Abstract
نظرية الألعاب تعرّف بأنها وسيلة من وسائل التحليل الرياضي لحالات تضارب المصالح، للوصول إلى أفضل الخيارات الممكنة لاتخاذ القرار في ظل الظروف المعطاة لأجل الحصول على النتائج المرغوبة. بالرغم من ارتباط نظرية الألعاب بالتسالي المعروفة كلعبة الداما، إكس أو، البوكر، إلا أنها تخوض في معضلات أكثر جدية تتعلق بعلم الاجتماع، والاقتصاد، والسياسة، بالإضافة إلى العلوم العسكرية، كما ويندرج تحت نظرية الألعاب عدة أنواع من الألعاب منها الألعاب التآلفية. يعطي هذا البحث للقارئ نظرة تفصيلية لإحدى أهم الألعاب التآلفية والتي تسمى لعبة (نيم)، قبل بدء اللعبة سنضع استراتيجية لتحديد الفائز مقدماً بمساعدة بعض المفاهيم الرياضية الأساسية مثل: الحد الأدنى المستبعد، أعداد غراندي، العدد XOR.
Highlights
Faculty of Science || Albaath University || Homs || Syria Abstract: Game Theory is defined as a means of mathematical analysis when interests collide with each other to reach the best possible decision-making options taking into consideration the given circumstances to get the desired results
Before the start of the game we will develop a strategy to determine the winner in advance with the help of some basic mathematical concepts like Minimum Excluded (MEX), Grundy Numbers and The XOR Number
The Problem of the Study: The important application in this Paper was to infer a strategy to predict the winner in a distinguished game called Nim before starting the game, A number of concepts have been introduced like Minimum Excluded and Grundy Numbers
Summary
Faculty of Science || Albaath University || Homs || Syria Abstract: Game Theory is defined as a means of mathematical analysis when interests collide with each other to reach the best possible decision-making options taking into consideration the given circumstances to get the desired results. Before the start of the game we will develop a strategy to determine the winner in advance with the help of some basic mathematical concepts like Minimum Excluded (MEX), Grundy Numbers and The XOR Number. The difference between them is that in Impartial Games all the possible moves from any position in the game are the same for all players, whereas in Partisan Games the moves for all the players are not the same like Chess In this Paper, we explore a new strategy to determine the winner before starting the game, as we know Nim is a combinatorial game and it is an impartial Game which means the two players have the same options. Example 3.2 The same previous example, if we have a pile of six coins and the only kinds of moves that we can make is either take one or two or three coins 1 ≤ coins ≤ 3
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