To study about the mathematical models of games of chance: Principles of an optimal mathematical intervention for responsible gambling

The near-miss has been regarded as a significant reinforcement factor in gambling activity, and prior research has focused more on its causes and effects related to the industry and less on the gaming phenomenon itself. Due to the unique features of these games, which involve the probability of pre-manipulation of award symbols in order to maximise the frequency of these "engineered" near-misses, the near-miss has traditionally been associated with games of slots and scratch cards. In this paper we argue that we can more accurately describe the fallacious elements of the near-miss cognitive effects and the inadequate interpretation and representation of the elementary mathematical definition of the classical (by pure chance) near-miss, generalizable to any game, and concentrating equally on the epistemology of its constitutive concepts and their mathematical description. In exploratory learning conditions that are random in nature, this study seeks to investigate how probabilistic reasoning occurs. In particular, the emphasis is on what learners with little knowledge with formal probability theories do and can do when coping with compound random circumstances in which opponents are offered to implement various probabilistic lines of reasoning. This research therefore indicates that probabilistic reasoning takes shape through a contextualization mechanism, i.e. through a compound process where cognitive behaviour oscillates between contextual perceptions and reflections, the focal event and new knowledge that comes into play. This study shows that students are able to formulate ideas of an underlying distribution of probability in the case of compound random phenomena before instruction. Geometrical and numerical considerations as well as statements representing the concepts of the rule of large numbers are discussed by the students. Main words/phrases: probabilistic reasoning, randomness, en-counters of compound chance, contextualization, distinction, elaborative variation.