Single-delete Nim

The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In this paper we generalize the game to include the case of n piles. On each turn, a player eliminates one pile and splits one of the remaining piles into two smaller piles. We specifically analyze the case where n=4, deriving the conditions for a winning strategy.