MVV-LVA: Most Valuable Victim – Least Valuable Attacker
MVV-LVA
Definition
MVV-LVA stands for “Most Valuable Victim – Least Valuable Attacker.” It is a simple, fast heuristic used primarily by chess engines to order capture moves. The idea is to prefer captures that win the most valuable enemy piece (the victim) while using the least valuable friendly piece (the attacker). In practice, engines rank captures by the value of the piece being taken (Q > R > B/N > P), and among captures of the same victim, they prefer the one made by the least valuable attacking piece (P < N/B < R < Q).
How It Is Used in Chess
MVV-LVA is a cornerstone of engine move ordering, especially for handling captures in the main search and in quiescence search (the phase where engines resolve forcing captures to stabilize the evaluation). Ordering promising captures first helps the search find good moves quickly and achieve earlier cutoffs, saving time and nodes.
- Engines score each capture by victim value and attacker value; higher victim value ranks earlier, and for equal victims, a lower attacker value ranks earlier.
- It is often combined with other priorities: transposition-table move first, then winning promotions, checking moves, then MVV-LVA-ordered captures, followed by other heuristics for quiet moves.
- For human players, MVV-LVA is a useful rule of thumb: when several captures are possible, consider taking the most valuable enemy piece with your least valuable unit, provided tactics justify it.
Strategic and Practical Significance
MVV-LVA aligns with common-sense material strategy: trades that gain material and expose less valuable pieces to recapture are often best. In engine terms, it dramatically improves efficiency. By examining likely “good” captures first, the search can prune large parts of the tree via alpha-beta cutoffs, making stronger play possible within strict time limits.
However, MVV-LVA is a heuristic, not a calculation. It assumes (temporarily) that the capture is reasonable; the engine still relies on deeper search or a Static Exchange Evaluation (SEE) to confirm that the capture is actually sound.
Example Position and Ranking
Imagine a position where Black’s queen sits on d5 and White has several ways to capture it. White’s pieces are placed so that the following captures are legal: c4xd5, e4xd5, Nf4xd5, Bf3xd5, and Qxd5. All these moves win a queen, but MVV-LVA orders them by the value of the attacker:
- 1. cxd5 (pawn takes queen) — best by MVV-LVA: biggest victim with the least valuable attacker
- 1. exd5 (pawn takes queen) — same top priority as another pawn capture
- 1. Nxd5 (knight takes queen) — next best among queen captures
- 1. Bxd5 (bishop takes queen) — tied in value with a knight capture in many schemes
- 1. Qxd5 (queen takes queen) — lowest among captures of the queen
If the available captures were instead Qxd5 (capturing a queen) and cxb5 (capturing a rook), MVV-LVA prefers Qxd5 because the victim (queen) is more valuable than a rook, regardless of the attacker. This simple prioritization helps engines test the most promising material gains first.
Engine Implementation Notes
- Piece values are abstracted; a common scheme is P=1, N=3, B=3, R=5, Q=9 (the king as a victim is excluded; as an attacker it’s typically treated as the most valuable and rarely used for captures in ordering).
- Many engines precompute a small victim–attacker table (e.g., a 6×6 matrix by piece type) for fast lookup.
- MVV-LVA is frequently paired with Static Exchange Evaluation (SEE): MVV-LVA orders captures cheaply; SEE then filters or de-prioritizes obviously losing captures.
- In full move ordering, engines typically prioritize: transposition-table move, good promotions, checking moves, MVV-LVA-ordered captures (possibly SEE-verified), then quiet moves via the history or killer heuristics.
Limitations and Pitfalls
- It ignores tactical consequences by itself. A capture ranked first by MVV-LVA might be a blunder if recaptures or intermezzos favor the opponent.
- It does not account for checkmate threats, king safety, or positional compensation; it only ranks captures by material considerations.
- Sacrificial ideas that start with “low-value victim, high-value attacker” (e.g., brilliant exchange sacrifices) will rank low by MVV-LVA, so engines need broader search and other heuristics to find them.
Example of the last point: in Kasparov vs. Topalov, Wijk aan Zee 1999, many moves in the famous combination involve sacrificial concepts that MVV-LVA alone would not prioritize. Modern engines still find them thanks to deeper search, checks-first ordering, and verification mechanisms.
Historical Notes and Anecdotes
MVV-LVA emerged from early computer-chess practice as a fast and effective rule for ordering captures on limited hardware. By the late 1980s and 1990s it had become standard in many engines and remains widely used today—often in tandem with more refined techniques like SEE and capture history. Its enduring appeal is its tiny computational cost relative to the search benefits it provides.