8.16
State Space Complexity bounds (log 10)
7.81 <= 8.16 <= ∞
Samples
1006001
Confidence
0.00
0: totally unreliable, 100: perfect
State space complexity (where present) is an estimate of the number of distinct game tree reachable through actual play. Over a series of random games, Ai Ai checks each position to see if it is new, or a repeat of a previous position and keeps a total for each game. As the number of games increase, the quantity of new positions seen per game decreases. These games are then partitioned into a number of buckets, and if certain conditions are met, Ai Ai treats the number in each bucket as the start of a strictly decreasing geometric sequence and sums it to estimate the total state space. The accuracy is calculated as 1-[end bucket count]/[starting bucklet count]
Playout/Search Speed
Label
Its/s
SD
Nodes/s
SD
Game length
SD
Random playout
77,005
176
5,119,060
11,566
66
8
search.UCT
75,913
1,234
71
9
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: Player 1 win %
48.70±3.09
Includes draws = 50%
2: Player 1 win %
51.30±3.10
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
53.56
0.00
46.44
66.59
5
UCT (its=6)
631
0
360
991
0.6063 <= 0.6367 <= 0.6661
50.96
0.00
49.04
68.10
18
UCT (its=19)
631
0
345
976
0.6160 <= 0.6465 <= 0.6759
53.18
0.00
46.82
70.07
29
UCT (its=30)
631
0
352
983
0.6114 <= 0.6419 <= 0.6713
50.15
0.00
49.85
72.55
43
UCT (its=44)
631
0
354
985
0.6102 <= 0.6406 <= 0.6700
49.75
0.00
50.25
73.36
61
UCT (its=166)
631
0
154
785
0.7746 <= 0.8038 <= 0.8301
52.74
0.00
47.26
68.77
62
UCT (its=451)
631
0
246
877
0.6889 <= 0.7195 <= 0.7482
50.86
0.00
49.14
68.71
63
UCT (its=1225)
631
0
271
902
0.6688 <= 0.6996 <= 0.7286
50.11
0.00
49.89
67.47
64
UCT (its=3330)
631
0
362
993
0.6050 <= 0.6354 <= 0.6648
53.58
0.00
46.42
67.57
65
UCT (its=9053)
221
0
181
402
0.5009 <= 0.5498 <= 0.5977
49.25
0.00
50.75
69.34
66
UCT (its=9053)
519
0
481
1000
0.4880 <= 0.5190 <= 0.5498
50.10
0.00
49.90
71.98
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
71.70
Branching factor
28.50
Complexity
10^92.66
Based on game length and branching factor
Computational Complexity
10^7.57
Sample quality (100 best): 1.74
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
Board Size
61
Quantity of distinct board cells
Distinct actions
63
Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Killer moves
1
A 'killer' move is selected by the AI more than 50% of the time Killers: Swap
Good moves
19
A good move is selected by the AI more than the average
Bad moves
43
A bad move is selected by the AI less than the average
Response distance%
52.01%
Distance from move to response / maximum board distance; a low value suggests a game is tactical rather than strategic.
Samples
1000
Quantity of logged games played
Board Coverage
A mean of 89.58% of board locations were used per game.
Colour and size show the frequency of visits.
Game Length
Game length frequencies.
Mean
71.70
Mode
[70]
Median
72.0
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 4% of the game turns. Ai Ai found 2 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
60.59
61.96
59.21
Mean no. of effective moves
11.42
17.72
5.11
Effective game space
10^58.73
10^38.89
10^19.84
Mean % of good moves
41.10
0.32
81.89
Mean no. of good moves
6.08
0.19
11.97
Good move game space
10^30.22
10^0.85
10^29.38
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
72.22%
A hot turn is one where making a move is better than doing nothing.
Momentum
25.00%
% of turns where a player improved their score.
Correction
23.61%
% of turns where the score headed back towards equality.
Depth
1.08%
Difference in evaluation between a short and long search.
Drama
0.00%
How much the winner was behind before their final victory.
Foulup Factor
11.11%
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
13.89%
Distance through game when the lead changed for the last time.
Decisiveness
19.44%
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.
Openings
Moves
Animation
e2,Swap,h2,g6,b8,h5
g6,Swap,h2,e2,b8,h5
e2,Swap,h5,d3,b5,e8
d3,Swap,h5,e2,b5,e8
b5,Swap,h4,e8,b8,h2
b5,Swap,b8,e8,h4,h2
e8,Swap,h4,b5,b8,h2
e8,Swap,b8,b5,h4,h2
e2,Swap,h5,d3,b5
d3,Swap,h5,e2,b5
b5,Swap,h4,e8,b8
b5,Swap,b8,e8,h4
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
4
1
61
3782
115412
3354512
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 4.
Puzzles
Puzzle
Solution
Player 1 (White) to win in 14 moves
Player 2 (White) to win in 14 moves
Player 2 (White) to win in 12 moves
Weak puzzle selection criteria are in place; the first move may not be unique.
