| Title: | Wager |
| Original Title: | Pari |
| Volume and Page: | Vol. 11 (1765), p. 942 |
| Author: | Jean-Baptiste le Rond d'Alembert (biography) |
| Translator: | Richard J. Pulskamp [Xavier University] |
| Subject terms: |
Analysis of gambling
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| Original Version (ARTFL): | Link |
| Source: | Originally published at http://www.cs.xu.edu/math/Sources/Dalembert/ ; used by permission |
| Rights/Permissions: |
This text is protected by copyright and may be linked to without seeking permission. Please see http://quod.lib.umich.edu/d/did/terms.html for information on reproduction. |
| URL: | http://hdl.handle.net/2027/spo.did2222.0001.120 |
| Citation (MLA): | d'Alembert, Jean-Baptiste le Rond. "Wager." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Richard J. Pulskamp. Ann Arbor: Michigan Publishing, University of Michigan Library, 2009. Web. [fill in today's date in the form 18 Apr. 2009 and remove square brackets]. <http://hdl.handle.net/2027/spo.did2222.0001.120>. Trans. of "Pari," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 11. Paris, 1765. |
| Citation (Chicago): | d'Alembert, Jean-Baptiste le Rond. "Wager." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Richard J. Pulskamp. Ann Arbor: Michigan Publishing, University of Michigan Library, 2009. http://hdl.handle.net/2027/spo.did2222.0001.120 (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Pari," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 11:942 (Paris, 1765). |
Wager, when two players A , B , play the one against the other, and that the expectation of player A is to that of player B by ratio of m to n , the wager for player A is also to the wager for player B in ratio of m to n ; or the number m is nothing other than the number of cases which could make player A win, and n is the number of the cases which could make B win. For example, if a player A wishes to produce 12 with two dice, one has m = 1, and n = 35, because there is only one case which could bring 12, and 35 which will bring another thing. See Die. Therefore in order to wager even, that is to say with an equal advantage, following the ordinary rules of the games, it is necessary that the stake of player B be to that of player A as 35 is to 1.
Similarly, if one wagers to produce in six throws a doublet with two dice, it is clear that the number of the possible throws is 36 6 , and that the number of throws where there is no doublet 30 6 ; whence it follows that the wager must be as 36 6 - 30 6 , that is to say, as 6 6 - 5 6 is to 6 6 .
For the remainder, these rules must be modified in certain cases, where the probability of winning is very small, and that of losing very great. On which see the article Game.