The Lambertville record. [volume] (Lambertville, N.J.) 1872-1968, 1908-01-15
THE TOSS OF A COIN,
Mathematics Of the Turning Of
Heads or Tails.
CHANCE AND THEORY CLASH.
Il Heads Turn Ten Times In Sequence,
Theory Says the Odds Are Against
Another Head, Yet Chance Says tho
Odds on the Next Toss Are Even.

VI Urn tcU tifneo w sequence
Theory Says the Odds Are Against
Another Head, Yet Chance Says tho
Odds on the Next Toss Are Even.
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
$1,000 times, and n pupil OF his, work
ing separately, spun penny $500
lines and also tested the drawing OF
1900 tickets from a bag.
II may seem strange that II learned
professor should put himself to such
an amount of trouble to demonstrate
what every schoolboy who had ever
Tossed q 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
arlthmetlclan, the theory Of runs
that Is, heads turning up repeatedly
or tails turning up repeatedly--is pre-
clsely as follows:
The chance of n head IL one-half; of
two heads following, Is one-half multi
piled by one. half-that Is, one quarter;
Of three heads In succession, one half
multiplied by half multiplied by
one-half-that *, one.eighth. Now,
what do you suppose is the chance OF
a run of eleven heads? 1t Is safe to
say that not many persons, however
accustomed to tossing coins, have req
soned this out The fact Is that one
run" of eleven heads h on the aver
age only TO be expected In 204S sets
Of coin tossing.
Although the man In the street may
not have reekoned this. he is always
quite positive that If. say, Il coin has
fallen ten times head upward lie is
safe to 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 It? At the eleventh toss the head
of the coin Is Just rs big as II ever
was What mysterious Influence can
n past event. the tossing of ten heads,
have on u future one which has no
link with them namely, the tossing
Of the coin the eleventh time? Surely
each toss Is an event by itself, as Sir
Hiram Maxim said OF game Mt rou-
lette at Monte Carlo:
TT Is II pure. unadulterated question
of chance, and 1t Is not influenced In
the least by anything which has ever
taken place before or that ever Will
take place In the future. -
A nasty piece of plain speaking this
for the cranks who had published
schemes for "brcakng the bank" and
whose plans depended entirely on the
theory that If one game ended In Il
win for red" the chances against 1t
ending red" n second time were less,
II third time less still. and so on.
This of course would be sound
enough argument provided that you
regard some dozens OF games of rou-
lette or losses of coin all rs one con-
tlnuous event. 1t Is quite SAFE for In
stance. to 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 scpa-
rate toss by itself, thus defeating his
own aims The odds against II coin
turning up heads eleven times are rs
has been shown. something like 1000
to |. But suppose you only start bet
ting at the tenth toss. What are the
odds against the eleventh toss again
being n head?
The odds. so far from being 1000 to
/. are actually to |. To use an
lrishism. the odds are even-that Is
to say. II 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 If
you view the eleven losses as one COM
bincd event and you offer preliml-
nary bet against the whole eleven re-
suits being heads you will have to
give gigantic odds.
All this goes 10 prove the absolute
uncertainty Of gambling The great
est mathcmatieiaus of the day cannot
be certain how n coin will fail, 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.-Penrson's Weekly