Republican news item. [volume] (Laport, Pa.) 1896-19??, 1908-01-09
TIE TOSS or / COIN.
Mathematics of the Turning OF
Heads or Tails.
CHANCE AND THEORY CLASH.

I
! If Heads Turn Ten Times In Sequences,
| Theory Says the Odds Are Against
! Another Head, Vet Chance Says tho
| Odds ca the Next Toss Are Even.
! a famous mathematician, Professor
J Kari Pearson. once spent the greater
! part of his vacation deliberately toss
| iu.s shilling and making careful notes
, Of how it fell he spun the shilling
250G0 times. and n pupil Of his, work
! ing separately. spun a penny $500
times and also tested the dra awing Of
$500 tickets from a bag.
| It may seem strange that learned
professor should put himself to such
an amount Of trouble TO demons te
what every schoolboy who had ever
tossed 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
arIthlnetician, the theory Of "runs"-
| that Is, heads turning up repes tedly
or tails turning up repeatedly-is pre-
clseiy as follows:
| The chance of q head is one-half; of
two heads following. is e-half multi
| Piled by -ha!f-that is one quarter;
of three heads In succession, one-half
multiplied by one-haif multiplied by
one-half f-that ia, one-eighth. Now.
what do you suppose Is the chance Of
q run Of eleven heads? 1t Is safe to
say thst 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 c,O48 sets
o! coin tossing.
Although the man III the street may
not have reckoned this, he Is always
quite positive that II, say. a coin has
fallen ten times head upward he Is
safe TO start backing tails. He puts
! his money TN 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 1t ever
| was What mysterious influence can
a rHst event. the tossing OF ten heads.
have on future one which has no
| lini: 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-
| Iet.c at Monte Carlo:
1T 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
4 nasty piece Of plain speaking this
! for the cranks who had published
schemes TO-. breaking the bank" and
whose plans depended entirely on the
theory that II one game ended In Il
| win for red the chances against 1t
ending "red" Il second time were less,
| a third time less still. aud so on.
This OF course would be sound
| enough argument provided that you
regard some dozens Of games of rou
lctte 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 losfsr does not DO this.
What he does Is to bet on each sepa-
rate loss by itself. thus defeating bis
own aims. The odds against coin
turning up heads eleven times are as
has been shown, something like 1000
% |. Rut suppose you only start bet.
ia i! I've tenth toss. What are the
o,;.s, a.:, = the eleventh toss again
| being 81 head?
1hc odds. so fur from being 1000 to
/. are actually l to 1. To use an
Egishisui. the odds are even--that is
10 say. ii you split up the eleven tosses
into eleven separate events to be bet
on separately your bets should be
even money al. the time. however
often beads tGrn UP running. Rut If
yGu view the eleven tosses AZ one COM
tiaad event and you offer preliml-
nary bet against the whole eleven re-
sGits being heads you will have to
give gigantic odds.
~. this goes to prove the absolute
uncertainty of gambling. The great
est Ilathema ticians Of the day cannot
be certain how coin VIII fall, so that
the man Of merely average abilities
who stakes anything important on the
toss of q coin is allowing that part OF
his fortune TO pass entirely outside his
control.-Pearson's Weekly