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The article offers information about two Hex tournaments held in 2018 Computer Olympiad in New Taipei, Taiwan and discusses the two contestants for each tournament: Deepezo from Japan, supervised by Masahito Yamamoto; and Mohex-3hnn from Canada, supervised by Ryan Hayward. Author also includes development of self-play game procedure by Chao Gao and Jakub Pawlewicz used for selecting the opening moves.

Kriegspiel Hex (aka. DarkHex) is a variant of Hex in which players do not see the opponent's stones. Due to incomplete information, there exist boards for which neither player has a (pure) winning strategy. The main contribution of this paper is a classification of small boards based on the outcome of the game for optimal players; (i) first player can win, (ii) second player can win, or (iii) neither player can win. For boards without winner, optimal players must follow mixed strategies that maximize their winning probabilities. In this context, solving the game means computing the corresponding Nash Equilibrium (NE). This paper provides then a brief introduction on how to compute these NEs and some preliminary results are given for the 4 × 3 board. [ABSTRACT FROM AUTHOR]

The game of Hex can be played on multiple boardsizes. Transferring neural net knowledge learned on one boardsize to other boardsizes is of interest, since deep neural nets usually require large size of high quality data to train, whereas expert games can be unavailable or difficult to generate. In this paper we investigate neural transfer learning in Hex. We show that when only boardsize independent neurons are used, the resulting neural net obtained from training on one base boardsize can effectively generalize – without fine-tuning – to multiple target boardsizes, larger or smaller. When transferring to larger boardsizes, fine-tuning provides faster learning and better performance. The strength of the transferable network can be amplified with search: with a single neural net model trained on games from a base boardsize, we obtain players stronger than MoHex 2.0 on multiple target boardsizes. [ABSTRACT FROM AUTHOR]

The article discusses the 2017 Olympiad's Hex tournaments. Participants of the tournament include Hexcited by Ma Shengjie from China, Ezo-CNN by Kei Takada from Japan, and MoHex by various authors from Canada, such as Broderick Arneson and Philip Henderson. An overview of the performance of each participants is also given in which the tournaments are won by Ezo-CNN.

In this paper, we study three connection games among the most widely played: havannah , twixt , and slither . We show that determining the outcome of an arbitrary input position is PSPACE -complete in all three cases. Our reductions are based on the popular graph problem generalized geography and on hex itself. We also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is W[1] -hard, short hex is FPT . Finally, we prove that the ultra-weak solution to the empty starting position in hex cannot be fully adapted to any of these three games. [ABSTRACT FROM AUTHOR]

Recently, Pawlewicz and Hayward successfully solved many Hex openings based on the Scalable Parallel Depth-First Proof-Number Search algorithm (SPDFPN), which was performed in a single machine with multiple threads. However, further parallelization is limited by the number of cores a single machine can possess. This article investigates adapting this SPDFPN solver to a distributed computing environment, using the previously proposed job-level upper-confidence tree algorithm (JL-UCT) in order to further increase parallelism. To improve on the adapted JL-UCT solver system, we make a new attempt to support transposition information sharing among jobs in JL implementations on top of a JL framework. A mix of shared-memory and database techniques was used to achieve this improvement. Our experiments show that the adapted JL-UCT solver is able to solve positions faster as the number of cores increases. Additionally, using a single machine with 24 cores, the adapted method is able to solve Hex openings with less time than the previous SPDFPN solver in four of five test cases. Overall, for the five test cases, the adapted JL-UCT solver, using 6 nodes each with 24 cores, obtained speedups of 1.6 to 2.6 over those for the SPDFPN solver using one node with 24 cores. [ABSTRACT FROM AUTHOR]

Over the past few decades, the image of war and the U.S. military in popular entertainment has waxed and waned along with the (un)popularity of specific conflicts. This essay explores the evolving role of the "hex" board game and the videogame genre of the military-themed shooter in maintaining positive portrayals of the U.S. military and war more generally within U.S. popular culture. In particular, these videogames are considered as both a remediated and interactive version of the Hollywood combat film and as virtual spaces where citizens can experience combat, interact with history, and become immersed in a larger militarized culture. [ABSTRACT FROM AUTHOR]

The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and the Brouwer fixed point theorem, and Baryshnikov showed that the impossibility theorem by Chichilnisky and the Arrow impossibility theorem are very similar. Thus, Chichilnisky and Baryshnikov are precedents for the result—linking the Arrow impossibility theorem to a fixed point theorem. [ABSTRACT FROM AUTHOR]

The article discusses the random-turn hex game, which involves two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. It requires the players to toss a coin before each turn to decide who gets to place the next stone rather than alternating turns. Its optimal strategy is very simple and a player wins by completing a path connecting the two opposite sides of his or her color. Details about the description of random-turn selection games are provided.

Abstract: Gale [D. Gale, The game of HEX and the Brouwer fixed-point theorem, American Mathematical Monthly 86 (1979) 818–827] has shown that the so called HEX game theorem that any HEX game has one winner is equivalent to the Brouwer fixed point theorem. In this paper we will show that under some assumptions about marking rules of HEX games, the HEX game theorem for a 6×6 HEX game is equivalent to the Duggan–Schwartz theorem for strategy-proof social choice correspondences [J. Duggan, T. Schwartz, Strategic manipulability without resoluteness or shared beliefs: Gibbard–Satterthwaite generalized, Social Choice and Welfare 17 (2000) 85–93] that there exists no social choice correspondence which satisfies the conditions of strategy-proofness, non-imposition, residual resoluteness, and has no dictator. [Copyright &y& Elsevier]

The game Whex is here defined, which is similar to Generalized Hex but the players are restricted to colour vertices adjacent to the vertex last coloured by one of the players. It is shown that the problem of deciding existence of winning strategies for one of the players in this game is complete for PSPACE, via quantifier free projections, and that the extension of first order logic with the corresponding generalized quantifier captures PSPACE and verifies a normal form. This problem is used to show that the problem of finding a proof in a proof system, like propositional resolution, in which the user is allowed to introduce auxiliary statements in order to help the system reach the theorem that he had set it to prove, is also complete for PSPACE via quantifier free projections. Also, it is established the complexity of the game Whex when restricted to graphs of outdegree at most 3, and, as a generalized quantifier, its expressive capabilities in the absence of ordering relation. [ABSTRACT FROM PUBLISHER]

The article focuses on the Hex Uniqueness Theorem according to which hex board cannot be colored such that winning conditions are satisfied for both players.