The sun. [volume] (New York [N.Y.]) 1833-1916, 1910-10-30
PROBABILITIES AT BRIDGE
SONE FIGTRES ON THE DIS
TRIM TION or TRI HPS.
Pointers for the Bidder AZ NYetIon bridge
Danger Always la O,rrF-siImatinE
value Of I.ong suit without IIonsrs
Nhrrr the Other CaF,is MHI IIP.

IN -idte ~ the constant and lECTsasl's
demand fur some reliable tablss II refer
eu"" showing the probabilities - certain
events ia the game u bridge. no one ha-
come forward 10 do or the bridge play
ers what DR. Pole did for the whist play
~r- in hi- famous book The Philosophy
Of Whist Probabilities
1h"s who are taking up auction bridge
come 10 realize very quickly that in COM
putting the number u tricks a hand should
h" good for one OF the most important
elements Ia the calculation IL the tric.;
taking power Of small cards IN the trump
suit
Writers on card games who are not
mathematician sometime fgll tntp curl
prs error IA their statements ~ prob
abilities H. ,lc~punt. for instance. -ay-
that II a player has seven diamonds hc
-npiiii d"rlArr diamonds ~ Troy are good
Tor three 'r,rf-. bat that II he has six
unlv DO" should make ~ spades IA the
hand j. uu, worth ANYTHING Commenting
uuun tii~. another writer ASKS How
can IN" small carl add three tricks 20 an
o'herNi-" worthless hand. 81 tho spade
max" ~ doubled they are worth four,
and a. the PLAYER has deliberately made
B his long suit of diamonds worthless he
/ stands 20 lose NOR" points in spades than
3 b." would have lost IN da'uondS
IN" ability To estimate the strength
q suit that il headed by high cards ia
quite common. hut the value 10 length in
small C,pis IL always everest imated.
SIX little tr7Imp- look ~ big as u house
10 IN" beginner. and even FIVE have
fatal fascination for some people Six
or seven trImrs have an absolute value.
easily calculated. hasad upon the prob
able distribution 81 the other trImp=
When these trlmps ara headed hy high
cards. such a. ace aud king. or ace-king-
queen. their average value - very much
increased because 81 the probability %
catching thu adverse trInps instead 81
being caught 10y them
The bridge player who knows the aver
age value u six or seven cards as 'rtImps
will find this knowledge - trick taking
power very useful when ha has - con-
z,der tho question uf doubling no
jrgmuer with a long suit and the lead.
IT," Fat" - many a rubber has he"n de-
Ciled ~ the ls9dsr' : correctly estimating
hi- chanc" Il making seven tricks In "A
-ut headed 10y nee and king, vet II you
ssk the NEXT twenty players YOU meet
what a-c the exact Ddd- ON dropping IN.
queen m two rounds they cannot even
make respectable guess ~ a. Such
probabilities are something that every
PLAYER should know. especially in auction.
wt"r" doubling Is ~ common.
Their, 81 and always will he this funta-
mental difference" hetvsan a long trump
SIlt and long plain suit that IN" trump
sut can always bring it-rlf into play. -
'hat no card q u r. ever lost, whereas a
plain suit must either hay" and keep.the
lead right along. or must get into u again
ty IA" help u some Other suit. With
ten irump- you must wan S"ycn tricks.
10 mati'T what your irImpF ~" or how
the uth"r trImp- an" distributed. bat with
ten 80 rd- - q plain suit "y"n IN no
t7Iuprr. you may never tax" u trick
Almost every bridge player hi- an in
Etinctl ~" aversion 10 declaring on four
tT1Irntr- and tho only eNCtI=" for such "a
declaration j. two good honors IA irIirTs
and two outEid" trucks, almost a NJ
trimp"r. In fact. The res son for thIS
hesitation about MAXI u GA four trImu-
j. a feeling - numerical weakness and ~.
fear that an adversary will Turn M with
more TRUNKS than YOU have This f"Ir
T. haSs.d Ou sound reasoning. beCa tI-s four
trumls ~" good only FOR the tricks that
can he ma'l" with H." high cards. except
Ia rare cas"-
With fiv. 'rinna. Their. comes. some
how or other an immctiatc fealing -
superiority. and we constantly see d'Clt-
raiiuns mad" on five tr,Imy- which would
mover h.. thought pf II pns 81 the trImr-
were removed. although the only possihi"
diferen-" that removal could make would
he On" trick.
This conhiencc = numerical superiority
j. well founded. although " H. probable
that not one bridge player in n million
could give . sound reason for II II Won
hold only four tTImps there are only los
times IA loo that you viii have NOR"
than any one else AZ the table In the
remaining sa5 ii''a some player will have
~ many ~ Yourself and in 3nN - thee.'
some ono will have more. Every tim"
vau declare on four trImp- only. remem-
her that " n 10 I that come player
at the table has FIVE OF more That ~
why short trump hands must have two
or ihrsa winning cards Ia make them
Giye yourself five trumps and the situa-
tion l. Immediately changed. because
Their" ar" not NOR" than ~ cases Ia 40
in which any player will hold NOR" tr,,mp-
than you There ar" only 81 in IuOo in
which any player will hold a. many. sr
that ~ J. 10 20 against that event Tho .
IL that ia SsO cases in .O0O Won |
will hav" the numerical superb rIty IN |
trumps over any one AZ the table III" !
81 the others We shall come .
t. presently.
When " comes 20 six trumps, none 81 /
them trick winners like the ace king and |
queen, lflFiF Nlllf u III Ililluk tbllA tNli I
ar. against you. Apart from the general |
aspect ~ tho hand. such a. singletons pr .
suits which can h. r1ifi"d NJ once '
the puesfi0 resolves itself into the chanc"
If surviving an adverse trump attack
When yTIr adverse Ties have th" good .
81 rts IN plain suits they will try 81 draw
your teeth by leading their high trumps.
With small trImp- II is frequently n
matter q nice calculation for tho plavor
~ know. especially In auction bridge,
how many tricks ho should 10 nhr 20
max" with sIs small tr1Imps, regarding
HON from tho numerical STANDPOINT
tlou". II there ar" high cards in IN" suit
'h.y are trick takers. whether they are
rurnp- or not; but when IL comes To- such
"a six 60 the jack or ton
few bridge players hav" any clear idea
NJ their exact value as found by the law
NJ probabilities For want of this
knowlodge th"v either under or over bid
thoir hands. according 90 temperament
II We suppoae thai Won hold siy cards
NJ given suit the remainder ~ IN" suit
must Il" distributed among the o'hcr
players In some ono Of eight different
ways and the number q timra that each
one 81 those eight ways should occur in
OOO trials can bo readily nEcertained 10y
~ ls not necessary hero 20
enter into tho process, hut these are tho
results
Hlrrfut0n Tin,s n 90