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 heuristic used to prioritize captures by preferring moves that take the most valuable opposing piece with the least valuable of your own pieces. In plain terms: if you can take an enemy queen with a pawn, that capture is ranked above taking the queen with a rook or queen.

Typical base values (context-dependent and not absolute) are: Pawn = 1, Knight = 3, Bishop = 3, Rook = 5, Queen = 9. The king is not assigned a capture value because it cannot be captured.

How It Is Used in Chess

Engine Usage

MVV–LVA is a cornerstone of move ordering in chess engines. When generating capturing moves, engines score each capture according to the value of the piece being taken (higher is better) and the value of the capturing piece (lower is better). The resulting order helps alpha–beta search find strong moves faster and reach pruning cutoffs earlier, improving speed and strength.

• In the main search, ordering captures well increases the chance of early cutoffs.
• In quiescence search, MVV–LVA helps explore the most forcing captures first to stabilize evaluations.
• It’s often paired with or followed by more precise filters like Static Exchange Evaluation (SEE) to discard losing captures.

Human Usage

For players, MVV–LVA is a practical way to scan candidate captures: first consider taking the biggest target with the smallest (least valuable) attacker. It’s a good “first pass” when calculating tactics, material trades, and simplifying into endgames.

Strategic and Historical Significance

Why It Matters

MVV–LVA transformed early computer chess by giving a fast, effective rule to prioritize captures without expensive calculation. This contributed to the dramatic improvement of search efficiency in engines from the 1980s onward. While modern engines also use sophisticated techniques like SEE, history heuristics, and neural evaluations, MVV–LVA remains a lightweight and reliable ordering tool.

Background

The heuristic became widespread in early microcomputer engines and was popularized through programmer notes and open-source code. Engines such as Crafty and many teaching engines and tutorials helped make “MVV/LVA” a standard term in computer chess literature. Today, it’s still found in many move generators as a fast pre-sort key for captures.

Examples

Example 1: Capturing a queen with a pawn

White to move. Black’s queen has wandered to e4, and White can capture it with multiple pieces. MVV–LVA says: if legal, capture with the least valuable attacker.

Position (White to move): 1. dxe4 is preferred over capturing with a bishop or queen because it wins the most valuable victim (the queen) using the least valuable attacker (a pawn).

Interactive board:

Example 2: Choosing the least valuable attacker among alternatives

If Black has a knight on e5 attacked by White’s pawn on d4 and bishop on d3, both 1. dxe5 and 1. Bxe5 win the same piece (a knight). According to MVV–LVA, 1. dxe5 is ranked higher because a pawn (1) is less valuable than a bishop (3), making the capture “safer” in terms of material risk, all else equal.

Example 3: Ordering captures in calculation

Suppose a tactical sequence gives White these legal captures on one move:

• 1. axb8=Q (promotion capturing a rook)
• 1. Rxe7 (rook takes a minor piece)
• 1. Bxh7+ (bishop check capturing a pawn)
• 1. Qxd7 (queen takes a minor piece)

MVV–LVA would likely rank them by the victim’s value first (captures of rooks/queens above minors/pawns) and, for ties, by the attacker’s value (pawn captures above piece captures), while engines usually interleave checks and good promotions as separate priority classes.

Related Concepts

SEE (Static Exchange Evaluation)

SEE calculates whether a capture on a square wins or loses material after all plausible recaptures. MVV–LVA is a fast rule of thumb; SEE is a deeper, local calculation. Many engines use MVV–LVA to order captures and SEE to prune obviously losing ones.

History and Killer Heuristics

These heuristics remember which non-capturing moves caused cutoffs earlier and try them sooner in similar positions. Together with MVV–LVA, they form a classic move-ordering toolkit in alpha–beta search.

Pitfalls and Limitations

• MVV–LVA ignores tactics like intermediate moves, pins, or discovered attacks. A high-ranked capture may still be bad if a recapture wins material back.
• It doesn’t account for piece activity, king safety, or positional compensation.
• Human players should treat it as a first filter, then verify with concrete calculation—much like engines pair it with SEE.

Interesting Facts and Anecdotes

• MVV–LVA is sometimes written “MVV/LVA.” You’ll see both in programming notes and engine comments.
• Even a dubious capture can be searched first under MVV–LVA if it wins a valuable victim with a small attacker; alpha–beta will quickly refute it if it fails, but the ordering can still speed up the search by provoking cutoffs in siblings.
• Many classic teaching engines and tutorials expose an MVV–LVA “capture table” internally—a 6×6 matrix scoring victim versus attacker—to keep the implementation fast.

Quick Takeaway

As a player: when scanning captures, look first for the biggest target you can safely take with your smallest piece. As a programmer: use MVV–LVA to order captures cheaply, then confirm with SEE or deeper search.