Jvsz 9, 1882.] 



KNOWLEDGE 



31 



and so on ; and if on the hypothesis U, the chance of the event 

 happening is C,, on the hypothesis U« the chance of the event 

 liappening is Co, and so on|; then, if the event hapjen, the chance 

 that H, is true is 



c,C, . 



c, C, + fo C» + C3 Cj + &c. ' 

 the chance tliat Ho is true is 



Co C; ; 



c, Ci + CoCs + CjCa + Ac. 

 and so on. 



(To le Continued.) 



SoLrTiox OF T's Problem. — Upon the line OB, taken = !>, con- 

 struct the n-sided polygon, OBGD, &c. (in the figure n=G). Join 

 the two alternate corners, O and G, by a diagonal OG. Upon OG 

 as a base construct the triangle GAO, making the two sides OA 

 and GA=a and e respectively, and taking care that A and B lie on 

 opposite sides of OG. 



Join AB, and on it construct the polygon of n-sides ABCLKI, 

 whicli is the polygon required. For 



By construction OA = a, and OB = b; also the triangles GAB and 

 BOC are equal ; because GB = BO, AB = BC, and angle GBA = CBO 

 (each being equal to the interior angle of the «-sided polygon 

 diminished by the angle ABOl. Hence OC = AG = <:. Q. E. D. 



Scholium. — If the point P' be determined on the same side of OG 

 with B, then the line BP' will be the side of a polygon fulfilling the 

 conditions of the problem, except that the point O will lie outside of 

 the polygon. 



iBuv 2231)151 Column. 



By " Five op Clubs." 



PLAY THIRD HAND. 



THE general principles which should guide the play third in 

 hand are — First, and chiefly, to help and strengthen your 

 partner as much as possible in his own suit ; secondly, to derive 

 all possible advantage from any strengthening cartl he may 

 play in your own suit ; and thirdly, to retain as long as 

 possible such partial command as you may have in an oppo- 

 nent's suit. You can generally toll (from the lead, the play 

 second hand, and your own hand) whether your partner has led 

 from strength, or to strengthen you, or from a weak snit in which 

 ho has no means of knowing your position. This will bo obvious 

 from what we have already said about interpretation of the lead 

 and the play second hand. Your play will be guided accordingly. 



Let us begin, tlicn, by considering the play third in hand : and 

 afterwards, as heretofore, with the lead and second hand, we can 

 consider the inferences to bo tlrawn from the play of particular 

 cards third in hand. 



If you hold Ace third in hand, and neither King nor Queen, yon 

 play it in plain suits, unless King or Queen has been led. Tlio only 

 exception to this is when ten has been led and you hold Ace, Knave, 

 when it is best to pass the ten. With Ace, King, you put on King, 

 as a rule. But with Ace, King, and more t'.ian one small one, a 

 good hand and four trumps, you should not put King on your 

 partner's Knave, but pass tlio Knave; fourth in hand is sure to 

 take the trick ; but when ti'umps are out you are tolerably sure of 

 getting in again, when you make two tricks at least, and [irobably 

 three in the suit. On the other hand, with Ace, King, and small 

 ones, but only three trumps, you should not pass the Knave. Tho 

 principle here applied is general. With good strength in trnmps, 

 you may usually finesse with advantage in a suit in which your 

 partner has led a strengthening card ; but when short in trumps, 

 such a finesse is unadvisable. 



With Ace, Queen, alone or with others, you should finesse tho 

 Queen, or the lowest card in sequence with the Queen — unless a 



single trick will make or save the game, when, of course, such a 

 finesse would be a Whist atrocity. 



With King, Knave, &c., some players finesse the Knave. This is 

 only right when you have such strength in the suit as to feel sure 

 your partner has led a strengthening card from a short suit. It is 

 nearly always wrong to finesse in your partner's suit. The finesse 

 from Ace, Queen, &c., is almost the solitary exception to this rule. 

 You should, therefore, in general play King, from King, Knave, 

 third hand. When nine is led, and you hold King, Knave, and 

 others, you pass the nine, if strong in trumps, and the state of the 

 game is not critical (supposing always that second player has not 

 covered tho nine). Otherwise, you may either finesse the Knave, 

 or not, as you may deem best. Fourth player is as likely to hold 

 .\ce and no other honour, as Queen and no other honour : if he holds 

 both Ace and Queen, it is indifferent what you play ; he will, in any 

 case, remain with an honour over you. 



(To be continued.) 



A correspondent points out what, of course, I had noticed myself, 

 that there is a double — really a single — error in my notes to th& 

 " Hand for Study," in No. 30. I had originally written out the 

 hands and ]>lay from memory, being, away from my books. I sup- 

 posed B had three tmmps, whereas in the actual game he had 

 but two. Hence, in my notes, referring to second trick, I said B 

 returns the highest of two cards left ; and referring to third, A leads 

 trnmps again, though he is drawing two for one. Of course, when 

 I saw the play of the hands, which had been taken direct from 

 Cavendish, I recognised my mistake. But from some cause or other 

 the necessary corrections were not made. The point of the game, 

 however, is not affected by the mistake. 



Vall-e of Good Play. — A correspondent asks whether good play 

 really counts much at Whist, and describes several tests to which ho 

 has subjected the matter, with the result that good players have no 

 better chance than bad ones. There is so much chance, unfortu- 

 nately, in Whist as actually played (it might be immensely improved 

 in this respect) that a casual observer, or one who watches play for 

 only a few weeks, or even months, might very well suppose that bad 

 players have quite as good a chance as the best players. But no one 

 at aU acquainted with the game practically can doubt that in the 

 long run good play must invariably get the better of bad play. Not 

 a Whist evening passes but a practised player will note half-a-dozen 

 cases or more in which tricks— sometimes two or three at once — 

 have been lost by bad play ; while not more than one or two cases 

 will occur during tho same time, in which bad play has, by an 

 accident, turned out well or good play ill. 



Cavendish's experience should suffice — owing to its wide extent 

 and carefully noted results — to settle this point finally and for ever. 

 He tells us that of 30,668 rubbers played from Januar\-, 1860, to 

 December, 1878, he won 15,648 rubbers and lost 15,020, and 

 counting points, which tell far more, he won in all 8o,l-S6 points 

 and lost 81,055, gaining thus a balance of 4,431 points. It is prac- 

 tically impossible that so largo a balance in his favour should be 

 due to mere chance. The difference must have been duo to play. 

 Were two good players matched in as many rubbers against two 

 bad ones, the difference would be far greater. 



^uv €l)ti5 Column. 



By Mepihsto. 



VIENNA INTERNATIONAL TOURNAMENT. 



After tho finish of tho 20th round on Saturday, June 3, the scoro 

 stood as follows : — 



Mackenzie 13i Zukertort llj I Tschigorin 8 



Stoinitz isi ■ Hruby 11 Weiss 8 



Mason 13 Wittek 91 Bird 7» 



Winawer 13 Schwarx 9 I Ware C^ 



Englisch 12t Meitner Si Floiasig 6 



Bluckbamo 12 Paulsen 8 



Dr. Noa has withdrawn from tho Tournament. From the nl)ovo 

 score it will be seen that tho English players arc well to the fore, 

 and we think that they will still more improve their position for 

 final place. 



On Thursday, Juno 1, Blackhumc had to meet Stoinitz, and tho 

 former won he conquering his mighty op]xinent in only twenty- 

 seven moves. Nevertheless, Stoinitz has dniwn well, ho having 

 reached Mackenzie's scoro, who had boon leading, by [>or«onalIy 

 vanquishing his rival for tho time being, in their second game, which 

 was iiluyed on Saturday, tho 3rd inst. Stcinitz's victory over Mac- 

 kenzie will have an important influence on the final issue. Zukertort 



