The hatchet. [volume] (Washington, D.C.) 1883-19??, 1900-06-17
A GAMBLERS CHANCES.
Tests Of the Law Of Probabilities In
Betting.

upon seems n contradiction in terms,
yet such is the law of probabilities.
In tossing a coin 100 times the law re-
ures that It fall heads fifty times
and tails fifty times. This discrepancy
between theory and practice fascin
ates the attention and invites inves-
tigation
A law to be capriclous, apparently
in its operation might be suspected
to be no law at ALL and the fact that
1t is not memorable in practice has
given rise to systems of gambling,
by which players seek to take advan-
tage of the law and to make a brokers'
commission on their dealings with
chance.
The best known Of these delusive
systems is the Martingale in all its
various notifications The basis of
this system is the method of doubling
the stakes after every loss, so that
when the player finally wins once he
recoups all former losses and receives
a profit equal to his first wager With
unlimited capital and under proper
conditions this would be an absolutely
certain method of continuous success
at gambling, whether the chances
were even or not But such condi-
tions are never realized. A Chicagoan
who has made study of the law of
probabilities and Of various systems"
talking on this subject few days
ago, said:
"Supposing the bank would permit
continued doubling let us examine
whether the player by the Martingale
system really has yoked the laws OF
chance to his chariot If you draw
cards promiscuously from a deck and
forfeit cent for every time you draw
a red card, winning one cent every
time you draw black card and doub-
ling your stake after every loss-you
will find that with a capital of thirty
two cents you can usually double it in
about gixty-four draws, although the
bet is always fair and the chances
even.
thirty-two when you will draw red
cards six times runuing-when you
will not be able to double your stake
and will lose thirty.two cents-about
the amount you had previously won.
| If one could get a copyright on the
elimination of that thirty-second
chance he could bankrupt the gam
bling world. Many have tried to de-
wise some plan of allaying the severity
of this thirty-second chance, but in
| the words of the humorist it is try
ing to unscrew the unscrutable.'
"Supposing the chances are even
and the player starts a Martingale
with 81 and loses; stakes 81 and loses;
81 and loses; So and loses; SIG and
| still loses. Now he has lost S31 in
all and has lost five times in success
sion. Mathematics assures us that
the chance of losing five times in
succession in an even game is one in
thirty.two, there being thirty-one
chances against It. theoretically,
then. our player will win thirty-one
times by his system, winning 81 each
time, but the laws of chance require
that he lose-on the average-the
thirty-second time, and he will then
lose $31, just the amount he has pre-
viously won.
'If he goes on losing until he has
staked in all $1,024-of which there is
one chance in 1,024-he will probably
have drawn the one unlucky chance
which out of 1024 plays, he would
be reasonably certain to draw, there
by losing 81 ,023, or all that he had
previously won, If the law of proba.
bilities were justified, If his capital
should be 81 100000, the process needs
only to be prolonged to bring out the
one unlucky chance by which he will
lose all he has previously won, the
chance being exactly one to one that
he will quit the game without loss or
gain, no matter how long he plays"
This discussion has had in view
only such gambling devices as offer
even chances to the player, since it is
obvious that if player cannot get any
advantages where the chances are
even he certainly cannot where there
is a percentage in favor of the pro-
prietor of the game, or where the price
he pays for a chance is more than
the mathematical value of the chance.
which is, of course, the case in all
games run for profit, such as faro
banks, lotteries, slot machines, and all
card games in which the dealer gets
commission on the sale of chips.
The fascination of gambling lies
largely in the capriciousness of the
law of probabilities when applied to
a small number of events. Mathe
MATES assures us that the precision
with which the law can be applied
increases as the square root of the
number of events to which it is APP
piled. There could be no attraction
in games of chance if the theory of
chances worked out accurately in a
small number of events-for example,
if in tossing pennies the coin were
certain to fall heads and tails alter.
nately as it should do to illustrate
the law of probabilities with pre-
cision.
If a gamblers capital allowed him
IN NAV lonp pnOugh in fair panna ha