The Salt Lake herald. [volume] (Salt Lake City [Utah]) 1870-1909, 1903-12-20
POSSIBLE COMBINATIONS in POKER

hands, those not containing q pair nor
sequence. nor flush, let US suppose
Two such hands opposed to each other
the one ace high the other seven high.
On the showdown the ace high hand
wins and every one takes it as quite
natural that ii should yet it can be
automatically demonstrated that the
seven high hand, containing no flush
or sequence is more difficult to get than
a pat flush. The exact proportion is.
4Ua seVen-high hands TO sos pat Pushes.
A player makes a bluff on a hand
Jack high and is called by a man hold
ing ace high. He admits the ace-high
, hand TO be the better without a
thought; but it is much more common
to hold ace high than jack high, with
out pair. The proportion IS 500 ace
nigh hands TO l27 jack-high-4 to T..
If il is true that the best hand at
poker should be the one that is the most
! difficult TO get, the lower the highest
card is, in a hand that does not con-
| tain pair, the more valuable that
hand should be. A hand which is jack
high must be made from suits Of ten
/ cards only, whereas the ace-high hand
has suits Of thirteen cards to draw
/ upon, and the permutations of these
/ Two numbers make the difference in
| the probability of holding the hands
The lowest possible hand not contain
ing pair, sequence or flush would be
seven high. That should be the best
, OF this class Of hands, and ace high
should be the lowest in rank
The same is obviously true of fushes.
and when a ten-high flush let's an ace
( high flush take the pot the holder OF
/ the ten-high flush is allowing the poor
er hand to take the money Every
time two Pushes are in a call. the best
| hand loses!
With pairs this injustice does not
prevail for the reason already ex-
planned, that the odds against any pair
are the same as against any other pair.
and the rank given to the individual
cards is simply a means Of deciding
between competing pairs. The primi-
/ tive game was therefore correct in, as
signing the proper value 20 these hands.
When we come to two pairs we intro
/ duce an element which increases the
sources Of error, mad find that the ratio
of probability and value is still further
inverted. player viii hold aces up.
/ that is, a pair of aces and another pair
| inferior to aces, twelve times as often
as he will hold threes up.
The reason is obvious. The odds
against his holding aces alone or threes
alone are the same But with his aces
he can hold any one of twelve different
inferior pairs. With his threes he can
hold only one inferior pair, deUces.
II the rank Of poker hands were de-
termined upon strictly mathematical
/ principles, giving the superior value to
! the hand which was the more difficult
TO obtain. in all hands belonging to the
/ class known as two pairs, it should be
the rule that the lower rank Of the
higher pair in the hand the better the
hand should be. At present, every time
two pairs, jack high. call two pairs,
/ queens up, the better hand does not win
the money.
In hands containing three of a kind
we get back TO the primitive game
again and find that such hands have
I their proper value assigned to them, the
/ respective merits of two competing
/ hands Of the same class being decided
simply by the artificial, but convenient.
arrangement of the rank of the indi-
/ vidual cards
/ Straights are a comparatively mod
ern innovation, and calculation shows
/ that they have their proper rank be-
| tween the triplet and the flush when
/ they are dealt pat. 1t can also be dem
/ onstrated that a player viii get four
! card straight in the deal about twice
/ as often as he viii a fOur-card flush,
and that if the straight is open at both
ends the odds against filing either
hand are very nearly equal.
! Taking these two things together. the
D
/ to and the odds against filing il. the
/ flush is more difficult TO obtain than
/ the straight, and properly outranks it
/ on the showdown.
If the straight is open in the middle
/ the combined odds are very slightly in
] favor Of the flush But how is a player
/ TO demonstrate that he filled an in-be-
/ tween straight and not one that was
/ open at both ends?
/ In full hands it is the rule to give the
/ pot to the hand in which the triplets
: are higher. regardless OF the pair.
/ Three skies and a pair of deuces will
! beat three hves and a pair of aces
This is as it should be, because it is
! not necessary, as in the two pairs class.
| that the secondary part of the COM
/ binatiOn, in this case the accompany
\ ing pair, shall be inferior to the pri-
I mary part. the-triplets.
/ As we have seen. the chances Of get
/ ting triplets are equal. and the triplets
/ outranA one another by virtue Of the
artificial order given TO the cards OF
\ THE suits. The accompanying pair new
! or enters into the decision. and as the
/ odds against all kinds Of pairs are
| equal, that is as it should be-
! The same is true Of fOurs Of a kind,
| straights and royal Pushes. Therefore.
/ FIVE out Of our nine classes Of hands
are. properly adjusted in value. while
] -FOUR classes are rlGnLlE ADJUSTED IN
I their relations to the other classes,
but are entirely wrong in thir adjust
ment Of their respective values Of the
hands in each class.
/ When we come to consider the draw.
I a peculiarly American innovation, and
I which marks the greatest departure
from the primitive form Of the game.
we must regard Il as an incident which
! in no way affects the value OF the hand
1 when IL is finally ehown in the call. be-
cause il is contrary to the whole spirit
/ Of the game to force a player 10 dis
! close the nature Of the hand dealt to
him before the draw.
! It is quite true that given two hands
/ both capable of Improvement in the
/ draw, IL may be easier 10 improve one
l than the other.
Every poker player knows that if he
: holds pair originally and draws three
/ cards. his chances Of Improvement are
] about one in I'VE. This is the combined
/ expectation or various improvements,
/ expressed by a common fraction.
/ There are varying odds against his
| making two pairs or threes or a fun
hand or four of a kind. All these odds.
I separately calculated and then taken
together by a process which II is not
necessary TO explain here. give the to-
tai chance Of Improvement I'm drawing
Z 90 pair as about one to FIVE.
I If another player holds two pairs.
tai chances Of Improvement are only
pair and the hand with two pairs were
On -rra "a