Evening star. [volume] (Washington, D.C.) 1854-1972, 1913-01-25
THE LAWS OF LUCK.
Chances of Heads or Tails in the
Tossing of Coins.

From HarperS Weekly.
Everybody knows that when a coin is
spun into the air it is pure chance
whether it falls head or tail upward; and
every year, apart from gambling, thou
sands of important sporting decisions, at
foot ball matches and the like, are set
tied by the simple test. Yet mathemati-
clans have pointed out that our ideas Of
chance in tossing are really quite
wrong, if We define chance as the uneX
pected.
1t is not because we believe in chance
that We spin coin, but because we be-
lieve in law. We know. or think We know.
that If penny were tossed a million
times head would have appeared. when
the total results We're added up. five hun
dred thousand times and tail five hundred
thousand times. A few odd figures over
on one side or the other would not prove
the prophecy wrong. The million losses
would be half one way and half the other.
as nearly as may be. and we should be
satisfied with the result OF the experiment
and say that it proved. what We already
believed, that 1.-The chances were equal"
This Is what the man in the street calls
chance. But suppose out of the million
losses we found, to our surprise, that an
enormous majority had turned up. say
tail: what should we call the result then?
Naturally, we should not call 1t law.
Surely we should Immediately cry, "What
an extraordinary chance" thus showing
that what we had believed in before the
test was something quite different. some
thing not genuinely chance at all.
If group of people are betting on the
results Of tossing a coin and the coin has
come down. say, five times running head
body at once begins to put his money on
tail. No one believes that the run can
continue much longer. thus testifying to
his utter disbelief In chance as such.
Yet chance caused that run of heads
and chance may continue 1t. The real
reason why the gamblers do not expect
the run to continue Is because experience
has taught them that some law, as sure
as the rising Of the sun. has in the past
prevented a tossed coin from eternally
turning I'D on the same side, and that the
Oftener it turns up on the one side the
larger becomes the probability that 1t
will turn up on the other.
Chance, in the eyes OF the sSientlst. IL
really knowledge. 1.-The knowledge OF the
average results Of many events used to
replace ignorance Of the result OF each
| individual event" Prof. Karl Pearson
spent a long time actually trying the toss
ing of a coin and noting the results scien-
tihcally. One summer he passed the great
er part Of his holiday in making 25.OOO
careful losses Of a shilling. doubtless
greatly to the amazement OF his neigh
bors.
A pupil Of his supplemented the shilling
| record by $500 losses Of a penny and the
drawing of 1000 tickets from a bag. while
| another gentleman sent to Prof. Pearson
the details of nearly $4,000 drawings OF
colored and numbered counters. The re-
suit Of tabulating this mass Of figures
was. according to the professor. I'm strik-
| ingly close agreement with theory, that
Is. with the theory that chance IS the
| knowledge Of the average results OF many
events
In other words. head and tail turned up
an approximately equal number or times
80 0spo
tuations from what was expected. Or
rather the fluctuations were expected
scientifically. for some fluctuations from
the average are the only reliable test OF
chance If In such an infinite number of
experiments heads and tails turned up q
precisely equal number OF times without