Monday, November 14, 2011

The Doctrine of Chances (1754)

(updated November 17, 2011, February 21, 2013)

In his treatises on whist, backgammon, piquet, quadrille, and brag, Hoyle had briefly discussed the mathematical aspects of each game. He provided a somewhat fuller treatment of probability in a 1754 work—An Essay towards making the Doctrine of Chances easy to those who understand Vulgar Arithmetick only. The book, a minor footnote in the histories of both gaming and mathematics, has quite an odd publishing history.

The title recalls a much more important work on probability by Abraham De Moivre, The Doctrine of Chances: or, a Method of Calculating the Probability of Events in Play (1718) with subsequent editions in 1738 and 1756, the last of which is freely available here.

In his landmark history of probability, Isaac Todhunter devotes nearly 70 pages to De Moivre's work and a scant two paragraphs to Hoyle's:
Some works on Games of Chance are ascribed to Hoyle in Watt's Bibliotheca Britannica. I have seen only one of them which is entitled: An Essay towards making the Doctrine of Chances easy to those who understand Vulgar Arithmetick only: to which is added, some useful tables on annuities for lives &c. &c. &c. By Mr Hoyle... It is not dated; but the date 1754 is given in Watt's Bibliotheca Britannica.
The work is in small octavo size, with large type. The title, preface, and dedication occupy VIII pages, and the text itself occupies 73 pages. Pages 1-62 contain rules, without demonstration, for calculating chances in certain games; and the remainder is devoted to tables of annuities, and to Halley's Breslau table of life, with a brief explanation of the latter. I have not tested the rules. (Todhunter p322)
Where De Moivre used games to advance the mathematical theory of probably, Hoyle used probability to provide rules of thumbs for gamesters—Hoyle's Chances lacks mathematical importance.

The publishing history of the Chances should be viewed in light of the unsuccessful publication of the treatise on Brag by John Jolliffe (1751), discussed here. Like Brag, the book was sold by subscription as is evident from a series of notices in the Public Advertiser:
Next month will be published, By Subscription, at Half a Guinea, The Doctrine of Chances made easy to those who understand Vulgar Arithmetick only. By Mr. Hoyle. Subscriptions taken in by the Author, and Mr. Jolliffe, in St. James's street. (Public Advertiser, January 23, 1754)
Beginning in late February and continuing into March, the same advertisement was published with the heading "Speedily will be published" and finally on June 16 it was announced as "This Day is publish'd."

The imprint of the book is curious, particularly in comparison with Brag. In 1751, Brag appeared with the imprint "printed for and sold by J. Jolliffe, bookseller." The words "printed for" suggest that Jolliffe was the publisher and had paid Hoyle for the copyright. In contrast, Chances is "sold by J. Jolliff (sic)" suggesting that Jolliffe was only a distributor. The book was not entered into the register at Stationers Hall, so we don't have that evidence as to the owner of the copyright, but it is likely that Hoyle retained the copyright—perhaps Jolliffe was unwilling to purchase it because of the poor sales of Brag.

Chances sold for half a guinea, and, like Brag, it did not sell well initially. From 1748 to1755 Thomas Osborne (and William Reeve) were selling various issues of Mr. Hoyle's Treatises (discussed here), followed by Osborne's "eleventh" edition in 1755 and "twelfth" in 1760. Just as Osborne began to advertise the "twelfth" edition, he began to promote two other books:
Tuesday next will be published, Dedicated to the Right Hon. the Earl of Northumberland, Price 3s. 6d. sewed in Marble Paper, An Essay towards making the Game of Chess easily learned, by those who know the Moves only, without the Assistance of a Mater. By Mr. Hoyle, Printed for T. Osborne, in Gray's Inn; R. Baldwin, at the Rose, and S. Crowder, at the Looking-Glass, in Pater-noster Row. 
Of whom may be had, Price 2s. 6d. sewed, Mr. Hoyle's Essay towards making the Doctrine of Chances easy to those who understand Vulgar Aritmetic only. To which are added, some useful Tables on Annuities for Lives, &c &c.
No Copies of these Books are genuine, but those that are signed by the Author. (Public Advertiser, December 24, 1760)
We'll save the disccusion of Chess for another time, and focus on Chances. This Osborne version is not listed in ESTC and but a single copy survives at the Bodleian Library, shelf mark Jessel e.647(1). An examination of the book reveals that it is a reissue of the 1754 edition with a cancel title page. Again, the imprint is odd: "London: Sold by T. Osborne [and others]." It seems that Hoyle had unsold copies of the book, terminated the arrangement with Jolliffe and hired Osborne as a new distributor, selling the book at a much lower price to coincide with the new work on Chess. It is also interesting that the verso of the cancel title has an erratum, noting that "in page 57, line 2, read for doing it instead of against doing it." Chess, by the way, has the imprint "printed for Thomas Osborne [and others]" suggesting that Osborne owned the rights.

It was only the 1760 reissue that sparked the Irish reprinters.George and Alexander Ewing reprinted the work in 1761, also incorporating it into The Polite Gamester.

(click to enlarge)

In 1764, Osborne reprinted the Doctrine of Chances, pictured at left and freely available for download here. Here the imprint suggests that Osborne and Baldwin owned the copyright: "Printed for T. Osborne, in Gray's-Inn, and R. Baldwin, at the Rose in Pater-noster Row." Note, by the way, the small piece of drab paper affixed to the title page. This is a remnant of the original paper wrapper for the book.

The autographs, pictured below, provide further evidence that Osborne and Baldwin owned the copyright. The title page notes "No copies of this book are genuine, but those that are signed by the proprietors on the back of this title"  Hoyle did not autograph the verso in any copy of this edition I have seen—only the signatures of Osborne and Baldwin appear. Osborne and Baldwin must have been the proprietors and Hoyle's contract with Osborne to sign his early works (see my "Pirates, Autographs, and a Bankruptcy" p144) did not apply to Chances.

(click to enlarge)

We are left with this list of separately published editions of The Doctrine of Chances:
  •   Chances.1: London: Sold by J. Jolliffe (1754) 
    • Chances.1.1: London: Sold by Osborne, Crowder, and Baldwin (1760), a reissue of Chances.1
  • Chances.2: Dublin: Printed for the Ewings (1761)
  • Chances.3: London: Printed for Osborne and Baldwin (1764)
  • Isaac Todhunter. A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. Cambridge and London: McMillan and Co. 1865. Reprinted New York: Chelsea Publishing Company. 1949.

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