Move ordering is extremely important for alpha-beta pruning efficiency because alpha-beta only prunes well when it finds strong moves early. Alpha-beta doesn’t change the final Minimax result (assuming correct implementation and same depth), but it can reduce the number of nodes explored from “almost everything” to “a small fraction,” depending on ordering quality. In the best case, good ordering makes alpha-beta approach the theoretical improvement where the effective branching factor drops dramatically. In the worst case (bad ordering), alpha-beta behaves close to plain Minimax and explores nearly the full tree. So, if you care about speed, move ordering is one of the highest-leverage improvements you can make.
The intuition is simple: alpha-beta maintains bounds (alpha for the best score the maximizer can guarantee so far, beta for the best score the minimizer can guarantee so far). If you try a move that quickly proves “this position is great for me,” you raise alpha early, which makes it easier to cut off later sibling moves that can’t beat that bound. If you try weak moves first, alpha stays low and you don’t get those cutoffs. Common ordering heuristics include: try the transposition-table best move first, prefer captures or forcing moves (checks, threats) early, sort by a shallow evaluation score, and use killer-move/history heuristics to prioritize moves that previously caused cutoffs. Iterative deepening naturally feeds move ordering: the principal variation from depth d-1 becomes the first line searched at depth d.
A concrete implementation pattern: generate all legal moves, score them cheaply, sort descending for maximizing nodes (ascending for minimizing nodes), then search in that order. The cheap scoring can be: “hash move first,” then “captures by MVV/LVA-like scoring,” then “promotions,” then “quiet moves by history score.” Even a partial ordering (bucketed ordering) helps a lot and avoids expensive full sorting. Outside games, the same principle applies anytime you do bounded search: try the most promising candidates first to tighten bounds earlier. If you’re using alpha-beta-like logic in a workflow that depends on retrieval (for example, selecting which evidence to show or which actions to take), ordering the retrieval candidates by a fast proxy score can make the deeper evaluation cheaper. If those candidates come from a vector database such as Milvus or Zilliz Cloud, you can use the initial similarity score (plus simple metadata rules) as a first-pass ordering before doing heavier re-ranking or deeper “what-if” evaluation.