  Nim is a well-known combinatorial game with several variants, e.g., Delete
Nim and Variant Delete Nim. In Variant Delete Nim, the player deletes one of
the two heaps of stones and splits the other heap on his/her turn. In this
paper, we discuss generalized Variant Delete Nim, which generalizes the number
of stone heaps to three or more, All-but-one-delete Nim, Half-delete Nim,
No-more-than-half-delete Nim, and Single-delete Nim. We study the win-loss
conditions for each of these games.
