Impartial Games with Multiple Optimal Strategies

Question

Impartial games such as Nim, and Neutral Tic-Tac-Toe all seem to have one single optimal strategy. I wondered what impartial games created have more than one optimal strategy. Or whether all impartial games simply only have one optimal strategy. Thanks for answering!

Answer 1

Nim can have multiple optimal strategies. For instance, if the initial heaps are of sizes $1,2,3,3$, then one optimal strategy is removing a single chip from the heap of 2, (yielding $1,1,3,3$) and another is to remove a heap of 3.