The sun. [volume] (New York [N.Y.]) 1833-1916, 1906-11-25
CHANCES NSIXTY CARDPOKER
EFFECTS OF ADDING EIGHT NEW
CARDS TO THE PACK.


" hu@e Way Do Nh@oNs
An effort has been made to overcome
the difficulty found in providing n suf-
ficien number of cards to meet the demands
of the draw in seven and eighI han
sames OF poker by the invention o. packs
containing. sixty cards. These pa cks of
sixty nave the same cards as the psLcks of
~ffty-two, with the addition Of tao cards
To each suit, an eleven M a twelve coming
in between the ten and the jack.
In sixty card poker, a. the game has
come to be called, these new cards take
precedence in the order of their spots.
elevens beating tens, twelves beating
elevens and jacks beating twelves. The
highest straight in the game is not made
with the ace, king. queen, jack and ten as
with a pack of fifty-two, but with the ace,
king, queen. jack and twelve "a very i'm
portant change to be kept in mind during
the sixty card game.
The use OF sixty instead Of ffty-two cards
In poker neoessitates an entire rehabilitation
Of the game. The long established preoe-
dence that one hand takes over another
is not materially altered. but the intro
duction Of the eight new cards adds :, So, $50
possible hands that may be held in the game,
making a total of 5,46l ,Si3 possible hands
in sixty card poker, against 2,59s, $50 pos
sible hands in fifty-two card poker.
The process by which the precedence
OF poker hands was originally determined
is one in arithmetic known as combina-
ton. A knowledge of combination would
prevent some poker players from arguing
that a straight should beat n flush, basing
their argument, as most of them do, on the
fact that a straight, open in the middle or
at both ends, is the more difficult of the
two hands to I'LL on a one card draw.
While such is actually the case, he rela-
tive value of poker hands is not determined
by the probability OF filing a hand on the
draw. The draw Is not considered in this
calculation at all.
A broken straight is easier 10 obtain on
the deal than a four flush, but when it comes
TO drawing one card the broken straight
will be the more difficult to complete. A
players chance to fill an interior straight
drawing one card in ffty-two card poker
is as 4 to A., while in sixty card poker it is
as 4 TO 55. A player has a chance of 1 in
5 2-sths to make a common flush with a
pack Of ffty-two, drawing n card, against
1 in 9 10th with apack Of sixty.
The first problem in sixty card poker is to
ullh ~ many Dbe0ibAV NDhhA y Noh
be made with sixty cards, taking five at q
time. The rule for determining IL is first
to find the product of the last five integers
ending with 80; that IL. 5Sx57x5sx5sx0o,
and divide this product by the product of
the integers leading up to the number Of
cards taken, 1x2x3x4x5. The operation
is long, but shows that 5.48I SIP different
hands Of five cards each can be made in
A. - - 1880 III
in kinds as follows:
Royal straight fiushes-Of these there
can be but one in each suit, o r four in all
out Of the great total.
Straight fiushes-Of these there can be
eleven in each suit, beginning with 1, :, 3,
4, s. and ending with IL, ~, j. .. X. As
there are four suits there will be 4 times II,
or ~ straight Pushes.
Four Of q kind-Any one OF the fifteen
cards in a suit can be combined with any
one Of the ffty-six cards that remain. max
ing in all 15x58, OF $40 possible hands Of four
OF a kind.
Full houses-As there are 90 cards II is
possible to form 30 triplets, but when a
triplet of any kind has been formed 81 cards
will remain. The total number Of sets Of ,
remaining to complete the fun house is
found by another example in combination
consisting in multi plying 57N56 and dividing
by Ike, which gives 1 500 such combinations
in all.
The total number OF pairs that can be
formed with 81 cards is much snla Her. As
any 4 cards of like denomination will make
pairs in 0 different ways, or as there Willie
IA possible kinds OF pairs left after the trip
let is removed, there will, OF course, be 9
times IA or 81 possit lie pairs which can he
combined with the other IS TO make a full
hand.
The 90 possible triplets multiplied by the
81 possible pairs gives 5,04O as the total
number of full house hands.
Common hlshes-TaSiny 5 cards at a
time out OF a total OF Is cards contained in
each suit it VIII he found, by combination,
that there are 3,Oo3 ways to make Pushes
in Zach one OF the suits. This, multipled
by the 4 suits. gives I2,ol2 from which must
Re deducted the Z roval straight Pushes and
the a. straight Pushes, leaving II 1854 posei-
BILE common Pushes.
Common straiPhts-Since any one OF the
5 cards can he taken from any one OF the 4
suits TO make a common straight the prod
uct OF 4 multi Piled by itself S times will give
the total, which Is I,O24. hut as I Of these
combinations will be Pushes they must be
taken out, leaving 1920. As the common
straiRhts may be ARRANGED in II different
ways beginning with 1, ., 3, 4, 5 and ending
with IL, j, Q, h, A. the remainder, 1920,
must be multiplied by IL, giving a total of
Il, 24o common straights.
Two pair Taking four cards of like
denomins ton, one from each suit, IL will
be found hat they can be put together
two at a time TO form pairs in six different
ways. As there are fifteen Cards in each
suit 8 times IS. which is 81, will be the total
possible number OF pairs.
When any two cards nave been taken out,
however. fifty-eight cards will remain,
from which must be deducted the two cards
Of the same denomination. as they take no
part in the hand to be formed. Starting
then with fsty-six cards. with which eighty
-four other pairs can DO made, IL must be
remembered that each OF these can be taken
with any one of the tfty-four cards re-
naming. or with those two Of the same
denomination. OF hfty-two in all.
BY taking each OF the combinations with
ninety pairs double the number OF two pain