The Baltimore County union. [volume] (Towsontown, Md.) 1865-1909, 1908-01-18
THE TOSS OF A COIN.

"A IduOuS LudluGuudtlCldu, lOlCo-
sor Karl Pearson, once spent the
greater part of his vacation deliber-
ately tossing a shilling and making
careful notes of how it fell. He spun
the shilling $4,000 times, and pupil
of his, working separately, spun a
penny 8, 200 times and also tested the
drawing of 5000 tickets from bag.
1t may seem strange that learned
professor should put himself to such
an amount of trouble to demonstrate
what every schoolboy who had ever
tossed 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 coin. In the words
of the arithmetician, the theory of
runs"-that is, heads turning up
repeatedly or tails turning up repeat
edly-is precisely as follows:
The chance of head is one-half !;
of two heads following, is one-half
multiplied by half-that is, One
quarter of three heads in success
sion, one-half multiplied by one-half
multiplied by one-half-that is, one
eighth. Now, what do you suppose
is the chance of run of eleven heads?
1t is safe to say that not many per-
sons, however accustomed to tossing
coins, have reasoned this out. The
fact is that one "run" of eleven heads
is on the average only to be expected
in 2,o48 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
because, 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 in
fuence can a past event, the tossing
of ten heads, have on future one
which has no link with them-name-
ly, 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 roulette at Monte Carlo:
"It is pure, unadulterated ques-
ton 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" second time were less,
a 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 tosses of coin all as one con-
tinuous event. 1t is quite safe, for
instance, to offer beforehand big odds
against a 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 1000
| to I. But suppose you only start
betting 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 I ! To use an
Irishism, the odds are even-that is
to say, if you split up the eleven
tosses into eleven separate events to
be bet on separately your bets should
be "even money" all the time, how
ever often heads turn up running.
But if you view the eleven tosses as
one combined event and you offer a
preliminary bet against the whole
eleven results being heads you will
have to give gigantic odds.
All this goes to prove the absolute
uncertainty of gambling. The great
est mathematician 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 en-
tirely outside his control.-PeayS0n'
Weekly.