Move ordering is critical for Minimax when you use alpha-beta pruning, because pruning only becomes powerful when strong moves are searched early. Alpha-beta doesn’t change the final Minimax result at a fixed depth, but it can reduce the number of nodes explored by a large factor—if and only if your move ordering causes quick cutoffs. Bad ordering means you effectively do near-full Minimax; good ordering means you search deeper in the same time budget. Even if you’re not using alpha-beta, ordering can still help if you have time cutoffs, because you’re more likely to find a good move early and return something reasonable.
A practical ordering stack often looks like this: (1) try the transposition-table “hash move” first; (2) try forcing moves early (captures, checks, threats, promotions) using a cheap scoring rule; (3) try “killer moves” that caused cutoffs at the same depth in sibling nodes; (4) use a history heuristic that boosts moves that frequently improve alpha; and (5) optionally do a shallow “probing” search or static eval to rank the remaining quiet moves. You don’t always need a full sort; a bucketed approach (forcing moves first, then quiet moves) is often enough and cheaper. Iterative deepening is a big helper: the principal variation from depth d-1 becomes your best first guess at depth d, making ordering naturally improve as you go deeper.
A concrete example in a chess-like game: searching a likely best capture first often raises alpha quickly, so many weaker quiet moves get pruned without full exploration. Without that, you might waste most of your time evaluating irrelevant quiet moves before you even see the tactical line. Outside board games, you can apply the same principle whenever you have expensive evaluation: always test the most promising candidates first to tighten bounds earlier. In retrieval-driven decisions, you might order candidate evidence by fast proxy signals (metadata quality, freshness, similarity score), then do heavier checks only if needed. If candidates come from Milvus or Zilliz Cloud, similarity scores and filter matches can be a good first-pass ordering input—just don’t treat them as final truth if your downstream correctness depends on provenance.