Coeur d'Alene evening press. (Coeur d'Alene, Idaho) 1907-1929, 1908-08-14
THE TOSS OF A COIN,
Mathematics Of the Turning Of
Heads or Tails.
CHANCE AND THEORY CLASH.

II Heads Turn Ten Times In Sequences,
Theory Says the Odds Are Against
Another Head, Yet Chance Says the
odds on the Next Toss Are Even.
A famous mathematician, Professor
Karl Pearson. once spent the greater
part OF his vacation deliberately toss
Ing a shilling and making careful notes
of how 1t fell. He spun the shilling
$4,000 times, and pupil OF his, work.
Ing separately. spun penny $500
times and also tested the drawing Of
1900 tickets from n bag.
II may seem strange that learned
professor should put himself to such
an amount OF trouble 10 demonstrate
what every schoolboy who had ever
tossed a coin already knew Yet, as
matter Of fact. few really do grasp
the laws which govern such an appar.
entity straightforward matter as the
tossing Of coin. In the words OF the
arlthmetician, the theory OF runs
that In, heads turning up repeatedly
or tails turning up repeatedly--is pre-.
cisely rs follows:
The chance Of Il head IL One.half; OF
two heads following, is one-half multi.
piled BY one-half-that Is. once quarter;
OF three heads In succession. one-half
multiplied by one-half multiplied by
one-half-that is, one-eIghth. Now,
what do you suppose II the chance OF
a run OF eleven heads? II Is safe to
say that not many persons, however
accustomed 10 tossing coins, have rea-
sOned this out. The fact IL that one
run" Of eleven heads Is on the aver.
age only TO he expected In 2,O4S sets
OF coin tossing.
Although the man In the street may
not have reckoned this. he IL always
quite positive that II. say. coin has
fallen ten times head upward he IL
safe 70 start backing tails. He puts
his money on tails turning up be-
cause, he says, II stands TO sense that
the run OF heads can't continue But
does itf At the eleventh toss the head
OF the coin is just as big as II ever
was, What mysterious influence can
past event, the tossing OF ten heads,
have on a future one which has no
link with hem-namely, the tossing
Of the coin the eleventh time? Surely
each toss II an event by itself, as Sir
Hiram Maxim said Of game at ron.
lette az Monte Carlo:
1T Il pure. unadulterated question
OF chance. and II Is not Influenced In
the least by anything which has ever
taken place before or that ever win
take place In the future"
A nasty piece Of plain speaking this
for the cranks who had published
schemes for breaking the bank" and
whose plans depended entirely on the
theory that II one game ended In a
win for red" the chances against It
ending "red" a second time were less,
a third time less stlll and so on.
This Of course would be a sound
enough argument provided that you
regard some dozens of games Of rou-
lette or losses OF coin all as one con-
tinuous event II is quite safe. for In
stance. to offer beforehand big odds
against q coin turning up heads ten
times running. but In practice the
public house loafer does not do this.
What he does Is TO bet ON each sepa-
rate toss by itself, thus defeating his
own aims, The odds against n coin
turning up heads eleven times are as
has been shown, something like 1900
to I. But suppose you only start bet.
ting at the tenth toss What are the
odds against the eleventh toss again
being head9
Tho odds. NO far from being 1000 to
/, are actually TO II TO use an
Irishism. the odds are even-that ls
TO say, II you split up the eleven losses
into eleven separate events TO be bet
on separately your bets should be
seven money" all the, time. however
often heads turn up running. but In
you view the eleven losses as one COM
bined event and you offeF a preliml.
nary bet against the whole eleven re-
suits being heads you viii have to
give gigantic odds.
AL this goes to prove the absolute
uncertainty Of gambling. The great
est mathematlcians OF the day cannot
be certain how a coin will fail. 80 that
the man Of merely average abilities
who stakes anything important on the
toaa Of Q coin Ii allowing that part OF
his fortune 10 pass entirely outside his
eontrol-Pearson's Weekly,