Paris: Jacque (sic) Quillau, 1708. First Edition. 4to (270 x 200 mm). xxiv, 189, . With three folding engraved tables, title-page with engraved monogram, four vignettes by Sebastian LeClerc showing games, 2 engraved illustrations of Trictrac boards in the text. Contemporary French speckled calf, spine gilt, red lettering piece, comb-marbled endpapers, edges sprinkled red. Binding extremities rubbed (most pronounced along fore-corners), covers with some scuffing or staining, verso of front endleaf with inscription erased; waterstain on first blank endleaf through first and second gathering (including title-page), A3 with old paper repair in the margin, gathering C slightly browned on account of the paper stock, other spotting in the text here and there, but a very good, unsophisticated copy, the paper quite strong and the binding sound and attractive. Very good. Item #3210
First edition of one of the great works in the development of probability theory, its importance summarized in a single sentence: "In 1708 (Montmort) published his work on Chances, where with the courage of Columbus he revealed a new world to mathematicians" (Todhunter, p. 78).
Montmort's "Essay" is "the first published comprehensive text on probability theory, and it represents a considerable advance compared with the treatises of Huygens (1657) and Pascal (1665)" (Hart, p. 290). Our copy is preserved in a contemporary binding and belongs to the second issue, i.e. with the three requisite engraved Tables that are not present in the first issue.
The "Essay" deals with the application of combinatorial considerations as they appear in elementary probability theory and gambling. But "the greatest value of Montmort's book lay perhaps not in its solutions but in its systematic problems about games, which are shown to have important mathematical properties worthy of further work" (DSB). Of particular significance is Montmort's approach the so-called Game of Thirteen ("jeu de treize") which he utilized as a vehicle for proposing a problem of coincidence. According to Takacs, Montmort's Problem had a great influence on the development of probability theory. Certainly it has remained current for more than 300 years and continues to resonate today through the analysis of the so-called "Hat Trick / derangement Problem," "frustration solitaire," game theory, coincidence theory, the number "e" in calculus, and theoretical computing.
The "Essay" contains Montmort's insightful Preface followed by four "On card games" (including the game of Pharaon and Game of Thirteen), "On combinations," "On dice games" (including Trictrac), "Solutions of various problems of games of chance" (including Huygens' five problems and de Mere's problem) and "Four problems to be solved" (pp. 185-189).
"Montmort continues in a masterly way the work of Pascal on combinatorics and its application to the solution of problems on games of chance. He also makes effective use of the methods of recursion and analysis to solve much more difficult problems than those discussed by Huygens. Finally, he uses the method of infinite series, as indicated by Bernoulli (1690). [...] Montmart's pioneering work had three features: 1) It demonstrated the four methods of solution mentioned above; 2) it gave the solutions of many important new problems; and 3) it inspired Bernoulli and de Moivre to generalize these problems and develop new methods of proof." (Hald, pp. 290 and 291).
Montmort was in the vanguard in the emerging field of combinatorial mathematics, answering questions and proposing others that continue to captivate historians of science. Not only did he examine the mathematics of games of chance, but -- perhaps more importantly -- he proved mathematically that certain methods of play that are based on "superstition" is less profitable than rational behavior, not only at the gaming table but in "real life" (sic).
This important work reflects and amplifies the goals of French Enlightenment philosophy, namely: the vanquishment of frivolous superstition through rationalism. Montmort's probability theory demonstrates that there exists no capricious superior power determining the manner in which the cards fall: there is only mathematics, and the calculable ratios between the chances for all possible outcomes. Kavanaugh reminds us that "This, however, is not the only lesson of the cards. Within the perfectly systematic calculations sustaining Montmort's analyses, the truly wise reader is invited to discover the careful hand of the Creator, the presence of a Newtonian first clause responsible for a perfect order. Anticipating Laplace by more than half a century, Montmort redefines 'le hasard' as nothing more than an index of our ignorance."
LITERATURE: David Bellhouse, "Banishing Fortuna: Montmort and De Moivre" in: Journal of the History of Ideas,
Vol. 69, No. 4 (Oct. 2008), pp. 559-581. Ibid., "The Problem of Waldegrave," in: Electronic Journal for the History of Probability and Statistics, Vol. 3, No. 2 (Dec. 2007). Anders Hald, A History of Probability and Statistics and Their Applications before 1750, Chapter 18 (and passim). Isaac Todhunter, History of the Theory of Probability, Chapter 7 (and passim). Lajos Takacs, "The Problem of Coincidences" in: Archive for History of Exact Sciences Vol. 21, No. 3 (4.VI.1980), pp. 229-244. F.N. David, Games, Gods and Gambling, pp. 140-160. Warren Weaver, Lady Luck: The Theory of Probability, pp. 135-140. T.M. Kavanagh, Enlightenment and the Shadows of Chance: The Novel and the Culture of Gambling in Eighteenth-Century France, pp. 12-13.