# Analysis, Generation, and Validation of New Boards for the Game Micro Robots
## 1 Introduction  
Board games or Eurogames [1] are a classic resource used in family or friend gatherings, and their market is constantly expanding. The news portal Deutsche Welle [2] reported that during the year 2020, the board game market registered a growth of 20%, mainly due to the COVID-19 pandemic. In this context, it is expected that this market will generate about USD 8.6 billion in 2024, with a compound annual growth rate of 3.52% from 2024 to 2028 [3]. The United States leads the market, with revenues of USD 2.74 billion, while countries like Germany stand out in the design of innovative and strategic games. The platform BoardGameGeek currently has more than 150,000 registered board games [4].  
This growing popularity of board games over time has garnered some interest in the academic field. For example, various studies highlight the usefulness of this type of games as an educational tool in different contexts. Their effectiveness has been observed in the teaching of various subjects such as history [5], geography [6], mathematics [7], biology [8] and social sciences [9], while also fomenting skills such as teamwork, decision making, creativity, and imagination [10], thus promoting crucial aspects for academic development, positive behaviors, and emotions [11]. Similarly, direct interaction with small groups of students promotes discussion and co-learning, facilitating comprehensive education that covers conceptual, procedural, and attitudinal content [12].  
There is a continuous search for new ways to develop board games' pedagogical potential. This potential also suggests possible applications in various fields such as health, business, and technological development; so, exploring and advancing in this area of knowledge will allow for the discovery of a wide range of practical applications. Board games are divided into various categories, including abstract strategy games. This category is often characterized by the absence of a theme or narrative and is based on a simple and straightforward design and mechanics, presenting perfect information to the players [13].  
Games in this category include Chess, Go, Mahjong, Ricochet Robots, and Micro Robots [14]. In Micro Robots, players compete simultaneously to find the shortest route to move a robot across a grid.  
In this context, this paper proposes an analysis of the game Micro Robots, including the generation and validation of new boards, focusing on its rules, mechanics, and interactions, to evaluate the variation in the gaming experience by modifying the arrangement of its elements. The algorithms that generate and validate different board configurations of the original game size (6 \(\times\) 6 squares) and reduced size (2 \(\times\) 2 and 4 \(\times\) 4 squares) are described.  
Board generation consists of two methods: (1) randomly rearranging the squares; and (2) sequentially rearranging the squares while exploring all possible combinations. Board validation is carried out through their representation in graphs. These are explored using a depth-first search (DFS) algorithm, which evaluates the connectivity between the squares and finds all their solutions. Finally, a digital board game prototype is developed to test the newly generated boards.  
This article is structured as follows: first, key concepts involved in the study are described, such as the board game itself, graph theory and its applications in other games, and search algorithms. Subsequently, the methodology used in designing and developing the program to generate new boards is defined. Then, the results obtained from the tool and the analyses carried out are described. Finally, the conclusions drawn from the data collection are presented.