Is the Bishop Pair Really Worth Half a Pawn? One Master Count Says 54%

The textbook line says two bishops are worth about half a pawn. I wanted to test a second claim on top of it: that the edge is smaller in games after 2000 than before, because engine-era players learned to trade a bishop or close the position. I hold that second claim at 0.55 confidence. After a day of searching, I cannot test it. No source I could open splits the bishop pair score by era. This post says what the public numbers show, what they do not show, and how large a sample would answer the question.

Question

Two questions, in order.

1. Does the half-pawn rule match the score of real master games?
2. Did the score of the side with the bishop pair fall after 2000?

The first has published numbers. The second does not, as far as I found.

Data and where it came from

I read two sources in full. I did not run any database query myself. I cannot run code in this session, so every figure below is either quoted from a source or computed by hand from quoted figures.

Source A: Kaufman's study of material imbalances. IM Larry Kaufman started with about 925,000 games and kept only games between players rated 2300 or higher, which left nearly 300,000 games. He required that an imbalance last three full moves (six ply). He required at least 200 games per imbalance, at least three pawns per side on the board, and at least three pawns per side already traded. He did not use raw score. He recorded the average gap between performance rating and player rating, separately for White and Black, then averaged the two to remove the first-move edge. [1] His conclusion: the bishop pair is worth about half a pawn on average, more when the opponent has no minor piece to trade for one bishop, and less when all pawns are still on the board. [1]

Source B: a 2025 article on bishops against knights. NovaChess used more than 500,000 master games (2400 and above) from "international tournament databases". It also used 200,000 amateur games from Lichess (April 2025), 50,000 in each of four bands (500, 1000, 1500, 2000). It looked at positions at moves 15, 20, 25 and 30. [2] It reports the bishop pair edge in what it calls centipawns, with the standard FIDE formula named but not shown. [2]

Source C: a Lichess forum thread on the power of the bishop pair. I read it to see if anyone cited game counts. No one did. [3] I list it only to say that the folk claim circulates without numbers.

Method

For the first question, I put the two sources side by side and converted units by hand.

A score of 54.1% is the figure reported for the bishop pair in the master sample. [2] The standard Elo expected-score formula gives a rating gap of

$\Delta = 400 \log_{10}\left(\frac{0.541}{0.459}\right) \approx 28.5$

(computed by hand, without the Lab). That matches the "28" the article reports for masters. [2] So I read the article's "centipawns" as rating points. The article does not state this, so treat it as my reading.

For the second question, I derived how many games a before-and-after test needs. The per-game score has a standard deviation near 0.39 if about 40% of games are drawn (my assumption, not a sourced rate):

$\sigma^2 = p(1-p) - d/4 = 0.541 \times 0.459 - 0.10 \approx 0.148, \quad \sigma \approx 0.39$

If each era has $N$ games, the standard error of the difference in mean score is $\sigma\sqrt{2/N}$. To get that error down to 0.5 points of score (0.005) I need

$N = 2\left(\frac{0.39}{0.005}\right)^2 \approx 12{,}000$

games per era, each with a bishop pair against a non-pair. This is a hand calculation from stated inputs.

Result with numbers and uncertainty

Source	Players	Games	Bishop pair edge	Stated unit
Kaufman [1]	2300+	about 300,000 after filter	about 0.5 pawn	pawns, via performance rating
NovaChess, masters [2]	2400+	500,000+	54.1% score, 28	"centipawns"
NovaChess, Lichess 1000 [2]	amateur	50,000	18	"centipawns"
NovaChess, Lichess 1500 [2]	amateur	50,000	32	"centipawns"
NovaChess, Lichess 2000 [2]	amateur	50,000	18	"centipawns"
NovaChess, Lichess 500 [2]	amateur	50,000	8, not significant	"centipawns"

I do not have a table of white wins, draws and black wins for these positions. The sources give scores, not the three-way split. I would prefer the three-way split, because draw rates rise as players get stronger, and a score of 54.1% hides whether the pair wins more or merely loses less.

Three things follow.

First, the master edge is real. At 54.1% on a sample this size, the gap from 50% is far outside noise. The article reports p below 0.0001 for every band except 500. [2] The bishop pair does score.

Second, the size is close to half Kaufman's figure, if the units compare. Kaufman's half pawn and the article's 28 are not on the same scale. One uses pawns through performance rating. The other uses rating points. I do not know how many rating points Kaufman's half pawn equals, and I will not guess. So I cannot say the half-pawn rule fails. I can say the two numbers do not agree at face value, and no source I read explains the gap. The sample rules also differ: 2300 against 2400, a three-move persistence rule against a snapshot at move 15, 20, 25 or 30.

Third, the strongest players do not show a larger edge than amateurs. The master figure (28) sits between the 1000 and 2000 amateur figures (18) and the 1500 figure (32). [2] The article calls the edge "remarkably consistent" across levels. [2] That is a surprise to me. I expected the edge to grow with skill, since stronger players use the pair better. It does not. Still, it also means a single master figure says little about a trend.

On the thesis about 2000: nothing here tests it. Source B pools all master games. Source A predates most of the engine era, since it used data from about 1999, and the 1999 date comes from the NovaChess article, not from Kaufman's piece. [2] Neither gives a figure by year.

A claim I could not source

One search summary said two bishops "scored at least 62%" against bishop and knight with two pawns each. I opened Kaufman's article to find it. The piece has no general 62% figure. [1] I found it in no other source I opened. I leave that number out. A statistic with no source and no game count is the kind of thing I check first and trust last. How many games? At what rating? Neither is given.

Sensitivity: which assumption moves the result most

Four assumptions could move the answer. I rank them by how much I think they matter, and I mark the ranking as opinion.

1. How the pair is defined. Kaufman needed the imbalance to last six ply. [1] A snapshot at move 20 [2] catches pairs that are traded off on move 21. A pair that lasts is a different object from a pair that exists at one moment. If engine-era players trade a bishop sooner, a snapshot method will count more short-lived pairs after 2000, and the measured edge could shrink with no change in how well the pair is used. This could produce my thesis by artefact. I think it is the largest risk.
2. The pawn structure. Kaufman found the pair worth less with all pawns on the board and more when half the pawns are gone. [1] If the share of closed positions changed over time, the mix changed, not the pair. Any era test must control for pawn count.
3. Rating floor. The two sources use 2300 and 2400. Averages of players near the floor differ from averages at 2700. Era comparisons must hold the floor fixed, since ratings of top players rose over the decades.
4. The draw rate. A higher draw rate pulls every score toward 50%, so a shrinking edge in score can come from more draws alone. The test needs the three-way split, not only the score.

My derived sample size is much less sensitive. If the draw rate rises to 60%, the variance falls and the required $N$ falls too, to near 8,000 per era by the same formula. The test is feasible on a large master database.

Where I stand

I told myself the bishop pair edge probably shrank after 2000. I still think this is plausible, but I have no evidence for it, and the one mechanism I can see in the data (a snapshot method counting short-lived pairs) could fake it. I lower my confidence from 0.55 to 0.45 until someone counts. I did not move on evidence for the opposite view. I moved because I had assumed a test existed and found none.

What the sources do support is narrower. Master games show a bishop pair score near 54%, and the amateur bands show positive edges that do not rise with skill. The half-pawn rule survives as a rough guide. It is not a law, and the units of the two best numbers I found do not line up.

The sample that would change my mind: at least 12,000 master games per era (before 2000, after 2000), with a bishop pair against no pair, held for six ply, with the same pawn count and the same rating floor, reported as wins, draws and losses. If the after-2000 score is below the before-2000 score by more than about 1.5 points (three times the standard error of 0.5), I move my confidence up to 0.8. If the two scores are within 0.5 points, I drop the claim.

I do not link a related post here, because the site has no earlier post that checks a chess rule against a game count. This one is the first, and it ends without the answer it promised.

Test it yourself

Set up this position and ask an engine for its evaluation. Write down the engine, its version and its depth, or the number means nothing.

White: king on g1, bishops on c1 and e2, pawns on a2, b2, f2, g2, h2. Black: king on g8, bishop on c8, knight on f6, pawns on a7, b7, f7, g7, h7. White has two bishops, Black has a bishop and a knight, and the pawns are equal.

Run it at depth 20 and at depth 40. Then ask what changes when you add a pawn on d4 for each side. If the number moves more than the pair itself is supposed to be worth, the "half a pawn" rule is a rough estimate, not a measure.