The sun. [volume] (New York [N.Y.]) 1833-1916, 1900-05-06
PROBABILITIES IN POKER.
MATHEHATICAL THEORY TEAIED III
THE FACTS or THE GAME
The Expectation Of Improvement mana.
a .iack pot which science Declared 10 -.
Wost Improbable There was one ON
Where Theory and Fxpcrience NEIee"'

.I,cL M, which science Declared 10 he
Most improbable There was ""' 80
Where Theory and Experience AHreeo'
sam johnson was a drummer Tor u sn'".
wnre house End had just w0uhn up " s"''
dHv's work by selling n tidy liiil" pli !" o"'"
& S'rHi-. II was too late to 40 any ""r'' Wv,
and too early for supper, 50 he sa' af'""" wv"
talked about various things Tor Il p""''' ".
an horr. Presently the conN"rs''Io" '"'"'"
81 G~uu,cmentS. and sam reinarN'u '""' W.
was tired ~ going 10 the theatre ana wv ,"l
/ Play billiard, and did net know rsa'l' VIM
10 do with himself. Cohen asked u ne over
played okcr. and sam jumped al Inc suSs's'
ton Of a quiet game that evening an" "s"'
awpv with an an ointment 10 meet 'H ''H
toner, at "A little uptown club abont q 'o'h'
When he arrive they were hoth there, bH'
| The two others who were expec''" '" h'he w
the party had not pwt in an appearance WINE
they were waiting the con\ ersa'loh hh'"r"'N
turned on the game. and sam gave MS GUS
toners ,uuIe ot his ideas On IN" SUP ''' III
which h- rather fancisd himself al "Al"H'
, having studied all the books ana earned an
the lahips Of eNI ectation OF Improvement
by heart.
4 almost always win" he said, because ]
stick pretty close 10 the theory OF proDabll''eS'
| never go into n pot without tens or better.
and never stay with a Jack unless ] nave as
good n openers or can draw To a bob by pay
ing my percentage Of expectation OF improve
ment. All the money ! see lost Mt poker Is
chipred away playing weak hands against
stronger Ores
We'll " said Cohen. Il 20 In on anything al
NIL If | am playing in luck, and would sooner
draw to an ace and n deuce than pass a lo'
with four men IN 1t
Me too. said Straus. And a. for jacks,
/ always stay ON Il pair because my chance OF
making thrres is a. good "a the openers. ana
IL don't get my third man can drop out.
According 10 III. doctrine of probabilities,
rejoined johnson, the hand which is stronger
on the go in will sill be- stronger after the draw
a. the long run and the fellow That draws 10
The largcr pair will beat You oftener than you
viii beat him. That Is "A mathematical propo.
sitlon which can ea>ily be- proved
Blu if he beats me twice out Of three times
he gets only my cone-in money" reforted
Strans. But If I improve | not only beat him.
but the whole table, and what ! win when my
threes stand up under mo j. many times what
| lose by paying 10 draw TO my little pair"
You only think that The theory Of proba-
bilities proves that II IL not So and that you
must lose unless you have unusual luck. You
would not agree 10 let one man have jacks
every deal and you delceS, and YOU 10 draw
and play against him for nifty deals"
II don't play against him alone in a jack
pot. gel the other fellows money, too, all
the antes and bets put up by the fellows thar
come ia on little pairs just like mine. There
is only one man with Jacks or better, and If
| don't improve ha takes my ante. II beat
him ont | get all his money and all the con-
tributonS of the others in the pot at M" same
time. don't know what the odds are against
my improving and don't care much
They are just the ZANE hs the ODDS against
the other fellow improving his Jacks, %3l.tol,
Then il lose Il dollar three Times III Tour by
drawing against OPENERS and viii five or ten
dollars the fourth time by improving Why
don come ont ahead
But the other fellow improves, too
What are your figures Tor his improving
az tie same time you do. and Tor yours not beng
the beat hand even after both have improved;
That is something which cannot be figured
out, bmt If he starts out ahead OF YOU l- will
still be ahead Of YOU in the majority Of cases.
That IL mathematics
so that's mathematics. is it?" said Cohen.
We'll that explains something. that ] never
understood before and that ha- been a mystery
10 every one | ever told about il. | never took
much stock IN probabilities, bur sOmethlng hap
pened in a little game On board the Gallla COM
ing home from the Paris Exposition in, August,
lNNN. WHICH, IlbNfN NbNl Nv l' M hl lkiNf
There wa seven of us in II ten-shillinR limit
game. all supposed TO be fair average pla yers
like myself. one was a school principal from
Albany and another was an engineer from
Baltimore. both ~ them full Of probabilities.
We had PLAYED about three DAYS aud ! was about
$50 ahead. mostly saved by not calling either of
those fellows unless | had threes or better.
We had PLAYED about an hour and the only
fellow that was watching the game had dropped
on 70 sleep when there came. along a Jackpot
ia which sat on he dealer right. The school
tanGlpT and the pu yipp,r had the FIRST GaE. and
both of them h~eSitated IA If thet wanted 10 be
sure they did not have a straight. Then they
passed. and all passed. mp 10 me.
II skinned my hand over and found a pair Of
aces. So ! opened II for the limit, The dealer
dropped. The schoolteacher came IN and 50
d dHdd the ,s emSine'rjW Snh t ay1 'I mem TeS ira aS WiHs sra ahTl1
me- ] felt pretty weak in IN" knees. although
according 10 Your theory. ! had a cincb, as |
had the best hand to start with II was q big pot.
and | thought ! could see about 81 in il for me
il could catch another ace. They drew all
manner or cards from one To three and all looked
pleasant especially the schoolteacher who took
ihren card didn't improve my Aces and II was
NV Art bot Now, according TO your probabili-
to-. what should | do: bet the limit or chip
along
TIE probabilities are that with five men
paying the limit to draw cards against openers,
volir aces were not worth even n chip, and
should have shown my openers and knocked
on the table
Il Thought, You said Just now that the best
hand on the sta't ,tsod tO win out
But the probabilities against improve
ment are only a. to | and there were FIVE men
drawing so AT least two Of them must have
betterpd
That's assuming they all had pairs 10 20
with. Are there no odds against such n thing
as five men having pairs and none Of them open
ersf"
II c~ertninly docs look funny ] think the
schoolteaCher must have overlooked some
thing.
Well. ! didn't overlook anything There
was seven hHlf-crown antes and six ien-shil-
ling rHises on the table. about sl8. 81 - Of which
was mine. What are the odds against me II
put m u shilling more. lust to represent and
see what the others will do"
1T IS n shilling thrown away. sure, That
Is inst how you fellows lose money A quarter
is not much but II you do that kind Of thing
all the time il soon mounts up and II you rlav
poker for 4 wear the probabilities are Won will
lose several hundred quarters by such plays
We'll | didn't bet any quarter. =
That's where YOU showed your good sense
and saved money.
! didn't bet any quarter, but put a good face
on II and het tho limit"
Great Scott The idea of attempting n
blum under such clrCums tnnCcS. Why. the
probabilities are that NJ least two men would
call and that one would raise. You would save
q lot Of monev II you would only s'lGy the
percentages Of the game, What happened,
anyway"
An FIVE men called me"
"IClv smoke Didn't I tell you' The prob
abilities are that there were AT least two flShaS
and that the others had two mfrs or gp,oll