## The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play |

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### Common terms and phrases

Arithmetic Progression bability Banker bility Cafe Caster Chances for losing Chances for taking Chances for winning Coefficient Corollary deduced Denominator denote Dice difference divided Doctrine of Chances equality of Skill Equation Expectation express the Probability find the number foregoing Four Stakes Fraction Gain Gamesters Geometric Progression given number Happen Index last Term Lemma let the number Letters likewise Loss Method Multiplied Nicholas Bernoully number of Cards number of Chances number of Games number of Pieces number of Stakes number of Terms number q o/Chances Plays Ending Ponte Proba Probabilities of winning Probability of taking Probability required Product Quantities Quotient Relation remaining required to find respectively Set be ended Solution subtracted from Unity supposed taken taking an Ace Theorem third throwing Wager whence it follows Wherefore the Probability whereof whole number whole Stake win Two Stakes winner winning the Set won or lost

### Popular passages

Page 1 - Probability of an Event is greater, or •lefs, according to the number of Chances by which it may Happen, compared with the number of all the Chances, by which it may either Happen or Fail. Thus, If an Event has 3 Chances to Happen, and

Page 120 - and let the Four Terms next following be taken likewife, without regard to their Coefficients; then prefix to them, in an Inverted order, the Coefficients of the preceding Terms: Thus the Four Terms following with their new Coefficients, will be

Page 120 - many of the Terms next following as have been taken already, but prefix to them, in an inverted order, the Coefficients of the preceding Terms. But if d be an even number, take fo many Terms

Page 40 - The Banker wins the Stake of the Ponte, when the Card of the Ponte comes out in an odd place on his right hand ; but lofes as much to the Ponte when it comes out in an even place on his

Page 120 - and prefix to them, in an inverted order, the Coefficients of the preceding Terms, omitting the laft of them ; and thofe Terms taken all together will compofe the Numerator of a

Page 40 - Thirdly, the Ponte may at his choice fet one or more Stakes upon one or more Cards either before the Banker has begun to draw the Cards, or after he has drawn any number of Couples,

Page 6 - Suppofe there is a heap of 13 Cards of one colour, and another heap of 13 Cards of another colour ; what is the Probability, that taking one Card at a venture out of each heap, I

Page 126 - TO Find what Probability there is, that in A given number of Games, A may win the number q of Stakes ; with this farther

Page vii - if they would take the fmall Pains of being acquainted with the bare Notation of Algebra, which might be done in the hundredth part of the Time that is

Page 7 - to the Power n. And if A and B play together, on condition that if either one or more of the Events in