Generated at 28/10/2020, 06:03 from 128787 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!
On each turn, a player places a single stone of his/her own colour into any empty cell; once placed, stones never move.
Play continues until the board is full or both players pass, at which point the game is scored. Any group of own-colour stones has a score equal to the number of exo-stones (stones lying outside the grid) that it contains. The owner of the highest scoring group wins.
If there is a tie for highest scoring group, then the tied groups are set aside and the remaining groups are compared; the owner of the highest scoring group among the remaining groups wins. If these groups are also tied, then the process is repeated (that is, the tied groups are set aside and the remaining groups compared) until a winner results. (It is impossible for group scores to be tied "all the way down.")
The Pie Rule applies: After Player 1 plays the first stone to the board, Player 2 can decide whether to play his/her own colour to the board, or alternatively, switch colours with Player 1.
Family: Combinatorial 2019
Mechanism(s): Scoring,Strict Placement
|alekerickson||8||A wonderful addition to the canon of hex-hex connection games. Preceded by close relative Global Connection.|
|mrraow||7||Good connection game; but it does seem like most hex strategies can be applied so to me ExoHex feels a more like a hex variant than a game in its own right.|
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.
|Playouts per second||93422.15 (10.70µs/playout)|
|Reference Size||413992.96 (2.42µs/playout)|
|Ratio (low is good)||4.43|
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.
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.
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.
|1: Player 1 (Black) win %||50.58±0.27||Includes draws = 50%|
|2: Player 2 (White) win %||49.42±0.27||Includes draws = 50%|
|Draw %||1.83||Percentage of games where all players draw.|
|Decisive %||98.17||Percentage of games with a single winner.|
|Samples||128787||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.
|Match||AI||Strong Wins||Draws||Strong Losses||#Games||Strong Score||p1 Win%||Draw%||p2 Win%||Game Length|
|2||UCT (its=3)||610||41||272||923||0.6524 <= 0.6831 <= 0.7123||47.78||4.44||47.78||127.92|
|9||UCT (its=10)||619||24||347||990||0.6069 <= 0.6374 <= 0.6667||48.59||2.42||48.99||127.81|
|15||UCT (its=16)||623||15||357||995||0.6033 <= 0.6337 <= 0.6630||49.25||1.51||49.25||128.97|
|23||UCT (its=24)||622||18||283||923||0.6529 <= 0.6836 <= 0.7128||49.84||1.95||48.21||128.03|
|30||UCT (its=31)||621||20||350||991||0.6063 <= 0.6367 <= 0.6661||47.93||2.02||50.05||127.41|
|38||UCT (its=39)||624||14||328||966||0.6226 <= 0.6532 <= 0.6826||49.28||1.45||49.28||128.28|
|46||UCT (its=47)||620||21||358||999||0.6008 <= 0.6311 <= 0.6605||49.25||2.10||48.65||128.10|
|55||UCT (its=56)||624||13||363||1000||0.6001 <= 0.6305 <= 0.6599||49.40||1.30||49.30||128.39|
0.5941 <= 0.6245 <= 0.6540
0.4676 <= 0.4985 <= 0.5294
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.
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.
|Samples||128787||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.
|Distinct actions||null||Number of distinct moves (e.g. "e4") regardless of position in game tree|
|Measure||All players||Player 1||Player 2|
|Mean % of effective moves||20.25||19.89||20.61|
|Mean no. of effective moves||3.50||3.62||3.38|
|Effective game space||10^42.79||10^23.68||10^19.12|
|Mean % of good moves||30.66||23.81||37.50|
|Mean no. of good moves||18.63||7.61||29.66|
|Good move game space||10^86.80||10^29.72||10^57.08|
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.
|Hot turns||64.06%||A hot turn is one where making a move is better than doing nothing.|
|Momentum||23.44%||% of turns where a player improved their score.|
|Correction||40.62%||% of turns where the score headed back towards equality.|
|Depth||3.24%||Difference in evaluation between a short and long search.|
|Drama||4.94%||How much the winner was behind before their final victory.|
|Foulup Factor||10.94%||Moves that looked better than the best move after a short search.|
|Surprising turns||0.78%||Turns that looked bad after a short search, but good after a long one.|
|Last lead change||82.03%||Distance through game when the lead changed for the last time.|
|Decisiveness||6.25%||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.)
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.
No solutions found to depth 3.