**Edward Winter**

Illustration 99 in *Chess: East
and West, Past and Present* (New York, 1968)

Matt Goddard (Hiram, GA, USA) mentions a peculiar list of piece
values on page 155 of *Hoyle’s Complete and Authoritative Book
of Games *(the 1952 edition from Garden City Books, Garden
City, New York, originally published in 1907 by the McClure
Company):

Our correspondent writes:

‘Are there other examples where these were given as the common values, and where specifically did these values originate?’

In no other edition of *Hoyle* that we have consulted is
the queen valued at more than ten pawns, and the evaluations given
in the illustration above are certainly unauthoritative. Below we
briefly list some further examples (pre-Second World War) of how
this subject has been treated.

- Pages 79-81 of
*Studies of Chess*by Peter Pratt (London, 1803):

- Chapter VIII of
*Amusements in Chess*by Charles Tomlinson (London, 1845) had a chapter ‘On the powers of the pieces and pawns’ (pages 129-138) which gave a number of lists, according to mobility.

The ‘final relative values’ (page 136) were:

pawn: 1.00

knight: 3.05

bishop: 3.50

rook: 5.48

queen: 9.94.

- ‘Vom Tauschwerthe der Steine im Schach’ by v. Oppen,
*Deutsche Schachzeitung*, January 1847, pages 8-13, March 1847, pages 70-79 and May 1847, pages 141-149. Detailed treatment which featured an overview of many previous attempts to evaluate the pieces.

- Page 34 of
*The Chess-Player’s Handbook*by Howard Staunton (London, 1847). The values he gave were those of Tomlinson (see above).

- ‘Ueber den Tauschwerth der Steine’ by Alexandre,
*Deutsche Schachzeitung*, July 1850, pages 225-227. Follow-up work by Alexandre to what had appeared in the magazine in 1847.

- ‘On the Relative Value of the Pieces’ by J. Pierce,
*BCM*, March 1884, pages 78-81. Pierce summarized ‘a very interesting and able paper by Mr Biddle ... in the*Educational Times*’ and included on page 79 the following chart:

Pierce then explained the conclusions in the Biddle paper:

‘The author lays down the law that the entire value of a piece is the product of its separate values for attack and defence. He shows that the value of a piece for defensive purposes varies inversely as its entire value and directly as its mean scope. Hence the square of the entire value is equal to the product of its attacking value and mean scope.

Thus we get ultimately the

entirevalues Q=10, R=5.84, B=3.53, Kt=2.89, P=.5.’

- ‘La Valeur absolue des Figures d’Echecs’ by Hermann Vogler,
*Schweizerische Schachzeitung*, January 1916, pages 1-6. Two sample pages are given below:

Page 83 of the March 1916

BCMgave a tepid reception to Vogler’s ‘curious’ article, although on page 125 of the April 1916 issue a reader, S.H. Gould, opined that theBCMhad dismissed it too lightly. Vogler’s article was reproduced on pages 65-70 ofLa Stratégie, March 1916.

- In
*La Stratégie*, May 1916, pages 129-132, Anatole Mouterde contributed an article entitled ‘De la valeur comparative des pièces’ which concluded with this comparative chart:

*BCM*, March 1922, page 95 and July 1922, page 271: brief mathematical items, notably on the respective values of the bishop and knight.

- ‘Zahlenwerte der Schachfiguren’ by Dr Kemmerling,
*Deutsche Schachzeitung*, March 1935, pages 65-68 presented calculations of the pieces’ values. Page 131 of the May 1935 issue had a brief follow-up item based on calculations made by Curt L’hermet in the*Magdeburgische Zeitung*of 23 November 1913.

- ‘Die Kampfkraft der Schachsteine’ by Gerhard Pusch,
*Deutsche Schachzeitung*, April 1936, pages 97-100. Detailed mathematical calculations which concluded with this table:

The above listings are, of course, by no means exhaustive but offer an overview of the old-timers’ attempts to allocate exact values to the chess pieces.

*(4897)*

From Robert John McCrary (Columbia, SC, USA):

‘Page 57 of my publicationThe Hall-of-Fame History of US Chess(1998) has an article tracing the scale of powers that were given inAmusements in Chessand in Staunton to an earlier source: an 1817 edition of Philidor’s analysis, apparently done by Peter Pratt. In that edition, Pratt devoted 40 pages to mathematical analysis of various factors, leading to his concluding scale of Q=9.94, R=5.48, B=3.5, N=3.05, P=1. He suggested rounding off the scale, but Staunton and Steinitz printed it with full decimal places.

I have subsequently found that Pratt, as early as 1805 and probably earlier, gave two different scales, based on different lines of reasoning. The first scale had P=2, N=12, B=14, R=15, Q=28, K=9, whereas his second scale was P=2, N=9.25, B=9.75, R=15, Q=23.75, no K value. Apparently Pratt later developed the mathematical analysis printed in 1817. The same figures were used not only by Staunton in hisHandbookbut also by Steinitz (on page xxxiii ofThe Modern Chess Instructor), and ultimately became our modern scale.’

*(4902)*

A question from Stuart Rachels (Tuscaloosa, AL, USA): who introduced the famous elementary system of values (pawn 1, knight 3, bishop 3, rook 5, queen 9)?

We can do no better than quote from page 59 of *The
Hall-of-Fame History of US Chess* by Robert John McCrary
(1998):

‘By the 1930s, the idea of a single numerical scale of values seemed to be losing favor. Instead, great players such as Capablanca and Tarrasch were generally avoiding giving a single scale of values in their books, preferring to discuss various kinds of exchanges on a case-by-case basis.

Then in 1942 Reuben Fine published his

Chess The Easy Way. On page 23 is the following historically important section:“Since there are six different kinds of pieces it is necessary to set up a table of equivalents in order to be able to know whether an exchange is favorable or not. Again such a table is based partly on the elementary mates (R can mate, B or Kt cannot) and partly on practise. If we take the pawn as 1 we may set up a table such as this:

pawn = 1

bishop (or knight) = 3

rook =5

queen =9.”Fine goes on to say that his table is satisfactory for rough calculation but not as accurate as a set of equivalents for certain exchanges he gives on the next page. Nevertheless, Fine apparently popularized our modern scale and indeed may have invented it. Does any reader know of an earlier publication of the modern scale? Perhaps Fine then should be considered the true “point-count” man of chess.’

*(7853)*

Mark N. Taylor (Mt Berry, GA, USA) notes this passage on page 227
of *A History of Chess* by H.J.R. Murray (Oxford, 1913):

Robert John McCrary (Columbia, SC, USA) writes:

‘Lasker’s Chess Magazinepublished a series of copyrighted articles by Emanuel Lasker on basic chess instruction, and on pages 188-189 of the August 1905 issue he discussed the value of pieces. After describing the methods of Jaenisch and the mathematician Euler, he gave, on page 189, a peculiar scale:“The values of the pieces calculated with sufficient accuracy for over the board play are as follows:

Pawn, 6; knight, 17; bishop, 17; rook, 24; queen, 47.

These values have not been found by executing the indicated calculation, but are those which come nearest to express my experience in hard fought games.”

Lasker then added some provisos and concluded by giving the king a value of 20.

I have yet to find any occurrence of these values elsewhere in Lasker’s writings.’

*(8859)*

Robert John McCrary refers to an 1857 edition of *Hoyle’s
Games* by Thomas Frère:

‘Frère was a significant chess author, so this edition is more accurate on chess than other works bearing the “Hoyle’s” name. Moreover, Frère’s Preface, dated March 1857, makes it clear that the book is original and unrelated to Hoyle’s traditional works. It states (page iii):“There isn’t a line of ‘Hoyle’ in it. Hoyle is a fossil, and suited only to fossil players.”

Although my copy is dated 1875, it seems to be an essentially unaltered reprint of the 1857 edition. All the chess content appears consistent with early 1857.

On page 235 Frère writes:“Relative value of the pieces. The relative value of the pieces is estimated as follows: the queen is worth, say, 10 pawns; the rook 5; the bishop 3½; the knight 3½.”

This is the earliest publication that I have seen which gives the bishop and knight the same value.’

*(8885) *

A further contribution from Robert John McCrary:

‘Page 137 ofGames and Sportsby Donald Walker, published in 1837 by Thomas Hurst, London, suggests a scale of values for chess pieces. The relevant section reads:“The values of the men – These have been calculated as merely regulating the odds sometimes given at the beginning of the game; for their value during the game must depend greatly on situation. The value of the pawn being taken as one; the knight is worth rather more than three; the bishop is of similar value; the rook is worth about five pawns, or two pawns and a knight or bishop; the queen is worth about ten pawns, and is therefore the most powerful of the pieces.”

‘However, on page 138 it is stated that the queen’s relative value is diminished toward the end of a game, when rooks have a “clearer” board and thus more power relative to the queen.’

*(8904) *

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Copyright: Edward Winter. All rights reserved.