Lexington gazette. [volume] (Lexington, Va.) 1871-1962, 1908-01-22
THE TOSS OF A COIN,
Mathematics of the Turning of
Heads or Tails.
CHANCE AND THEORY CLASH.
n Heads. Turn Ten Times In Sequences,
Theory Says the Odds Are Against
Another, Head, Yet Chance Says the
Odds on the Next Toss Are Even.

Isoaue. " rh ION lines IN sequences
Theory Says the Odds Are Asalns
Another, Head, Yet Chance Says tn,
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 and making careful notes
of how 1t fell. He spun the shilling
$4,000 times, and pupil Of his, work.
Ing separately, spun penny 5000
times and also tested the drawing of
1900 tickets from bag.
1t may seem strange that a learned
professor should put himself to such
IN 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 coin. In the words of the
arlthmetician, the theory of "runs"-
that is, heads turning up repeatedly
or tails turning up repeatedly-is pre-
cisely 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;
VI 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
run Of eleven heads7 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. coin has
fallen ten times head upward he Is
safe to start backing tails He puts
bis 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 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:
ut Is 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 breaking the bank" and
whose plans depended entirely on the
theory that II one game ended In a
win for red" the chances against 1t
ending "red" second time were less,
a 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-
ette or losses Of a coin all as one con-
Llnuous event. 1t Is quite safe, for in
stance. to offer beforehand big odds
against coin turning up heads ten
lines running. But In practice the
public house loafer does not do this.
What he does is to bet on each sepa-
ate toss by itself. thus defeating his
,wn aims. The odds against n coin
urnlng up heads eleven times are as
las been shown. something like 1000
o l. But suppose you only start bet
ing nj the tenth toss. What are the
dds against the eleventh toss again
icing headf If
The odds. so far from being 1000 TO
. are actually ! TO /! To use an
the odds are even-that Is
o say, if you split up the eleven losses
ntO eleven separate events to be bet
n separately your bets should be
even money" all the time, however
ften heads turn up running. But II
on view the eleven losses as one COM
ined event and you offer prelimi-
airy bet against the whole eleven re-
ults being heads you will have 10
I've gigantic odds.
All this goes to prove the absolute [
ncertalnty of gambling. The great q
st mathematician Of the day cannot
e certain how a coin Will fall, so that I
le man Of merely average abilities t
no stakes anything important on the b
'ss of coin Is allowing that part Of t
Is fortune to pass entirely outside his {
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