April 



1882.] 



* KNOWLEDGE • 



561 



Example 2. — / am waiting for the morning post. I reclton the 

 chance that I shall get a letter from a certain correspondent, A, at 



i : the chance that I shall get a letter fiom B at _ ; the chance that I 

 aet a letter from C at - : and, finalbi, the chance thai a letter will 



reach me fn " ' ' 



I get a letter by said post ? 



Here we must not multiply the several chances tojrether, because 

 the question is, not whether I get a letter from all the sources 

 named, but whether I pet a letter at all. Clearly, however, we 

 shall get the chance that I do not get a letter by multiplying toge- 

 ther the chance that I do not get one from each of the four several 



eoorces. Now, the chance that I get a letter from A is -, so that 



2 



the chance that I do not get a letter from him is -. In like manner, 

 ^ 3 



3 

 the chance that I ilo not get a letter from B is - ; the chance that 



4 



I do not get one from C, - ; and the chance that I do not get a 

 '6 



<) 

 letter from any other source, — . Hence the chance that I get no 



3 5 9 _ 3 



letter at all is 



3 4 



c _ X _, or -. That is, the odds are 5 to 3 : 

 G 10 8 



favour of my getting a letter. 



Example 3. — The chance that there vHll be rain on any day of the 

 year is -. A prophet announces that there will be rain on one of 

 th ree successive days. What are the odds in favour of the prophesy ? 



The chance of failure on the first dav is -, on the second -, on 



the third - ; the one chance of failure on all three days is, tin 



1 l" 1 1 

 fore, 2 X 2 X 2' °'" 8- 

 the prophet. 



The odds are, therefore, 7 to 1 in favour of 



(J^ur 2231) I6t Column. 



By " Five of Clubs." 



Play Second Hand (Plain Suit.s). 

 (Continued.) 



WE can now do, for play second hand, what wc have already 

 done for the lead, viz., reduce it to system by showing, not 

 as heretofore, what card to play from particular hands, but under 

 what conditions such and such cards should be played. This, as in 

 the case of the lead, has a double advantage; it gives simpler rules, 

 and it combines with the rules for play the inferences from play. 



Ace, Second Hand, 

 ia played on King, Queen, or Knave, from Ace and small ones ; on 

 Knave from Ace, Queen, and small ones ; and from Ace four small 

 ones, on a small card led, if the game is in a critical state or there 

 ia reason to believe that the lead is from a singleton. 



King, Second Hand, 

 is played on Queen or Knave, from Ace, King, with or without 

 small ones, and from King not more than two small ones ; on Queen 

 from King, ten, &c. ; on a small card, from Ace, King, with or 

 without small ones j from Ace, King, Knave ; from King one small 

 one, only when second player has special reason for desiring a lead. 



Queen, Second Hand, 

 is played on Knave, from Queen and not more than two small ones, 

 and from Queen, ten, and others ; on ten, from Queen and one 

 other ; on a small card, from Ace, Kim;, Queen, with or without 

 others ; from Ace, Queen, ten ; from King, Queen, with or mthont 

 others ; from Ace, Queen, and three others, or more, only if weak in 

 trumps ; from Queen one small card,' only when a trump lead is 

 specially required. 



Knave, Second Hand, 

 is played from Queen, Knave, and not more than one small one ; 

 and from Ace, Queen, Knave. 



Ten, Second Hand, 

 is played from Knave, ten, and not more than one small one ; from 

 Ace, Queen, Knave, ten ; and from King, Knave, ten. 



one small one ; from 



Nine, Second Hand, 

 is played from ten, nine, and not more thai 

 King, Knave, ten, nine. 



Lowest, Second Hand, 

 is played in all other cases, nnless to signal, when the lowest but 

 one is played. 



Problem 3.— Solutions by Phiz, K. M., U. C. T., .1. Harrison, S. 

 Febrook, M. ilurchison. Hanky Panky, correct. Piiiz, U. C. T., M. 

 Murchison, and others, ask (unnecessarily) if trump lead may 

 not come first. Of course it does not matter in what order the 

 first three tricks are made so that Ace of Spades takes cither first 

 or second trick.— Five of Clubs. 



Problem 4. — We have received twenty-sevon more solutions, all 

 correct. Several suggest that solution should not be published, but 

 we have (implicitly) promised solution. Will defer it. As a help to 

 several who hare failed, note that if after thirteenth trump led V 

 discards a heart, the problem — as Chief Editor pointed out — can 

 not be solved if A lead small heart. Hence infer A's proper lead.^ 

 Five of Clubs. 



A Two Suit Hand. 

 A correspondent, J. F., writes : " The other evening playing Whist 

 I had the following hand of cards dealt me ; six diamonds, seven 

 hearts (clubs being trumps) . This occnrred in the midst of a long 

 evening's play, the cards being shuffled before each deal in the 

 ordinary manner. Required the probabilities against the occurrence 

 of such a hand." 



A set of six cards all of one suit can be formed in 

 13 ■ 12 ■ 11 • 10 • 9 ■ 8 

 1 • 2 • 3 • 4 -5 • 6 

 ways, and a set of seven cards all of one suit can be formed in as 

 many ways, since for each set of six cards of a suit there is left a 

 set of seven cards of that suit. The total number of ways, then, in 

 which a Whist hand can be formed of six cards of one suit and seven 

 cards of another is given bv the formula — 



/ IS ■ 12- 11- 10- 9 ■ 8 y ^ 4-3 , ^^ 



Vl-2-3-4-5-6/''l-2'^''^ 



if the two suits may be any whatever, in which case there are -— 



ways in which the available suits may be taken 2 and 2 together. 



4 ■ 3 

 But if the two suits are not to be trumps, then for - — , we must 



3 ' 2 



substitute in the above expression r— ;-^ 



tions of the three available suits 2 and 2 together. In the former 

 case the number of possible hands being 



52 ■ 51 ■ 50 • 49 ■ 48 ■ 17 ■ 16 • 45 ■ 44 • 43 ■ 42 • 41 ■ 40 ,g. 

 1 • 2 ■ 3 • 4 • 5 • 6 • 7 • 8 ■ 9 • 10 • 11 • 12 • 13 ^ ' 

 the chance of a two-suit hand, six cards being of one suit and seven 

 of the other, is represented by a fraction having A as numerator 

 and B as denominator. In the latter case there are only 51 cards 

 available for the hand, as the dealer cannot hold it, and the 

 required chance is represented by the fraction. 



/ 13- 12- 11 -10 • 9- 8\ ,. 3-2 



\l-2-3-4-5-6/ 1-2 



4 ■ 

 1 • 2 

 the number of combina- 



51 • 50 ■ 49 • 48 • 47 • 46 • 45 • 44 • 43 • 42 • 41 ■ 40 • 39 



• 5 -6 -7 -8 -9 ■ 10 • 11 ■ 12 • 13 

 736164 ^^ jg j^j^gj. jggg ^jjj^^ 1^. 



39ti»8347475 53912 



the odds then are rather more than 53911 to one against the 

 occurrence of such a hand aa J. F.'s. 



The probability of such a two-suit hand, whether trumps or not, 



is obviously equal to the above multiplied by - . — or by - ; whence 



1 



35941 

 35910 to 1 against the ocoarrence of the hand 



1 • 2 • 3 

 This reduces to 



the chance is rather less than 



52 ' 2 



or the odds rather more than 



-Ed. 



An Unsound Finesse. — Clay was looking on when second player, 

 " whom he favoured not," holding Ace. King Knave, finessed the 

 Knave. " Tha Queen made, third hand; Ace and King were after- 

 wards trumped. The player then turned to Clay, and asked 

 whether the finesse of the Knave was justifiable. To him the 

 following crushing rejoinder, spoken very deliberately at the wall 

 opposite, instead of to the querist : — 



•• ' At the game of whist, as played in England (pause), you are 

 not called upon to win a trick (another pause) unless you please ! ' " 

 — Cavendish's " Card-table Talk." 



