The Democratic advocate. [volume] (Westminster, Md.) 1865-1972, 1908-04-17
THE TOSS OF A COIN.
Mathematics of the Turning OF HEADS
OF. Tails.

0I Il uilSs
famous mathematician, Professor
Karl Pearson, once spent the grealei
mart of his vacation deliberately toss
ing a shilling and making careIui
notes OF how it fell. He spun the shli-
ling 25 900 times, and pupil OF MS
working separately, spun a penny o.
200 times and also tested the drawing
of 5000 tickets from bag.
1t may seem strange that a learned
professor should put himself 10 such
an amount of trouble to demonstrate
what every schoolboy who had ever
tossed a coin already knew. Yet, as
a matter of fact, few really do grasp
the laws which govern such an ap-
parently straightforward matter as
the tossing of a coin. In the words
of the arithmetician, the theory OF
''runs''-that is, heads turning up re-
peatedly or tails turning up repeatedly
lis precisely as follows:
The chance of head is one-nalf; OF
two heads following, is one-half multi
piled by one-half-that is, one-quart-
err; of three heads in succession, one
half multiplied by one-half multiplied
by one-half-that is, one-elghth. 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,O4S sets
of coin tossing.
Although the man in the street may
not have reckoned this, he is always
quite positive that if, say, 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 time? Surely
each toss is an event by itself, as Sir
Hiram Maxim said of a game at rou-
lette at Monte Carlo:
ct is a pure, unadultered question
of chance, and it 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
theory that if one game ended in a
win for red the chances against it
ending red" a second time were less,
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 as one con-
tinuous 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 sepa-
rate toss by itself, thus defeating his
own aims. The odds against coin
turning up heads eleven times are as
has been shown, something like 2,0G0
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
1, are actually 1 to l. To use an Irish
ism, the odds are even-that is TO
say, if you split up the eleven losses
into eleven separate events to be bet
en- separately your bets should be
even money" ali the time, however
often heads turn up running. But il
you view the eleven tcsses as one COM
bined event and you offer c prelimi-
nary bet against the whole eleven re-
suits being heads you will have to
give gigantic ODDS.
All this goes to prove tie 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 a coin is allowing that part of
his fortune to pass entirely outside his
control.-Pea rson's Weekly.