The Wheeling daily intelligencer. [volume] (Wheeling, W. Va.) 1865-1903, 1874-03-09
Something about Cards.


In yesterdays Sunday NtUs there ap
pears problem relating to the recurrence
In play Of certain hand held OF whist
and as tho same subject has appeared II
various papers, with different statements
as 10 the chances involved, permit me L
state what believe TO be the true ratio
Of probabilities in the case. In pack d
tiity'two cards, euch as Is used in playine
whist, there are four suits Of thirteen cardi
each, and when the first four cards are
dealt 10 the players, the chances that q
given suit will appear but once In the
Tour, are Just equal, as the possibility ol
TWO or more Of the same suit being dealt
is counterbalanced by the probability Of
none appearing in the next, or In tho sue.
ceeding four when distributed. This be.
Ing accepted, the chances are then three
TO one that the person dealing does not
receive q card OF q given suit, be being
equally likely 10 get one from the three
remaining suits. Should he succeed In
doing so, however, his chance ofreceiving
another card oil the same suit when the
succeeding tetrad Is dealt, Is precisely the
same as 10 the former instance, 70 that
the probabilities being three to one
against him in the first case, and
In the event Of his success still
three TO one against him in the second
deal OF four cards, 1t follows that the
chances opposed to his receiving two
cards OF the same suit successfully are as
nine to one. This Is qualified when the
following four are thrown 10 the players
by the possibility Of receiving another
card Of the suit, the chances for which
are as before, being one In its favor to
three against It. This would be twenty
seven to one that the player would not re.
ceiVe three cards oil the same suit con-
secutively. Hence It follows that this
ratio continuing throughout the deal, the
probability ot any player having an entire
suit given him, would be expressed by the
figure three raised to the thirteenth power,
or ! ,594 1898, opposed TO 1t, as against one
in It's favor.
The exaggerated estimate which ap-
pears in the Sunday NepS is doubtless
due to the calculation having been effect.
ed BY permutation, and which would be
correct If definite hand was dealt In a
prescribed order to each player. Thus,
If when the cards were properly ahuffled
an ace was dealt TO each player, and was
followed up by giving a deuce, three,
four, five, and so on until all were dis.
tributed, 30 that each complement Of
thirteen cards was an entire suit dealt in
the manner indicated, then the recur.
renee OF such hands received in the above
order, would, on the doctrine of chances,
take place once In vastly greater mum.
Der OF times than that mentioned. II anv
Of your readers have sufficient curiosity
and patience TO exactly ascertain this
number, they can do SO by multiplying
together any two terms OF the series be-
tween one and tiIty.two, and then success
lively increasing this product by multiply
Ing it by all the other numbers in the
series. Twenty-three raised TO the thir-
teenth power, or las nearly as I can com.
pute Il by logarithms) 592 ,585, ,909, ,090,-
100000, will express the number Of
deals which the doctrine of chances
would require for the repetition oil q full
suit given TO each Of four players at whist. |
These figures hardly convey to the read
cr's mind proper conception OF the vast
number implied, but as an illustration |
will mention that il the ten million adults
Of the United States were TO engage in
playing whist, and would have q new
deal every five minutes, provided they
were to play unintermittingly day and
night, the average chances would demand
10000 years for q duplication Of the
hands to occur. AS, however, there Is lit
tie possibility Of the experiment being
practically made, leave the theory for
what 1t Is worth. ARTTHMos.