• i. Combinatorial Games and Nim: P/N positions, Bouton’s theorem, misère Nim, Moore’s Nim, staircase Nim and the variant table.
• ii. Sprague-Grundy: every impartial position is a Nim heap; mex, XOR of sums, certified periods (Kayles, Dawson), Lasker’s Nim, coin-turning games.
• iii. Hackenbush and Partizan Games: green Hackenbush on any graph (colon and fusion), Blue-Red stalks, dyadic game values and the simplicity rule.
• iv. Loopy Games and Retrograde Analysis: win / loss / draw with optimal lengths on cyclic game graphs, and the generalized Sprague–Grundy function for sums.
• v. Game DP, Minimax and Game Search: advantage DP, negamax, alpha-beta, PVS, Zobrist hashing, proof-number search, MCTS with UCT.
• vi. Games on Graphs and Matchings: vertex geography via Gallai–Edmonds, cops and robber via dismantlability, and which graph games are PSPACE-complete.