Daily Kennebec journal. [microfilm reel] (Augusta, Me.) 1870-1975, 1895-09-09

Pat Fours Are Due Once in 4,165 Deals.
Now, Are You "Cominy I'M,
One would expect that every lover Of
the great American game of draw poker
would find it to his pleasure and protit to
become thoroughly posted in regard to the
various chances of the game. both on the
deal and on the draw. Yet ii is fact that
many players know little or nothing about
matter SO important to them. and that
even those who claim TO be considered au
thorities on the subject differ widely
among themselves. For instance, the
American Hoyle, n standard work. saws
tnat the chance OF getting pair is 10
times IN IL deals, but Mr. Proctor is of
the opinion that 1t Is about 10 times in 23
deals. Neither of these assertions is ex-
actly correct, Mr. Proctor being nearly so.
The chance of getting pair is very close
to 20 times in AZ deals.
calculations can be verified with the
expenditure of little patience and time,
oy dealing number of experimental
hands, the problem being, What are tho
chances of receiving the different kinds of
hands on the deal? The method of calcu-
lations and the calculations themselves are
simple.
10 begin with, it must be ascertained
1lrst how many combinations of five cards
can be made out of pack of So cards.
Algebra shows that this will be made APP
parent by dividing 52x51x50x49x4S by 1x2-
x3x4x5, the result being 2,59S, 900 sets
Now it is desirable to find out how many
of these 2, 59S, 900 possible combinations
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 so remaining
cards, provided that these three cards are
all of different denominations and that
mono of them is of the same denomination
as the pair is Out of so cards can be
formed 4Sx44x40 divided by 1x2x3 combi-
nations which fulfill these conditions and
therefore the total number of possible
pairs will be rs times 4Sx44x4O divided
by 1x2x3, which equal 1,O9S, $40. The
chances of obtaining pair on the deal
are, therefore, ,09S, $40 divided by 2, $685.
900, or about 90 in AZ deals.
Now, as to the two pair hands, There
arc the IS pairs above mentioned, and any
of these may be combined with one of the
~ pairs of different denomination, Civ
ihg 1912 divided by 1.2, or g sos possible
sets of two pairs. Each of these sets may
be combined with one of the A cards
which remain after the two pairs and the
four cards of the same denomination have
been taken out, and so is obtained 2,S0S
times Al as the total number of two pair
hands. The chance Of two pairs on the
deal is therefore 1873, 552 divided by 2, $685.
$50, or about once in 81 deals.
Triples come next. Out of the four
cards Of each denomination can be made
four threcs, by simply leaving out each
suit in turn This gives times Is or SO
triplets which can be made from a full
pack Out of the As cards left can be
made 4Sx44 divided by 1x2, or 1 ,O56 COM
binations of two cards each, remembering
that none of these combinations can be al
lowed to be pair. The total number of
hands containing three of kind will
therefore be 52x1, 05G, or 54,012, and a
triplct may be expected about once in Al
deals.
Straights and flushes are somewhat
harder to calculate, and it is with them
that mistakes are often made. Out of the
10 denominations 10 straights can be
made, as follows: 2, 3, I, 5, 6; 8, 4, ., 6,
&; g. 6, Z, s. 8; 6, 2, 8, ., 10, jack; s, 0,
10, jack, queen; o 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 G., 4, 4, 4,
y, or 1920 straiglts are possible. OF
these, however, 10 are not only straighla,
but straight llushcs, as will be shown
hereafter. Sllbtracting these, therefore,
there are left 10, 200 possible straights, and
one about once in 255 hands dealt may be
expected
FIushes are determined in the following
manner: From the ID cards of each suit
can be made
Is 10 IL 10 9