The Scranton tribune. [volume] (Scranton, Pa.) 1891-1910, 1895-08-24
CHANCES IN POKER.
Twenty Pairs In Forty Deals Is o
Fair Avcrage-Thrccs Once In the Same
Number Of Deals aud Straight Flush
Once In SA.O7A Deals.


Fair Avcrnge-Thrccs Once In the Same
Number Of Deals. and q Straight FIust
Once In Saba Deals.
From the st. Louis Post-D.spatch.
One would expect that every lover OF
the great American game of draw poker
would find 1t to his pleasure and profit
to become thoroughly posted in regard
to the various chances of the game
both on the deal and on the draw. Yet
II IL IA fact that many players know
little or nothing about a matter 80 i'm
portant to them, and that even those
who claim to be considered authorities
ON the subject differ widely among
themselves. For instance, the Ameri-
can Hoyle, a standard work. says that
chance OF getting pair Is ten times
In IL deals. but MIR. Proctor Is of the
opinion that u Is about 10 times In %
deals. Neither OF these assertions is
exactly correct, Mr.. Proctor being near
ly So The chance of getting a pair Is
very close to 20 times In ~ deals.
Calculations have been verified with
the expenditure of little patience and
time. by dealing a number Of expert
mental hands, the problem being what
are the chances OF receiving the diff
ferent kinds of hands on the deal? The
method of calculations, and the calcula-
tions themselves, are simple.
An Exercise In Mathematics.
To begin with. II must be ascertained
first how many combinations Of five
cards can be made out Of pack of So
cards. Algebra shows that this will be
made apparent by dividing 52x5lx50x4 49,
x4Sxlx2x3X4x5, the result being 1885, 800
sets. Now. 1t is desirable to find out
how many OF the 1886. $50 possible COM
binations will contain pair, how many
two pairs,and SO on. Seventy-eight
pairs can be formed, six different pairs
of aces, six Of kings. and so on. Each
of these pairs may be combined with
any set of three cards that can be made
out of the fifty remaining cards. pro-
vided that these three cards are all of
different denominations and that none
OF them Is of the same denomination
as pair Is. Out of the so cards can be
formed 4sx44x4O divided by lx2x3 comb
nations. which fulfill these conditions,
and therefore the total number OF pos
sible pairs will be rs times 4sx44xiO di-
vided by 1x2x3. which equal 1.O9S, ,24O
The chances OF obtaining pair on the
deal are, therefore. 1905. .240 divided by
2,5SS960. or about 20 in AZ deals.
Now. as to the two-pair hands. There
are the Is pairs above mentioned. and
of the 72 pairs of different denomina-
tion, giving 7S.72 divided by 12. or
2,SOs possible sets of two pairs. Each
of these sets may be combined with one
of the Al cards which remain after the
two pairs and the four cards of the
same denomination have been taken
out, and so Is obtained 2,sOS times A as
the total number of two-pair hands. The
chance of the two pairs on the deal is
therefore 123.552 divided by 2,59s,96 or
about once in q deals.
TripletS come next. Out Of the four
cards of each denomination can be
made four threes. by simply leaving out
each suit in turn. This gives times
IL, or SO triplets which can be made
from full pack. Out of the 4S cards
left can be made 4Sx44 divided by lx2,
or .056 combina tions of two cards each,
remembering that none Of these COM
binations can be allowed to be a pair.
The total number OF hands containing
three of kind will therefore be 52x
LOSS, or 54.S12, and a triplet may be ex-
pected about once In AZ deals.
Difficult TO Calculate.
Straits and fiushes are somewhat
harder to calculate, and ii Is with them
that mistakes are often made Out of
the IS denomina tions 10 straights can be
made. as follows 2. 3, 4. 5, 6; 3, 4. 5. s, Z;
s. 6. Z. s, 3; 6. Z, s. 8. 10: Z, 8, 3. 10, jack:
8. 3. 10. Jack. queen; .. 10, jack. queen
king. and 10. jack, queen, king. ace. But
as each card Of the straight may be OF
any one of the four suits. 10 times
a. 4, 4. ~, or 1920 straights are pos
sible. OF these. however. 40 are not
only straights, hut strait fiushes as will
be shown hereafter. Subtracting these
therefore, there are left 10000 possible
straights, and one about once in 255
lands dealt may be expected
Flushes are determined in the fol-
lowing manner. From the l3 cards OF
each suit can be made lS IL II 10 3