11 x 11 Domineering is Solved: The first player wins

We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. This enables the solution of known positions so far (up to the 10 x 10 board) much quicker (measured in number of investigated nodes). More importantly, it enables the solution of the 11 x 11 Domineering board, a board up till now far out of reach of previous Domineering solvers. The solution needed the investigation of 259,689,994,008 nodes, using almost half a year of computation time on a single simple desktop computer. The results show that under optimal play the first player wins the 11 x 11 Domineering game, irrespective if Vertical or Horizontal starts the game. In addition, several other boards hitherto unsolved were solved. Using the convention that Vertical starts, the 8 x 15, 11 x 9, 12 x 8, 12 x 15, 14 x 8, and 17 x 6 boards are all won by Vertical, whereas the 6 x 17, 8 x 12, 9 x 11, and 11 x 10 boards are all won by Horizontal

New Results for Domineering from Combinatorial Game Theory Endgame Databases

We have constructed endgame databases for all single-component positions up to 15 squares for Domineering, filled with exact Combinatorial Game Theory (CGT) values in canonical form. The most important findings are as follows. First, as an extension of Conway's [8] famous Bridge Splitting Theorem for Domineering, we state and prove another theorem, dubbed the Bridge Destroying Theorem for Domineering. Together these two theorems prove very powerful in determining the CGT values of large positions as the sum of the values of smaller fragments, but also to compose larger positions with specified values from smaller fragments. Using the theorems, we then prove that for any dyadic rational number there exist Domineering positions with that value. Second, we investigate Domineering positions with infinitesimal CGT values, in particular ups and downs, tinies and minies, and nimbers. In the databases we find many positions with single or double up and down values, but no ups and downs with higher multitudes. However, we prove that such single-component ups and downs easily can be constructed. Further, we find Domineering positions with 11 different tinies and minies values. For each we give an example. Next, for nimbers we find many Domineering positions with values up to *3. This is surprising, since Drummond-Cole [10] suspected that no *2 and *3 positions in standard Domineering would exist. We show and characterize many *2 and *3 positions. Finally, we give some Domineering positions with values interesting for other reasons. Third, we have investigated the temperature of all positions in our databases. There appears to be exactly one position with temperature 2 (as already found before) and no positions with temperature larger than 2. This supports Berlekamp's conjecture that 2 is the highest possible temperature in Domineering

Set Matching: An Enhancement of the Hales-Jewett Pairing Strategy

When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a coverage ratio of 2.0. In this paper we present a new strategy, called Set Matching. A matching set consists of a set of nodes (the markers), a set of possible winning lines (the groups), and a coverage set indicating how all groups are covered after every first initial move. This strategy needs less than two markers per group. As such it is able to prove positions in k-in-a-Row games to be draws, which cannot be proven using the Hales-Jewett pairing strategy. We show several efficient configurations with their matching sets. These include Cycle Configurations, BiCycle Configurations, and PolyCycle Configurations involving more than two cycles. Depending on configuration, the coverage ratio can be reduced to 1.14. Many examples in the domain of solving k-in-a-Row games are given, including the direct proof (without further investigation) that the empty 4 x 4 board is a draw for 4-in-a-Row

A Handbook for Elders and Overseers

Quaker Hill Pamphlet No. 2 Excerpt: The objective pursued in these pages has been to produce for elders and overseers in Friends meetings a body of literature which \u27is problem centered. The swiftly moving historical scene during the last generation has been the cause of immense and widespread confusion about the important spiritual testimonies which characterize the Christian life. The automobile. the radio, the motion picture-to mention only a few of the products of the last quarter-century-have had revolutionary effects upon society. The older Quaker communities have been rooted out of their former isolationism from the rest of the world where the Christian life as envisioned by Friends could be taught the young without interruption from the outside world. The vast population movements in the last twenty-five years have affected Friends as they have everyone else and have made us now veritable children of the dispersion in this modern world. Our homes suffer the shock and strain of modern life, as other homes do with the economic arrangements of our time that bring varying hours of employment during the night and day and split apart the activities of the members of the family who work, and, in addition, the multitudinous claims of present day society from outside the home that constantly intrude upon our families and tend to break them down. The two world wars in our generation have been successively more totalitarian \u27in their effects upon the life of the people. All these circumstances and more have shaken us to the foundations , and the bewilderment and confusion which beset the people in our churches is not of itself to be mistaken for any less earnest Christian desire on their part. The persons who occupy the positions of elders and overseers in our meetings are almost certainly as devoted and in many cases, as courageous-as any who have exercised these responsibilities in the past. But in the light of the present situation these people are in need of help by way of defining their responsibilities as elders and overseers in the light of contemporary situations, and illuminating their imagination with the momentous possibilities which their positions offer for meeting the human need in this present hour.https://digitalcommons.georgefox.edu/quakerbooks/1058/thumbnail.jp

Review of Kalah Game research and the proposition of a novel heuristic-deterministic algorithm compared to tree-search solutions and human decision-making

The Kalah game represents the most popular version of probably the oldest board game ever-the Mancala game. From this viewpoint, the art of playing Kalah can contribute to cultural heritage. This paper primarily focuses on a review of Kalah history and on a survey of research made so far for solving and analyzing the Kalah game (and some other related Mancala games). This review concludes that even if strong in-depth tree-search solutions for some types of the game were already published, it is still reasonable to develop less time-consumptive and computationally-demanding playing algorithms and their strategies Therefore, the paper also presents an original heuristic algorithm based on particular deterministic strategies arising from the analysis of the game rules. Standard and modified mini-max tree-search algorithms are introduced as well. A simple C++ application with Qt framework is developed to perform the algorithm verification and comparative experiments. Two sets of benchmark tests are made; namely, a tournament where a mid-experienced amateur human player competes with the three algorithms is introduced first. Then, a round-robin tournament of all the algorithms is presented. It can be deduced that the proposed heuristic algorithm has comparable success to the human player and to low-depth tree-search solutions. Moreover, multiple-case experiments proved that the opening move has a decisive impact on winning or losing. Namely, if the computer plays first, the human opponent cannot beat it. Contrariwise, if it starts to play second, using the heuristic algorithm, it nearly always loses. © 2020 by the authors.European Regional Development FundEuropean Union (EU); Ministry of Education, Youth and SportsMinistry of Education, Youth & Sports - Czech Republic [LO1303 (MSMT-7778/2014)]; internal grant agency of VSB Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, Czech Republic [SP2020/46

The Dynamics and Implications of the Coffee Economy in Tubah Sub-Division, 1934-2005

That the coffee economy in Tubah is at a development cul-de-sac and requires an overhaul is unquestionable. The article introduces the sustainable coffee challenge and the circumstances that made the sector unsustainable and suffered a decline in Tubah. It has been argued that coffee economy in Tubah was introduced as a substitute to the legitimate trade and owed its unsustainability and eventual decline to the outbreak of the economic crisis in the 1980s. Such argument is often pegged to the grievances of the poor angry farmers who were victims of the economic crisis and appear to have written off the benefits of the coffee sector on their livelihoods in the past. Contrary to such orthodox, this paper argues that the natural environment of Tubah alongside colonial influence provided the potential for the emergence of the coffee economy. It is further illustrated that coffee cultivation and commercialization mechanisms in Tubah evolved with time and circumstances. The lack of farm subsidies and the fall in the price of the commodity in the world market left the farmers in a state of dilemma. The paper also exposes the view that the coffee economy, in spite its constraints, resulted in beneficial socio-economic mutations in Tubah. A plethora of problems especially the economic crisis and the incessant exploitation of farmers by buying agents contributed in placing the coffee economy on a bad course. Using the case of the world’s coffee industry, the paper argues that coffee which was at the centre of Tubah economy had unprecedented implications on the wellbeing of the people prior to its gradual unsustainability and decline in the late 1990s. The reactivation of this sector, the paper suggests, requires short and long term measures that go beyond State action alone. Keywords: Dynamics, implications, economy, economic crisis, colonialism, Tuba

Women and the Superintendency

The purpose of this study was to determine whether past and present female superintendents in Colorado felt their career paths were gendered. In addition, what strategies they used to navigate their experiences were examined. A qualitative multi-case study design was used to structure this study. A social constructionism philosophy as described by Crotty (2003) guided the study. The multi-case design and epistemology support collecting multiple experiences within a phenomenon (Crotty, 2003). Participants were selected through purposeful snowball sampling. The community of female superintendents in Colorado is small and connected. This study included four retired female superintendents and five who are still currently serving in the role in Colorado. Qualitative data were drawn from three different resources. Interview transcripts, follow-up questions, and newspaper and website publications were gathered, analyzed, and coded for major themes. The data analysis suggested that female superintendents in Colorado have gendered experiences within their path towards and service within the superintendency. The findings regarding whether their experiences were gendered included themes of discrimination, gendered leadership expectations, and what motivated these nine women to pursue the superintendency. The first two were significant challenges for the women. To help navigate their way to the top, the nine women employed various strategies, including hard work, collaboration, and maintaining a strong support system. The participants felt as though they had to work harder to be noticed and had to do others\u27 dirty work at times. They relied heavily on collaborative working relationships with others, and they discussed the need to have a supportive team when reaching the top. The study has significance in helping aspiring female leaders understand the experiences and strategies of these nine female superintendents in Colorado who successfully attained the role that other women find difficult to reach. In Colorado, only about 30% of school district superintendents are female even though women make up the majority of the workforce in education (Carli & Eagly, 2016; CASE contact list; Fitzsimmons & Callan, 2016)