The Richmond palladium and sun-telegram. [volume] (Richmond, Ind.) 1907-1939, 1908-01-11
THE TOSS OF A COIN.
Mathematics of the Turning Of
Heads or Tails.
CHANCE AND THEORY CLASH.
II Heads Turn Ten Times In Sequence
Theory Says the Odds Are Against
Another Head. Yet Chance Says the
Odds on the Next Toss Are Even.


Odds on the Next Toss Are Even.
A famous mathematician. Professor
Kari Pearson, once spent the greater
part Of his vacation deliberately toss
ing a shilling aud making careful notes
Of how it fell. He spun the shilling
$4,000 times. and i pupil of his. work
ing separately, spun penny 5000
times and also tested the drawing OF
5000 tickets from a bag
1t may seem strange that a learned
professor should put himself to such
an amount OF trouble 10 demonstrate
what every schooIboy who had ever
tossed a coin already knew Yet. as
matter of fact, few really do grasp
the laws which govern such an appar-
emily straightforward matter as the
tossing of a coin. In the words of the
arithmetician. the theory OF runs
that is, heads turning up repeatedly
or tails turning up repeatedly-is pre-
ciseiy as follows:
The chance OF a head is 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 one-half multiplied by
one-half-that is. 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 rea-
soned this out. The fact Is that one
'run" of eleven heads is on the aver
age only to be expected in 2,04S sets
of coin tossing.
Although the man in the street may
not have reckoned this he is always
quite positive that if. say, a coin has
fallen ten times head upward he is
safe to start backing tails He puts
his money on tails turning up be
cause. he says. it 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 as big as it ever
was. What mysterious influence can
a past event, the tossing of ten heads,
have on future one which has no
link with them-namely. the tossing
Of the coin the eleventh time7 Surely
each toss is an event by itself, as Sir
Hiram Maxim said of game at rou
lette at Monte Carlo:
1T is pure, unauthorized 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 breaking the bank and
whose plans depended entirely on the
uoT q
win for red" the chances against it
ending red" 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 a coin all as one con
tinuous event. 1t IS quite safe. for in
stance. to offer beforehand big odds
against n 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 a coin
turning up heads eleven times are as
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 head?
The odds. so far from being 1000 TO
!, are actually l to /. To use an
Irishism. the odds are even-that is
TO say, If 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
bined event and you offer n prelimi-
nary bet against the whole eleven re.
suits being heads you will have to
give gigantic odds.
All this goes to prove the absolute
uncertainty of gambling. The great [
est mathematicians of the day cannot
be certain how a coin will fall, so that
the man Of merely average abilities
who stakes anything important on the
toss of a coin is allowing that part OF
his fortune to pass entirely outside his
/ control.-Pearsons Weekly.