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The endgame stage of Go presents a unique challenge for scientific research. Contrary to previous stages, in the endgame the key to a successful analysis is board decomposition into smaller, independent local positions. Go players typically analyze these positions separately and prioritize moves based on their value. In this paper, I introduce a novel program that automates this decomposition-based analysis for the endgame stage of Go. AlphaZero has revolutionized Computer Go, by applying a generic move-selection mechanism, based on neural network judgments and the MCTS search algorithm. However, it does not specifically address the complexity of endgame in the aforementioned manner. On the other hand, by leveraging the decomposition-based analysis, my program reaches decisions in the endgame with relatively little computation. Additionally, it offers insights for Go practitioners by providing accurate move value evaluations. Notable prior work on automated endgame analysis was done by Martin Müller (1995). His program Explorer checked all possible variations in every undecided position and aggregated the results based on an algorithm inspired by the Combinatorial Game Theory (CGT). However, due to the exponential growth of the number of variations, Explorer’s application was limited to small, tightly bounded local positions. In contrast, my program leverages a neural network to predict optimal local moves, dramatically reducing the number of variations that need to be explored. Provided that the neural network’s predictions are correct, the program can accurately evaluate move values by considering relatively few variations, just like human Go experts do. Thanks to this approach, it is the first program capable of analyzing large, unbounded local positions, which are commonly encountered in real games. The neural network was fine-tuned from a pre-trained AlphaZero reimplementation on the task of optimal local move prediction. Training data was gathered from KataGo self-play games, utilizing KataGo’s network to perform board decomposition.

Pairing players during a Go tournament is a complex task. One must register the players, pair them using a pairing system, gather the results and display the information to the players. Several standalone programs offer these functionalities, however they are often game-specific and maintained and developed by a single person. The pairing itself is non-trivial, because of different pairing systems and of many parameters influencing them. This creates challenges for an intuitive user interface which can be used by non-experts tournament organizers. In this article, Pairgoth is presented, a new pairing software inspired from Opengotha, a mainstream Go pairing software heavily used in Europe. Several improvements have been added to the pairing algorithm, which has also been made more generic. New pairing systems can easily be implemented in Pairgoth. Although initially designed for Go, it can easily be used for other games such as Chess, Shogi or Scrabble. Pairgoth consists of a pairing engine coupled with a web-based user interface. This allows management of the tournament from several machines, including smartphones. It already supports Swiss and MacMahon pairing systems, while more options are currently under development (Round-Robin, accelerated Swiss, Amalfi, …). Pairgoth was tested in real conditions at the international Grenoble tournament (TIGGRE 2024, 5 rounds Mac-Mahon tournament with top group and super top-group, 158 players from 29k to 7d) and at international Paris tournament (51st TIP, 6 rounds Mac-Mahon tournament with top-group, 160 players from 30k to 8d). Pairgoth was also successfully used during the 2024 European Go Congress in Toulouse, where nearly a thousand players participated. It was used for the prestigious main tournament as well as the majority of the side tournaments. It was recently used in the 2024 KPMC edition, making Pairgoth used in several countries. On top of presenting Pairgoth, this article also tackles challenges encountered in pairing engines such as deterministic randomness, non-uniqueness of pairings, and the computation of fair standing criteria.

This article presents findings from a classroom-based research project examining the innovative integration of the ancient board game Go in third-grade classrooms within a suburban U.S. school district. The study involved six teachers and over 100 students. In Phase 1, the Go teacher provided six weekly on-site lessons and four monthly lessons in Phase 2. Each lesson consisted of approximately 10-15 minutes of instruction and 20 minutes of gameplay. The research sought to answer three key questions: 1) What adaptations are necessary for implementing Go as a game-based learning tool in classrooms? 2) What natural opportunities for learning and using mathematics arise from playing Go? 3) How do teachers and students perceive the game of Go? Adapting the Go game was essential to make it better suited to the practical demands of the classroom setting. Smaller boards allow Go to fit easily within class periods and match students’ beginner levels. Emphasizing the “natural” objective of the game — ensuring stones survive forever on the board — along with a simplified scoring rule based on counting surviving stones provided a student-friendly, concrete approach to gameplay. Additionally, rearranging the remaining stones into recognizable number shapes helped students count, recognize numbers quickly, and easily calculate and verify scores. These key adaptations also created a low-pressure, interactive way for students to practice foundational math skills in a game-based learning environment. Data analysis revealed that students employed essential math skills aligned with the Common Core State Standards for Mathematics (CCSS-M) during Go games. Students with varying mathematical abilities demonstrated high levels of engagement and focused attention during Go lessons and games. As the project progressed, students moved away from counting stones individually and using skip counting to more efficient approaches to calculating their final scores, such as using number shapes and arrays for multiplication. This practice allowed students to engage in perceptual and conceptual subitizing - critical number sense skills that promote mastery of arithmetic. Arrays also helped students grasp the critical concepts of commutative and distributive properties of multiplication, which are visually evident on the Go game board. This research provided empirical support for the connections between Grades K-3 CCSS-M standards and Go. Teachers observed that their students frequently applied math skills during Go gameplay and experienced valuable opportunities to reinforce concepts from their ongoing math curriculum. Students reported using their math skills while playing Go. For example, when asked how to introduce Go to their friends, they noted that it can help them learn how to be a good leader and help them practice math skills. Some students described Go as “a cool, fun strategy game that’s sometimes challenging and uses a lot of math skills.” Notably, students with special needs, including those with Attention Deficit/Hyperactivity Disorder and Autism Spectrum Disorder, actively participated in Go games with their peers without disabilities, without needing their classroom aides. Teachers noted that Go games created an alternative low-anxiety math learning space in their mathematics classrooms. In addition to its mathematical benefits, teachers recognized that Go improved students’ attention, engagement, collaborative learning, and decision-making.