DE MOIVRE. 165 



Honour, and 2nd, that in which the card turned up is not an 

 Honour. Thus we should have for the required probability 



_4 8 25 . 26 . 25 9^ 4^ 25 . 24 . 26 . 25 ^ 

 13 ■ T * 51750 . 49 "*" 13 * 1 . 2 ' 51 . 50 . 49 . 48 ^ 



and this will be found equal to -^^ . 



loob 



De Moivi'e has two Corollaries, which form the chief part of 

 his investigation respecting Whist. 

 The first begins thus : 



From what we have said, it will not be difficult to solve this Case 

 at Whisk; viz. which side has the best, of those who have viii of 

 the Game, or of those who at the same time have ix? 



In order to which it will be necessary to premise the following 

 Principle. 



1° That there is but 1 Chance in 8192 to get vii. by Triks. 



2° That there are 13 Chances in 8192 to get vi. 



3" That there are 78 Chances in 8192 to get v. 



4" That there are 286 Chances in 8192 to get iv. 



5° That there are 715 Chances in 8192 to get iii. 



6° That there are 1287 Chances in 8192 to get n. 



7" That there are 1716 Chances in 8192 to get i. 



All this will appear evident to those who can raise the Binomial 

 a + b to its thirteenth power. 



But it must carefully be observed that the foregoing Chances ex- 

 press the Probability of getting so many Points by Triks, and neither 

 more nor less. 



De Moivre states his conclusion thus : 



From whence it follows that without considering whether the viii 

 are Dealers or Eldest, there is one time with another the Odds of 

 somewhat less than 7 to 5; and very nearly that of 25 to 18. 



The second Corollary contains tables of the number of chances 

 for any assigned number of Trumps in any hand. De Moivre says, 



By the help of these Tables several useful Questions may be re- 

 solved; as 1°. If it is asked, what is the Probability that the Dealer 

 has precisely iii Trumps, besides the Trump Card ] The Answer, 



. rp . . 4662 

 by Tab. i. is .^^^^ ; ... 

 158y5 



