Show lr f j 4 s 's i If zT V r B Bridge rl dg e like e eam t M Marria am B v h a. a ae V MV e e ei i I 1 1 i it i wF J 11 T Shows S. S to S People People Up I n p b Cn u. u r h y vA l i ry J r 1 r J rr a 1 f lye dh M 1 yr 4 Y 1 r Chance Plays Little Part Partin a J tt l y Your F i in Favorite t i y f Y Y S Sy 6 r ti v y F 9 i a r y A a aY i Card Game Game It It Is Cold Y f r Jr n I t m m N J t Mathematical Deduction Deduction- f t. t i r A C. D fa Ap tY Y m r w. w vy'S y p 4 rK J vy fy j. j fa S y K i l J. J Says This rh s 's College C Q 11 ege Professor P ro f im sis and Concentration Is the Only 7 i L l d i m r i. i A t. t m mft S t G t t I 1 a a t Way ay to o 0 Win In X r h w 5 i ro r f f l J J r t J rf rt i 4 Y r l h N sY v b. b i r r J lt 1 l I Y h 1 l J vf s' s i c 4 C r ry t II f r i Y n a y I at r e rr IJ J II 1 4 6 to r r Q 4 It t- t or a.-or Or O 0 S f h d' d J r t J rl r ft- ft vC 3 r l 4 j 6 f r r T lf V t t l a S y v r r r k t r Y rr Y TY y in R Nf 4 b tr C Y f C a J e n aC a F t O o. o Q Q J i iI Ip 40 O 7 h r r ot Z Y 1 rt i aJ r d r r J r kC i S r r v d fL a X r 7 64 V i-V iVr up f 0 2 ti t- t r r 4 ti J 1 hilI i I. I 7 I 60 y f e 19 F E S T l r w r I J 3 tt y f r Y r. r r Y j i 4 4 ii 4 Crl IV 1 r I y 1 r I 9 r rF t F p 64 4 k cK r J n I T r rf l r 2 K 1 a 3 II QC Q- Q r 4 af 1 h f C 1 E r 11 l 1 y li r rV V 1 j y I i S S f rrt f t i A effect No Trump hand which accord accord- ing t to Mr fr Gibs Gibso ie 1 turns up only once in int t about deals f- f I As Carol Bird I 1 pop b bridge ld 4 players are those wife who know knour r when to make exceptions to the standard ule uld for lor b bidding a and play those thOe who dp do not ot to deceive dve their partners deliberately when this thin will not partners partner a and themselves them them- selves dam damage ge but will tOUl hurt their opponents nt I those who donot do not play hun hunches he or double a abid I bid of 0 four on onge g raZ P principles sr I I Poor bridge players are t those se who h always do tile the sane same things thIng in the same ame circumstances t I so o O that ater lI you U have played playe with th them m for a awhile a awhile I I while yo you can anticipate them TN IN INTHIS THIS HIS succinct ct Sa fashion on Theodore Gibson n head of the e m mathematics mathematic dear department ent cf if f Long Island S University Brooklyn N. N Y ca classifies star r and h ham hambridge 4 am L JI bridge players player and you can can figure e out for yo y yourself self v vin in which category your p brand of o f play r.- r. rightfully p ces you Mr dir Mr Gibson amplifies these statements statement too so that if you read on on you will I thoroughly understand why You lyou are considered eyed a 1 br brilliant lUant bridge player or or on the other h hand nd why when you ask a a. certain you young g wo woman n to b be your bridge partner for an evening she me pleads a sick h headache adache and then tells your rival she's tired o of beings being set back several hundred every a she plays with you You wIn will learn leam too how hO important it ft is 15 to have havea a mathematical mind when and how to finesse e when and when not to redouble when it is safe sate to w bluff and when not to to ho how w you have have- mathematically t ally cally about one chance in fo forty ty bU billion bUllon of holding a perfect hand hanCl In a game of bridge ge and t th that t you have a fair talc chance of winning by the method of t 4 deduction deduction and Uon and predicting P g what what- your partner and arid all U hands around the bridge table hold r r r 1 y 7 1 r J r r I f J. J J r p py v A i dr v ry t p f y y l nr v 3 r J yar 1 f lF n 7 T R C Yi Yip y p N S Ul Y il 4 br R Rr r fy r M MS t n j S 4 lp r f ln F F 2 f a I a o S t 5 y a lr r. r ch s' s r Y try l 1 jr C A i r H 7 y Theodore Gibson a her t ry ti k mat mathematician h and J f fY Y f t 1 r ij Y y bridge expert expert f p a Tr r declares declares' too r r. ruch t re w i vI L N lias den ulen en f t 4 Ji ss r r t pl placed aced ed o on ti bidding bidding J in re recent ent y years ars and r b NC Jy y n 1 r J f Y A Ky r r. r Yr i S i l thai that s skillful playing y da Ai G k r iia r fi 1 11 y k r fJ-r o of f brid bridge g c h hands ands h has J C r l y i r been neglected i because of this 41 t say a V y J k r a Y Y Wr i r C Cr sided one i instruction t tr J i 4 3 9 R 6 0 16 7 rr s Z 7 S A 9 1 O l K K P Z 3 so 4 10 10 42 2 11 l 2 o. o J 10 k Al y s. s A A 9 8 V m J t 43 5 t 2 A. A r 4 60 86 10 AK 75 5 Q O. O Q Q Q i r rr ti l a t i r Mr r. r Gib Gibson n who is is' considered l. l a bridge bride E Einstein I ha has i introduced discussion bridge into 1 his his' classroom 1 1 because he believes that to 1 due duc the wide wide- spread d dad cia In interest in is the game It t holds the attention attention- tt of t better Detter z than df dry I mathematics problems in which mythical persons ons or or- meaningless m committees commit t t tees and gro groups pa of people figure figur He says sara 1 4 r that mathematical deduction deductIon pl plays la s an Im important Important im- im part partIn in bridge he has haa work worked d out the mathematics mathematical 1 chances of winning t a ridge bridge game under stated conditions M Mand and declares that bridge is Isa a crucible in which men's mens c Characters i nay cay be tried a and d tested o e tc UCH been Jus been written about bridge a but in my opinion all aU of ot the books 1 p pay y too m much ch attention n to the bidding instead d of the play said Mr Gibson J who satin sat in 1 his s classroom m completely con le ly s 's surrounded sur cu r rf rounded by blackb blackboards blackboards' ardS' ardS chalked up witha with witha a array rr y of figures an and f a handy b book k of 1 logarithms p at t. t his el elbow w. w A As Asa a result of m stressing the importance of bid S ding there ther is an ari a actual and marked de de- de S cline In P plaY g ability these d days ys coniE continued con continued con con- iE tinned the ii tb i who then took up tip the t matter of- of the tricky finesse andi and i other bri bridge problems in which m matte mathe mathematical the the- 7 j nati ded deduction tOn vand cI logical reasoning 1 r t uT Take J the q q- q quest question iOD on of whether to r finesse or or n riot riot 1 t said saki MR Mr Gibson You You Youcan i can can- caniell i tell u In advance with a a fair aino amount I t t at crease ea In So some some e cases cans what chances chances' you Yu o our 4 r i. i have of your ur finesse e working t if It f for rI instance Iri- Iri stance you have ve all the trumps except t f four ur and nd and three others are ue r aa A 1 tri out out against you y you 1 can n. n lead a a trump mp 1 S and if it the e second ond hand plays a small one one K then the chances han ate are ie that t if U you finesse dpi v i y you U will WU Twin twiny w n threes I. I times Umes es to every o oner one r y time you IJ lose Is to a three three to one 1 f ct i f chance c ce However r there th re are certain circumstances cir o lire i c ta in which It it would not t be W f worthwhile W Ulf bU e to tae Ul chance c ha- ha habe nee because be pf t w winning ni the the finesse will give you only t i-t six p points Of and and ancl l loins g it It rould penalize i r s 4 TA M-TA- r JI l J yo you fifty points 1 t the three one t r one e c chance ce 4 i h r of winning would not be Justified in view fr k of ol th the eli eight one to t to tc ne nen penalty n of losing i Another A o. o point which do does S- S Snot not receive wv much uch attention n on brid bridge ge is the i r t fact tut ct that ln in many cases cases- th the longer mier you 1 k f. f lIU u r l t I I r I of j t i i r r 1 S J. J 0 Ji t f d delay trying better cantell can a finesse the you tell teU y your ur chances han es' es of making it IL Take this ex example mple In InNo T InNo No T Trumps uns where where your expect ex ex- pact to finesse the Spades if you play other suits there tt ere is s S a a very good chance of ot your discovering that one n of the players players players players' play play- ers ers ers' Is la short in one ant of the other suits This means that that his chance of having more more than the normal allowance of ot Spades will be increased and arid if there is isan Isa isan a an cha chance ce of the finesse working that it m must t be through gh him that the finesse should be played Chance does not play a very great IT rale le In bridge but but- mathematical deductIon deduction deduc- deduc tIon does It If is 15 very seldom eldom that that- two superior players players' will g go through a whole evening losing to two inferior r players merely because of ot the way the cards run Even though chance t favors vors the poor players the good ones will usually come out ahead As I s said ld the good player knows when not to be hampered by hidebound hidebound hide hide- bound rules such for instance as playIng playing playing play play- ing the fourth best in his longest and ana strongest s suit butt And Ancl even at at- atthe the risk of incurring his partners partner's temporary amazement amazement amazement amaze amaze- ment arid and ire tre by misleading her In hi a play he will be daring e o gh to disregard disregard disregard gard this this' rule if af at the same time it it will not damage their interests but will on the contrary by misleading the opponents opponents oppa- oppa f rth r them cc W RILE mathematical deduction plays YV its part in th bridge there are ate are certain tain conditions which arise arse which cannot be figured out ut except In hi advance and nd used as the s the a action requires because the calculations calculations lations necessary ry take so long a time to work out ut But there are sItuations many situations in which rapid calculation will show that a. a certain Course urse of ot procedure should be followed Powe t I. I For or inS instance nce it might seem natural t to assume that in a case we where th there re are are al six bc cardin cards card in a S suit salt o out t against agal t tou you ou that these six cards will be evenly enly divided d more marc often than otherwise but this this' is Ia not at all aU true true for there will wUI be bea bean ian a an J e even even en division only t s' s out of t two thirty tf wo a and d the most likely division Is hand and two in the other I t f I I I 1 i t t Y j v. v I L B f t a n Y f t H which v. times out o of thirty thirty- two The cards will wUl be divided one five 1 six times s and nd six none six once out of thirty thirty- two It Is s riot riot o necessary sart to to employ Y ma mathematics mathe mathe- mathematics he- he matics In calculations like this for by simply tak taking ng a a. a apack pa pack k of cards and removing re- re moving six sift cards at a a. time and tabulating the results as ai to red redl and black whether the division is three-three three two four-two five five- one or six none it will be found that in sixty four tries the division will run rim very close t to the the percent percentages g S' S given above The important thing in the whole proceeding in n th this s distinction Is that piat you like Uke to say that the two three chance is worth taking Butt But it it is not 1 if you are going to lose more than twice as much as you ou will WUl gain If It you have been asSuming that division was likely I 1 am sure your game will improve if you revise this assumption t TD I G to the subject of ct-of of bridge RE tv types let yet m roe me s say y that that- the 10 lowest scale lof bridge player is t the e pe person n who t if he c has to either ither aJack or a Ten en ona ona on ona a higher card card puts invariably on on- n the Ten en A player of a little r grad of Intelli Intelligence l gence is the one who invariably puts the the J Jack ck on to fo fool l the opponents but the highest-grade highest player Is the o one one e who puts itS the Ten when on- on when the oppOnent figures he be will wUl put the Jack on von If he has has' it It Itris t- t is 15 the same me with aitchi Ditching ng batting and other sports lou ou i ou can outsmart theother the other fellow by making a m move ve does he-does not expect you t tomake m ke though you can can can- carry tills this trick to extremes and overwork it to your own own disadvantage ge r It It requires only a slight knowledge knowledge of ot the subject of probability to determine determine- I that the chances of a hand containing only cards of one me particular suits suit b being dealt to a particular person are about one o out t of Since there are re four suits the chance for any U unit 1 t isone is one oyt of but there four players in a game the chance of Orl some me player receiving thirteen of oti souse some m suit is one out of about Th The chance of h holding four Ass ACes in one hand r 1 l t f of i t 4 i. i i J iV i f V. H r i fit t t j I Gett Getting e in ng the e eVYn L Lowdown ow d' d own VYnn n BRIDGE RIDGE reveals e. e ea s personal i ii i which are not i discovered in n everyday contact i A ma man with a had bad tem temper er erwill will air air it d during ring a a bridge game The crank cranky pers person n will how I his hie irascibility while playing The man man who is pr prone rove e to toi i blame his hie shortcomings en on bad I ii i I 1 lucks instead instead d 0 of f. f on h- h himself Imse If i is I s com comes cornea 8 to light s s The The woman woman with the supers jf I i critical 1 sense In indulges Jd 1 ge in In h her r. r i ilo l lo love c of fault finding while playing play PisY- i ing bridge The h stickler for or conventions s insists on exacting penalties a Sullen 5 u 11 en qua qualities I. I goo good d' d sportsmanship sports ii i i manship nervousness geniality concentration concentration concentration- ri bluffin bluffing i intolerance t ler i mice ance irritability forgiveness a optimism pe pessimism all all these arc shown 7 in in those w who o tem tem- por rily lose themselves in the has fascination ri of of a bridge game i a a Theodor Gibson ibson G Mathematics Mathematics- r i ia ts' ts t Professor p Oi r. r Zon Long Island laland l N. N Y Y j Y University lIv r ty i a 4 isone ione is ne out of f five honors one out put of 09 n four honors In one hand one one out of nineteen The chance of holding a perfect No Trump hand su such h as Ace Kl King Queen of oft t three ee suits stilts and and d the A Ace e. e King ng Qu Queen en and andI I Jackie the th the fourth is about one in 60 60 These T se are are the the spectacular figures of of probability in bridge yet few realize realise what real leai a help the science of chance can caa bein be i in scientific play A plan of play which las has three out of succeeding UCc a three out four f-four chance sue suc- c J g lv would note ot b be justified losing If If l losing W ul c v t the e opponents five times es as s 2 II a as' as 1 you would l gain bY by IY win win- t 7 t J i l 2 ti iM i ii u. u r. rf M hr Ll 0 v w f 1 A E ye fp tO t y ning On the o other er hand It U would be perfectly sound bridge to take t kea ra out one-out- of-four of chance if you you would win five times as s much as you ou w would lose tc FOR OR a suit sui t with th C ou outstanding the division will b be be- beas as follows Twenty times Im s' s out of ot two thirty two on the average the division will be three two e ten times Umes one four and twice e nv five However fora suit with four cards in the opponents opponents' hands the cards lie wUllie three three- one sixteen times Umes out of two thIrty the even division twelve times and the none three division n four times It should be remembered though that 1 it LS is frequently I necessary to make allowances in these thee figures 1 if your opponents h hays have ve shown by their bidding cr or their play that all is not as it might b be expected ted to be And in bidding you mey normally expect your partner to have ave his average a allowance of one of each of the face cards yet |