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185:. It is a zero-learning based algorithm, as in AlphaZero, but with novelties: boardsize invariance thanks to fully convolutional neural networks (as in U-Net) and global pooling. This allows growing architectures, meaning the program can learn on a small board, and then extrapolate on a large board.
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Cazenave, Tristan; Chen, Yen-Chi; Chen, Guan-Wei; Chen, Shi-Yu; Chiu, Xian-Dong; Dehos, Julien; Elsa, Maria; Gong, Qucheng; Hu, Hengyuan; Khalidov, Vasil; Li, Cheng-Ling; Lin, Hsin-I; Lin, Yu-Jin; Martinet, Xavier; Mella, Vegard; Rapin, Jeremy; Roziere, Baptiste; Synnaeve, Gabriel; Teytaud, Fabien;
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techniques resulting in some notable improvement in playing strength. The "Havannah
Challenge 2012" was held October 15–19, 2012 during which Freeling played ten games against three of the strongest Havannah-playing programs available, playing (at least) one game as black and one as white against
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In 2002 Freeling offered a prize of 1000 euros, available through 2012, for any computer program that could beat him in even one game of a ten-game match. For many years, computer programs lagged far behind human players. However, since 2010 several
Havannah-playing programs have applied
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Unlike in Hex, in
Havannah draws are technically possible, in practice they are extremely rare. There has been one known draw between human players. Tactics are much easier to master than strategy, and differences in playing level are considerable.
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In Hex, when the board is completely filled, exactly one player will have a winning connection; in
Havannah a completely filled board will have usually more than one winning structures (but the game ends with first winning structure).
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An example of all three winning combinations is shown above. The structure in the centre of the board is a ring; the structure on the left-hand side is a fork; the structure on the right-hand side is a bridge.
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and is based on using ring-threats to represent the geography graph. In detail, since
Lichtenstein and Sipser have proved that generalized geography remained PSPACE-hard even if the graph is only
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is generally implemented for fairness. This rule allows the second player to choose whether to switch positions with the first player after the first player makes the first move.
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Players of different strength can still play an interesting game when the weaker player (as white) is allowed to place two or more stones on the first turn.
212:, it only remains to construct an equivalent Havannah position from such a graph, which is accomplished by constructing various gadgets in Havannah.
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A player wins when they complete one of three different structures from unbroken lines, or paths, of connected stones, all of their colour:
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Teytaud, Olivier; Ye, Shi-Cheng; Ye, Yi-Jun; Yen, Shi-Jim; Zagoruyko, Sergey (2020-01-27). "Polygames: Improved Zero
Learning".
73:. Havannah has "a sophisticated and varied strategy" and is best played on a base-10 hexagonal board, 10 hex cells to a side.
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and several universities), won four times in a row on the board of size 8 against the human player with the best ELO rank on
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One player plays as black; the other plays as white. White starts, after which moves alternate. The rules are as follows:
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192:. It is played on a base-8 board and sometimes also on a base-10 board. During this competition the pie rule is used.
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each opponent. Freeling lost the challenge when he had to resign a game with white against the
Lajkonik program.
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is a loop around one or more cells (no matter whether the encircled cells are occupied by any player or empty);
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Examples of the three winning structures in
Havannah, on a base-8 board. From left to right, they are the
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This result was achieved by the same program as the one used for beating best humans at
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375:"Open-sourcing Polygames, a new framework for training AI bots through self-play"
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424:. The 8th Intl. Conf. on Computers and Games. Keio University, Yokohama, Japan.
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Until 2019, the best humans were still by far stronger than computers. However,
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with respect to the size of the input graph. The proof is by a reduction from
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Since the first player to move in
Havannah has a distinct advantage, the
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Bonnet, Édouard; Jamain, Florian; Saffidine, Abdallah (14 August 2013).
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http://www.mindsports.nl/index.php/arena/havannah/49-havannah-rules
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This article is about the board game. For the
English village, see
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Each player places one stone of their color on the board per turn.
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Stones are never moved, captured, or otherwise changed.
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Handscomb, Kerry, ed. (Winter 2002). "Front Cover".
61:. It belongs to the family of games commonly called
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178:, who was also the winner of various tournaments.
76:The game was published for a period in Germany by
339:"Human against Computer: 7-3 - Press release"
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172:Facebook Artificial Intelligence Research
300:, John Wiley & Sons, Inc., pp.
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422:Havannah and TwixT are PSPACE-complete
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188:Havannah is a recurring game at the
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210:bipartite and of degree at most 3
357:, Facebook Incubator, 2020-05-28
290:Schmittberger, R. Wayne (1992),
504:Board games introduced in 1981
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247:(12). Carpe Diem Publishing.
440:10.1007/978-3-319-09165-5_15
276:As clarified by Freeling at
354:facebookincubator/Polygames
298:New Rules for Classic Games
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140:Difference compared to Hex
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454:"Jeux & stratégie 09"
196:Computational complexity
65:; its relatives include
509:Abstract strategy games
160:Monte Carlo tree search
22:Havana (disambiguation)
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20:. For other uses, see
206:generalized geography
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223:Jeux & Stratégie
200:Solving Havannah is
519:Ravensburger games
59:Christian Freeling
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18:Havannah, Cheshire
190:Computer Olympiad
153:Computer Havannah
52:abstract strategy
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498:Categories
406:2001.09832
384:2020-05-29
361:2020-05-29
293:"Havannah"
231:References
168:MetaTotoro
84:Game rules
55:board game
431:1403.6518
266:Hexboards
253:1492-0492
485:Havannah
476:Havannah
131:pie rule
48:Havannah
39:and the
216:Reviews
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302:116–17
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110:bridge
41:bridge
35:, the
426:arXiv
401:arXiv
71:TwixT
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183:Hex
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