March 3, 1882.] 



♦ KNOWLEDGE ♦ 



395 



lit tramps, five of which were in one hand, between ns, we lost 

 Kf tricks out of the thirteen." 

 . follomng game is made np to show liow this might happen : — 



A. 



-K, 10, 9, 8. 



-A, K, 10,0, \.-Z 

 s— 10, 3, 2. 

 londs — none. 



.— Kn. 

 res— Kn. 

 i[ Spades — A, Q, 8, 7, 5. 1 

 Diamonds — 5, 4, 3, 2. 



ji-B mako 

 doace of Hearts 



r. 



C; libs— A, G, 4,3,2. 

 Hearts— Q. 

 Spades — K. 

 Diamonds- A,K,Q,Kn, 

 8,6 



Z. 

 CUibs—Q, 7, 5. 

 Hearts— 8, 7, U, 5, 3. 

 Spades — Kn, 0. 

 Diamonds — 10, 9, 7. 



> trick, and card below it leads next. 



REMARKS AXD INFERENCES. 



1. — I'knows that -B is not play- 

 ing a false card in his (B'x) partner's 

 salt, so that B will be able (pro- 

 bably) to over-trump second round. 



2. — A, of course, continues his 

 suit. If he did not know that B 

 can trump the suit, he would not 

 force the adversai-y, being himself 

 strong in trumps. His play should 

 suggest to T that A is strong in 

 trumps, and he should give up the 

 line of play he had intended to 

 follow. He must peld to the force ; 

 if he declines, he will be forced 

 again next round, and must either 

 yield then under less favourable 

 conditions, or let Z ruff, who must 

 be weak in trumps. It is betterto 

 throw the lead at once into Z's 

 hand. If he had done this, Z would 

 have made the second trick with 

 trump, have played the Ace of 

 Spades, and then forced I'mththe 

 Queen. 1' might then have led 

 Diamonds, in order to force A 

 (which, as it happens, would come 

 off in the first round) leaving A 

 either to lead trumps under un- 

 favourable conditions, or to force 

 F, which i'could accept, being able 

 to force back with his Diamonds, 

 when Z would be left with length 

 in trumps. As it is, T, after throw- 

 ing away the commanding card in 

 trumps, is absolutely powerless. 



3. — The rest of the hand plays 

 itself. Y's discard of the Diamond 

 Ace at trick 9 is intended to show 

 his partner that Y has entire com- 

 mand of the Diamond suit, but 1' 

 gets no chanoe of leading Diamonds 

 or any other suit. 



He that will not whe.n" he may, 

 &(.-. — The follomng singular combi- 

 nation of cards is worth recording, 

 as it may be made to point a moral. 

 It came under my observation at the 

 Portland, Clay and my father being 

 partners. The game was four-all. 

 The dealer turned up a small 

 heart. Clay led a Diamond. The 

 second hand had Ace, King, Queen, 

 Knave, ten, nine, and two, of 

 trumps. With these cards, the 

 problem is how to lose the odd 

 trick. 



The second hand contrived it in 



this way. He had no Diamond, 



and trumped the card led, with the 



(third hand) also had no Diamond, and 



only one trump, the three with which he overtrumped. In the end, 

 the holder of the sixieme major only made his six trumps, his 

 adversaries having six winning cards in the uuplayed suits, which 

 neither of the opponents coulil trum]i. They therefore lost the odd 

 trick and the game. Had the second player ( B) trumped with the 

 nine originally, he must have won the game, however the cards lay. 

 For, his partner being dealer, held the trump card, and consequently 

 B, by then leading trumps, must make seven tricks, even if all the 

 remaining trumps are in one hand against him. No doubt B re- 

 garded the chance of the third hand's having none of the suit in 

 which he himself was void as practically nil. Nevertheless, he 

 might have made the game practically sure. 



The moral is : Never throw a chance away. 



" Card Table Talk," " Cavendlsh." 



All the Tbcmps ix one Hand. — A correspondent (J. Heaton, 

 Stirrey) asks what are the odds against all the trumps falling in the 

 dealer's hands, and whether it has ever happened. Two cases were 

 recorded a few years ago in the 'IVestminster Papers (we will look 

 the case up), and the editor made the remark that this showed 

 mathematicians to be wrong in stating that the odds were, in round 

 numbers, 159 thousand millions to one against such an occurrence. 

 ^Ve cannot see it. It would not be very much out of the way to 

 suppose that among all the wliist-plaj-ing nations of the earth a 

 million whist-partics play per diem ; and, say that in each case there 

 are twenty deals. Then it would require only 7,950 days, or not 

 much more than 20 years, to give 159,000,000,000 trials, wliich, of 

 course, would give an even chance that any particular hand would 

 be turned up once at least. [This is not quite correct, there are 

 two possible results in tossing a coin, but it does not require two 

 trials to give an even chance of tossing head once at least. Evi- 

 dently my papers on chance should soon be started. Let me note 

 that the exact odds against the dealer having thii-teen trumps are 



158,753,389,899 to 1. 

 Pretty long odds. — Ed.] The odds against the occurrence must, we 

 should think, be diminished by the cii'cumstance that when a ruffing 

 game has been played, there are several cards of the same suit 

 arranged one in each of several sets of four cards, after tricks are 

 gathered. Supposing them to occupy the same position in each 

 set, which might readily happen, that there is verj' little shuffling, 

 and that the same suit is trumps in the next hand, it will easily be 

 seen that four or five trumps might be ah-eady en train to fall to 

 dealer, so that the chance of the remaining trumps falling to him 

 alone would have to be considered. [Say the chance of this hap- 

 pening in the case of five trumps, besides the turn-up card were 

 only 1-1,000. There are thus 20 cards disposed of in the five tricks 

 supposed to have come together, in this special manner, in dealing. 

 There remain 32 cards, one of which is the turn-up. Out of the 31 

 cards, 7 are trumps, and form one set of 7 out of 

 31 ■ 30 ■ 29 ■ 28 • 27 ■ 26 ■ 25 

 1-2-3-4-5-6-7 

 possible sets of 7, or 2,629,575. Hence the chance of both events 

 coming off and all 13 trumps falling into one hand is one- 

 2,629.575,000th, or the odds only 2,629,574,999 to 1 against the 

 event. — Ed.] Five of Clubs. 



A CoERESPONiiENT (' Why ') asks whether certain whist rules 

 presented in doggrel rhyme are sound as far as they go. " They 

 appeared in London Society, he says, some time ago, and were said 

 to have been copied from some provincial club wall." They are 

 Pole's, and are sound as general rules. But scarce one of them may 

 not on special occasions be departed from ivith advantage. Sup- 

 posing, for example, you want the odd trick to win, and have five 

 small trumps, viz., one four-card weak suit and two suits of two 

 cards each. It would be absurd in this case to follow Pole's rule 

 respecting trumps — " When you hold five " 'tis always right to lead 

 them. Five of Clubs. 



J. ToMLiNSON.— Surely by not leading trumps when he gets the 

 chance, Z shows unmistakably that he has not been wanting trumps 

 led. and therefore he has not signalled. 



Geadatim. — Yes ; from Ace, six others in tramps lead Ace. The 

 lead of Queen from Queen, Knave, nine, and others (three others 

 vou specify) is now generally rejected. Hoyle advised it, with the 

 object of finessing the nine, on the return of the lead. This might 

 do in long whist, but not in the game as now played. 



Five of Clubs. 



W. F. — In Problem I. B leads trumps fourth round, because his 

 jiartncr, not knowing what B knows, would be at a loss how to play 

 after making the successful finesse in Diamonds. If he continued 

 the Diamond lead, B would have to lead from his tenace in Hearts. 

 The lead of trumps manifestly puts T at a disadvantage. He must 



