| Title: | Clean sweep of the dice |
| Original Title: | Rafle de dés |
| Volume and Page: | Vol. 13 (1765), pp. 755–756 |
| Author: | Louis, chevalier de Jaucourt (biography) |
| Translator: | Richard J. Pulskamp [Xavier University] |
| Subject terms: |
Calculus of probabilities
|
| 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.did2222.0001.122 |
| Citation (MLA): | Jaucourt, Louis, chevalier de. "Clean sweep of the dice." 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.did2222.0001.122>. Trans. of "Rafle de dés," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 13. Paris, 1765. |
| Citation (Chicago): | Jaucourt, Louis, chevalier de. "Clean sweep of the dice." 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.did2222.0001.122 (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Rafle de dés," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 13:755–756 (Paris, 1765). |
Clean Sweep of the Dice, [1] it is a cast where the thrown dice all come on the same point. If you want to know the advantage of the one who would attempt to produce in a cast with two or more dice, a determined clean sweep of the dice , for example terne, you will consider that if he took among them with two dice, he would have only one chance to win, and 35 to lose, because two dice are able to be combined in 36 different ways; that is to say, that their faces which are six in number, are able to have 36 different lies, as you see it in this table,
| 1,1. | 2,1. | 3,1. | 4,1. | 5,1. | 6,1. |
| 1,2. | 2,2. | 3,2. | 4,2. | 5,2. | 6,2. |
| 1,3. | 2,3. | 3,3. | 4,3. | 5,3. | 6,3. |
| 1,4. | 2,4. | 3,4. | 4,4. | 5,4. | 6,4. |
| 1,5. | 2,5. | 3,5. | 4,5. | 5,5. | 6,5. |
| 1,6. | 2,6. | 3,6. | 4,6. | 5,6. | 6,6. |
this number 36 being the square of the number of faces 6 on two dice. If one had 3 dice, instead of 36, square of 6, one would have 216 for the number of the combinations among 3 dice; if one had 4 dice, one would have the fourth power 1296 of the same number 6, for the number of the combinations among 4 dice, and thus in succession.
It follows thence that one must put only 1 against 35, in order to make a determined clean sweep of the dice with two dice in one throw. One will know by similar reasoning, that one must put only 3 against 213, in order to make a determined clean sweep of the dice with three dice in a throw, and 6 against 1290, or 1 against 215 with four dice, and thus in succession, because of the 216 chances which are found with three dice, there are 3 of them for the one who holds the die, since 3things are able to be combined 2 by 2, in three ways, and consequently 213 contrary to the one who holds the die: and that of the 1296 chances which are found among four dice, there are 6 of them which are favorable to the one who holds the die, since four things combine two by two in six ways, and consequently 1290 contrary to the one who holds the dice.
But if you want to know the advantage of the one who would undertake to make any clean sweep of the dice on the first throw with two or more dice, it will not be difficult to know that he must put 6 against 30, or one against 5 with two dice, because, if of the 36 chance which are found among two dice, one takes off six chances which could produce a clean sweep of the dice , there remain 30. One will know also very easily that with three dice, he is able to put 18 against 198, or 1 against 11, because if of the 216 chances which are encountered among three dice, one takes off 18 chances which are able to produce a clean sweep of the dice , there remain 198, etc .
Notes
1. This refers to an old game of dice in which 3 dice were cast. The one who cast three alike won. If this did not occur, the one who threw the highest pair won.