The Logan Republican. [volume] (Logan, Utah) 1902-1924, 1908-02-05
THE TOSS OF A COIN,
Mathematics Of the Turning Of
Heads or Tails. -
CHANCE AND THEORY CLASH,

u Heads Turn Ten Timse In Sequence
Theory Says the Odds Are Against
Another Head, Vet Chance Says thu
Odds on the Next Toss Are Even.
A famous mathematician. Professor
Karl Pearson. once spent the greater
part Of his vacation deliberately toss.
ing shilling aud making careful notes
OF how II fell. He spun the shilling
$4,000 times, and a pupil of his. work.
ing separately. spun a penny $500
times and also tested the drawing OF
1900 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 appar.
emily straightforward matter as the
tossing OF n coin. In the words OF tho
arithmetician,' the theory of runs
that Is, heads turning up repeatedly
or tails turning up repeatcdly-is pre-
cisely MS follows:
The chance Of Il head Is one-half; of
two heads following. Is onc-half multi
piled by one-half-that IL. one-quarter:
Of three heads in succession. one-half
multiplied by one-half multiplied by
one-half-that is, one-eigh,h. Now.
what do you suppose IL 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 he expected in 2.O4S sets
of coin tossing
II Although the man in the street may
not have reckoned this. he is always
quite positive that II. 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. 1t 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 1t ever
was. What mysterious influence can
past event, the tossing Of ten heads,
have on a 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 at rou
lette ut Monte Carlo:
ut is a pure. unauthorized question
) of chance, and 1t Is not Influenced ir
the least by anything which has ever
taken place before or that ever will
c take place in the future"
A nasty piece of plain speaking this
for the cranks who had published
Q schemes for breaking the bank ant
whose plans depended entirely on tho
j theory that IL one game ended In 1
win for "red" the chances against +
ending "red" second time were less
a third time less still, and so on.
+ This of course would be SOUND
u enough argument provided that yol
regard some dozens of games Of rou
lette or losses of coin all as one con
y tinuous event. 1t Is quite safe, for In
l. stance, to offer beforehand. big odd
against coin turning up heads tel
y times running But In practice tn
public house loafer does not do this
. What he does Is to bet on each sepa
: rate toss by itself. thus defeating hi
own aims. The odds against a coll
, turning up heads eleven times are a
has been shown. something like 200
y to /. But suppose you only start bel
u ting at the tenth toss. What are til
y odds against the eleventh toss agai
being head?
q The odds. so far from being 1000 I
:" 1. are actually to !! To use a
:, Irishism. the odds are even-that
J, J, to say, II you split up the eleven tosse
;" into eleven separate events to be bt
= on separately your bets should b
!. 'even money" all the time, howeve
- often heads turn up running. But
,, you view the eleven losses as one con
;" bined event and you offer prelim
nary bet against the whole eleven n
suits being heads you will have
give gigantic odds.
III All this goes to prove the absolut
3 uncertainty Of gambling. The grea
Ut est mathematician of the day came
10 be certain how a coin will fall, so tn,
'k the man of merely average abiliti'
a. who stakes anything important on II
10 toss Of coin is allowing that part I
10 his fortune to pass entirely outside h
Ut control-Pearson's Weekly