Clarke courier. [volume] (Berryville, Va.) 1869-1997, 1908-02-05
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, Vet Chance Saws III,
odds' on the Nest Toss Are Even.
\ famous mathematician. Professor
Karl Pearson. once spent the greater
part of his vacation deliberately toss
Ing shilling and making careful notes
or how it fell He spun the shilling
%o.OOO times, and pupil OF his. work
ing separately. spun a penny $500
times and also tested the drawing OF
1900 tickets from Il bag.
IL may seem strange that a learned
professor should put himself to such
an amount OF trouble TO demonstrates
What every Schoolboy who had ever
tossed 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
arithmetician. the theory of runs
that Is. heads turning up remarkable
or tails turning up repeatedly-is pre-
I
The chance of a head is one-half; Of
two heads following. is one-half multi
piled by one-half-that Is. one-Quarter:
or three heads in succession. one-half
multiplied by one-half multiple by
one-half-that is, one-eighth. Now.
what do you suppose is the chance OF
run OF eleven heads? II Is safe 70
say that not many persons. however
accustomed 10 tossing coins. have rea-
soned this out. The fact is that one
run of eileen heads is on the aver
Hgc only to IL expected in 2.O4S sets
90 coin tossing.
Although the man in the street may
not have reckoned this. he is ALWAYS
quite positive that II. say. n coin has
fallen ten times head upward he Is
safe TO start backing tails. He puts
his money on tails turning I'D be-
cause. he says. it stands to sense that
the run OF heads can't continue But
does III At the eleventh toss the head
OF the coin Is just as big as Il ever
was. What mysterious influence can
past event. the tossing Of ten heads.
have on n future one which has no
link with them-namely, the tossing
or the coin the eleventh time? Surely
each toss is an event by itself. as Sir
Hiram Maxim said OF n game at rou-
lette ut Monte Carlo:
1T is pure. unadulterated question
or chance, and IL is not Influenced in
the least by anything which has ever
taken place before or that ever will
take place in the future"
\ nasty Dippn ~ yo1ofp
for the cranks who had published
schemes for breaking the bank" and
whose plans depended entirely on the
theory that If one game ended in n
win for red" the chances against IL
ending red" a second time were less.
third time less still. 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 n coin all MS one con-
tinuous event. II Is quite safe. for in
stance, 10 offer beforehand big odds
against 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
turning up heads eleven times are as
has been shown, something like 1000
TO l. But suppose you only start bet
ting at the tenth toss. What are the
odds against the eleventh toss again
being head?
The odds. so far from being 1000 to
i, are actually ! TO l, To use an
lrishism. the odds are even-that is
TO say, IL you split up the eleven losses
into eleven separate events to be bet
on separately your bets should be
even money all the time, however
often heads turn up running But II
you view the eleven losses as one COM
bined event and you offer a prelimi-
nary bet against the whole eleven re-
suits being heads you will have 10
give gigantic odds.
All this goes TO prove the absolute
uncertainty of gambling. The great
est mathematicians OF the day cannot
be certain how coin will fall, so that
the man of merely average abilities
who stakes anything important on the
toss of n coin is allowing that part OF
his fortune to pass entirely outside his
control.-Pearson's Weekly.