*Author for correspondence Indian Journal of Science and Technology, Vol 11(10), DOI: 10.17485/ijst/2018/v11i10/121388, March 2018 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 Probabilistic Kriegspiel: A First Approach Francisco Javier Moreno Arboleda, Daniel Esteban Guevara Vergara and Luis Humberto Bermúdez Torres Computing and Decision Systems Department, Universidad Nacional de Colombia, Sede Medellín, Bloque M8A; fmoreno@unal.edu.co, deguevarav@unal.edu.co, btluish@unal.edu.co Keywords: Chess Krieg Spiel, Probability, Strategy, Uncertainty Abstract Objectives: In this paper, we proposed a Kriegspiel (invisible chess) variant where we consider probabilistic information about the positions of the opponent’s pieces. Methods/Statistical Analysis: For dealing with probabilistic Krieg spiel, we took as a basis the proposal of Ciancarini, DallaLibera & Maran. They consider four Krieg spiel patterns which we modified to fulfill the probabilistic requirements of the tackled endgames. A strategy was also proposed for when none of these patterns is fulfilled. We developed an automaton which implements the proposed probabilistic patterns. Findings: Our results showed the feasibility of our proposal, where White won or drew as expected. To the best of our knowledge, this is the first proposal that considers probabilistic Krieg spiel. Our automaton shows that when working with probabilities in Krieg spiel, it is not always convenient to play considering the higher probability. Our proposal develops a strategy that can help competitors to make better decisions when they have incomplete information about a specific situation, e.g., to choose between two alternatives, each with its respective probability. Application/Improvements: We believe that our proposal may be useful in areas where uncertainty occurs. It can help analysts, particularly in the economics and artificial intelligence, to make decisions when uncertainty occurs. 1. Introduction Kriegspiel (from the German Kriegspiel, with double‘s’: war game) is a variant of chess that is played between two players assisted by a referee. Each player has his own chessboard and knows the position of his pieces, but not those of his opponent. Te referee knows the posi- tion of the pieces of the two players. When a player has to move, he informs the referee of his move and the referee will inform him whether it is legal or illegal. If it is legal and a piece is captured or a check occurs, both players are informed; if a piece is captured it is informed that a capture was made, but it is not indicated which piece was captured. If it is illegal (e.g., a player tries to advance a pawn and a piece blockades it, a player tries to move the king to a square where it would be in check) the player must choose another move. One of the challenges posed by this variant (also called invisible chess), is to try to deduce, from the infor- mation given by the referee, the position of the opponent’s pieces as this would allow (as in conventional chess), e.g., to capture enemy pieces, to determine whether a pawn should be advanced to try to promote it, to simultane- ously attack two enemy pieces (a fork), to prevent the loss of own pieces, among other actions. Additionally, this variant has allowed applying eco- nomic methodologies that are used for decision making when uncertainty occurs. 1-4 In many problems of life and particularly in the economic feld, most decisions are made in uncertainty conditions (either total or partial). Tus, economic competitors ofen have incomplete infor- mation about a specifc situation to make their decisions. For example, suppose that an analyst of a company A has this information: a) a competing company B plans to