Full Report for Dodo by Mark Steere

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!

INTRODUCTION

Dodo is a two player game played on a hexagonal grid of any size. The two players, Red and Blue, take turns moving their own checkers, one checker per turn, starting with Red. Players are not allowed to pass. Mark Steere designed Dodo in May, 2021.

MOVES

All moves are to unoccupied cells. Players can move their checkers one cell directly forward or diagonally forward. Unlike Chinese Checkers, there is no jumping or capturing in Dodo.

OBJECT OF THE GAME

If at the beginning of your turn you have no moves available, you win.

Miscellaneous

General comments:

Play: Combinatorial

BGG Stats

BGG Entry	Dodo
BGG Rating	null
#Voters	null
SD	null
BGG Weight	null
#Voters	null
Year	null

Kolomogorov Complexity Analysis

Size (bytes)	24361
Reference Size	10293
Ratio	2.37

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	66649.34 (15.00µs/playout)
Reference Size	597442.94 (1.67µs/playout)
Ratio (low is good)	8.96

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	39313690
State Space Complexity (log 10)	7.59
Confidence	29.26	0: totally unreliable, 100: perfect
Samples	739753

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	118,956	3,864	7,069,894	230,009	59	27
search.UCT	121,485	7,400			111	31

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 %	51.30±3.10	Includes draws = 50%
2: Black win %	48.70±3.09	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	255	886	0.6815 <= 0.7122 <= 0.7410	50.11	0.00	49.89	59.57
3	UCT (its=4)	631	0	355	986	0.6095 <= 0.6400 <= 0.6693	49.49	0.00	50.51	60.55
7	UCT (its=8)	631	0	345	976	0.6160 <= 0.6465 <= 0.6759	53.18	0.00	46.82	63.63
13	UCT (its=35)	631	0	152	783	0.7767 <= 0.8059 <= 0.8321	50.70	0.00	49.30	63.87
14	UCT (its=96)	631	0	259	890	0.6783 <= 0.7090 <= 0.7379	49.21	0.00	50.79	70.31
15	UCT (its=261)	631	0	248	879	0.6872 <= 0.7179 <= 0.7466	54.49	0.00	45.51	71.52
16	UCT (its=710)	631	0	234	865	0.6989 <= 0.7295 <= 0.7580	49.02	0.00	50.98	75.60
17	UCT (its=1929)	631	0	257	888	0.6799 <= 0.7106 <= 0.7395	47.64	0.00	52.36	84.13
18	UCT (its=5245)	631	0	247	878	0.6880 <= 0.7187 <= 0.7474	51.48	0.00	48.52	90.22
19	UCT (its=14256)	425	0	146	571	0.7070 <= 0.7443 <= 0.7784	54.12	0.00	45.88	93.69
20	UCT (its=14256)	506	0	494	1000	0.4750 <= 0.5060 <= 0.5369	53.60	0.00	46.40	98.83

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	105.81
Branching factor	6.54
Complexity	10^73.93	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

Board Size	37	Quantity of distinct board cells
Distinct actions	181	Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves	106	A good move is selected by the AI more than the average
Bad moves	74	A bad move is selected by the AI less than the average
Response distance%	43.63%	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 97.31% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean	105.81
Mode	[133]
Median	127.0

Change in Material Per Turn

Mean change in material/round	0.00	Complete round of play (all players)

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.)

Red: removal, Black: move, Blue: Add, Grey: pass, Purple: swap sides, Brown: other.

Trajectory

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 8% of the game turns. Ai Ai found 13 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	63.13	75.27	50.99
Mean no. of effective moves	3.31	3.58	3.04
Effective game space	10^37.97	10^19.26	10^18.71
Mean % of good moves	35.43	36.14	34.72
Mean no. of good moves	1.85	1.52	2.17
Good move game space	10^23.22	10^10.52	10^12.71

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	62.50%	A hot turn is one where making a move is better than doing nothing.
Momentum	17.31%	% of turns where a player improved their score.
Correction	28.85%	% of turns where the score headed back towards equality.
Depth	6.80%	Difference in evaluation between a short and long search.
Drama	5.26%	How much the winner was behind before their final victory.
Foulup Factor	38.46%	Moves that looked better than the best move after a short search.
Surprising turns	7.69%	Turns that looked bad after a short search, but good after a long one.
Last lead change	67.31%	Distance through game when the lead changed for the last time.
Decisiveness	35.58%	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.)

Openings

Moves	Animation
c4-d3,f3-e3,b5-c4,e5-d5,b4-b5,f5-e5,a4-b4,f4-f3
d2-d3,e4-e3,d3-e2,e3-d4,c3-d3,e5-d5,b3-c3
b5-c5,e4-d4,a7-b7,e5-e4,a6-a7,e4-e3,b4-b5
b5-c5,e5-d5,a7-b7,d5-d4,a6-a7,e4-e3,b4-b5
b6-c6,e4-e3,a7-b6,f4-e4,a6-a7,d6-d5,a5-a6
a7-b7,e4-d4,b5-c5,e5-e4,a6-a7,e4-e3,b4-b5
a7-b7,e5-d5,b5-c5,d5-d4,a6-a7,e4-e3,b4-b5
a7-b7,e4-e3,b7-c6,f4-e4,a6-a7,d6-d5,a5-a6
d2-e1,e4-e3,e1-e2,e3-d4,c3-d3,e5-d5,b3-c3
c4-d3,f3-e3,b5-c4,e5-d5,b4-b5,f5-e5,a4-b4
b6-b7,d6-c7,b7-c6,d7-d6,c4-d4,f2-f1
c4-d4,d6-c7,b6-c5,d7-d6,c5-c6,f2-f1

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

0	1	2	3	4	5	6	7	8	9
1	13	179	1478	10348	53403	244345	928041	3254289	9996598

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 9.

Puzzles

Puzzle	Solution
White to win in 27 moves
Black to win in 23 moves
White to win in 21 moves
Black to win in 7 moves
White to win in 13 moves
White to win in 13 moves
White to win in 5 moves
White to win in 7 moves
White to win in 3 moves
Black to win in 19 moves
Black to win in 15 moves
White to win in 13 moves

Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.