Nim, Hackenbush, and Friends

Two players take turns removing tokens from heaps, and whoever makes the last move wins. Who should win? Starting with one and two heaps, I build winning strategies for Nim through pairing and mirroring, and show that writing heap sizes as sums of powers of two settles every position. There is a token-sliding game that is Nim in disguise, and Red-Blue Hackenbush, where each player may only cut edges of their own colour. There is also an activity round of Toads and Frogs, Domineering, Traffic Jam, and Southwest Queen.