You reduce Minimax branching factor by pruning or filtering moves in a way that preserves correctness where you need it, and clearly trading correctness for speed where you choose to. The only “free” reduction is alpha-beta pruning, which doesn’t change the result at a fixed depth. Everything else—move filtering, selective search, beam search—changes the explored tree and can change the chosen move, so you must treat it as an approximation. The right approach depends on whether your goal is correctness (puzzles, perfect play in small games) or strength under time constraints (real-time AI).
A practical toolkit includes: (1) generate only legal moves (avoid pseudo-legal noise), (2) order moves well so alpha-beta prunes more, (3) use quiescence search instead of searching all moves deeper, (4) apply selective extensions only in critical positions, and (5) apply selective reductions for clearly unpromising moves (late move reductions) when you can tolerate some approximation. Another safe-ish tactic is to use a fast static move ordering evaluation and only fully search the top N moves at some nodes (beam-like). This can work well but risks missing tactical resources that are not obvious statically. If you do this, keep it conservative at shallow depths (where missing a defense is catastrophic) and more aggressive deeper in the tree.
A concrete example: in a tactics-heavy game, you might always fully search forcing moves (captures, checks, threats) but reduce search on quiet moves late in the move list. This preserves tactical correctness more often while keeping runtime manageable. In non-game decision trees, branching factor reduction is often necessary too: you can’t evaluate every possible action. If your branch generation involves retrieval of candidates, you can cap candidate counts early and refine later. With Milvus or Zilliz Cloud, you can retrieve a moderate topK (say 50) for breadth, then re-rank and keep only the top M for deeper evaluation, ensuring your pruning is based on measurable signals (similarity, metadata filters) rather than arbitrary guesses.