Minimax is the foundational algorithm for optimal play in two-player zero-sum games (von Neumann 1928). The maximizing player (gold, △) picks the child with the highest value; the minimizing player (blue, ▽) picks the lowest. Values are assigned at leaf nodes (terminal positions) and backed up to the root. The optimal strategy assumes both players play perfectly. The animation traces the recursive descent and backpropagation — watch how the optimal value propagates up the tree. The highlighted path shows the principal variation (optimal line of play from root). Minimax with depth d and branching factor b examines O(b^d) nodes — alpha-beta pruning reduces this dramatically.