There are many variations of Nim, most of which can be analysed mathematically in a similar way to Nim.
Misère Nim is identical to Nim, except that the player to take the last dot loses.
The Subtraction Game
The Subtraction Game starts with one or more heaps, like Nim, but there is a limit on the number of objects that each player may remove. For example, the game might start with a single heap of 10 objects, and each player is allowed to remove up to 3 objects.
Grundy's game starts with a single heap, such as of 10 objects, and the players take turns in dividing the heap into two heaps of different sizes. Thus, a heap of six objects may be divided into heaps of 5+1 or 4+2, but not 3+3.