Restrictions Of Large/Small Nim

Nim is one of the classic impartial combinatorial games in game theory. By putting the largest pile restriction and the smallest pile restriction on Nim respectively, Large Nim and Small Nim can be got.This paper studies three kinds of restrictions on Large Nim and Small Nim in depth. By putting blocking restriction on Large Nim and Small Nim, we get new game models Blocking Large Nim and Blocking Small Nim; by making modular restriction on Large Nim and Small Nim, we obtain new game models Modular Large Nim and Modular Small Nim: by making restrictions of the largest and smallest number of tokens which can be moved in each move, we get four new game models which are Rounded Large Nim. Rounded Small Nim. Bounded Large Nim and Bounded Small Nim. This paper is divided into four chapters:The first chapter is introduction. We mainly introduces the development of impartial combinatorial games and the latest research.The second chapter, we research the new game models Blocking Large Nim and Block-ing Small Nim, besides, we also show all the P-positions of them under the normal play conventions.The third chapter, we find out all the P-positions of Modular Large Nim and Modular Small Nim. under the normal play conventions thoroughly.The fourth chapter, we study four new game models:Rounded Small Nim. Rounded Large Nim, Bounded Small Nim and Bounded Large Nim. Then we find out all the P-positions of the first three game models under the normal play conventions thoroughly.