The sun. [volume] (New York [N.Y.]) 1833-1916, 1910-11-06

hand. That is to say. only l, times in 100
will he hold five or more OF IL and lead it.
But even il the leader does start out
with a five card suit there is always the
chance that your partner. the dummy
can stop il. In considering this possibility
IL is hardly worth while ~ 60 below the
four honors. A X Q J. II is -, to 1 against
all four being in the hands Of the adverse
RES and IL IL IL tn I against their holding
three out Of the four. In 10 cases out 81
70 dummy ought 10 hold two or more OF
the high cards in a suit in which the dealer
has no high cards. SO that It - almost an
even bet that dummy will he able to
stop suit in which the dealer has
nothing better than a nine
There is another aspect Of these figures
This IL the improi,abiIty that the suit
will ne led when such "A lead would just
sIi Uyou. Let US suppose that your shortest
suit m n no trumper IL a guarded king
The odds against that suit being led up
tn you at the start. You holding only two
cards Of il. are % 60 81, or about : to I.
A twice guarded queen has even less
chance.
Many players will tell You that a qua r,isd
king il a sure trick II tho other suits are
strong. because, they say. your short
suits are always oper,ed by the aiver-
saries The odds are the "a ne whether
you have the trey and deuce or the deuce
and king. II IL > To against the suit
being led.
The other class of probabilities. which
" Of paramount: importance TO the bidder
at auction includes the chances 81 finding
certain winning cards in the hand Of the
partner Let vs. take n typical cas- first:
Every one knows the bridge pl,yer who
holds I'D his hands in holy horror when
you go no trumps without an ace The
only excuse he will listen TO is four king
queen suits. or At least Two honors in every
suit. one of them the king.
What the bridge player is afraid of is
io0 aces. In auction 100 aces are not i'm
IL no more than the penalty for rhe loas
OF a single trick in doubled spades. The
only dangerous part OF four aces at auc-
-ion is their trick taking power when one
has 20 make more than the odd OF pay
penalties. Any auction bridge player
would pe quite willing. however. TO con-
rsdc four tricks 10 four aces il he could
win the other nine and the game.
Two or three aces 10 considered a sins
qua non in no rrumper at bridge. One
ACs' IfldhcH 'fr rEAiNWIs DHN III
auction bridge one cannot wait for two
or three aces TO bid no trlmps. and unless
he N willing To go no trumps occasionally
without an ace in his hand he will miss
many golden opportunities OF going game
and Of forcing the other side toa contract
| that they cannot carry out Let us look
at the mathematical expectation Of the
distribution Of the aces when the bidder
has none himself.
! II has been repeatedly stated in print
I that the odds against rhe adversaTies ~
| tho dealer holding i0G aces are ~ TO 1.
40 he need not he afraid Of IT, This state
nens 10 an error borrowed from the old
calculation 81 DR. Pole Tor trimp@ before
the deal When the dealers hsni -
known the probability fraction for the
| - unknown cards ia 3pH 3rS 81 u 70
! ara which - tha number ~ possible
po@ifiona for tho four aces Divide this
| by the cards - on" hand. i2Si2SIiS 10
! Il lao. which i. the number of posit ions
favorable TO ell four aces being in that
hand. and we get the otids 0i IIs 20 I
against any narned player holding the
four aces But as there are two adveT-
earies it 10 only half that or about 81 to 4,