The sun. [volume] (New York [N.Y.]) 1833-1916, 1893-08-06


single guinea that ten sevens would not be
thrown. He points out that with pair ol
dice. there are thirty six possible throws, and
six OF these give seven as the total Tins the
chance OF throwing seven IL one sixth. and the
chance Of throwing seven ten times running Is
obtained by multiplying six into !tseli ten sue
cessve times, and placing the resulting num-
Der under unity to represent the minute frac-
tional chance required 1t will be found
that the number thus obtained is co.
| +60,170. and. instead OF 1000 guineas.
fairness required that 6O.40d.175 guineas
should have been wagered aRainat one
| guinea so enormous are tho chances against
| the occurrence OF ten successive throws Of
| seven. Nevertheless. when the nine throws of
| seven had been made, the chance Of a tenth
throw OF seven was simply one-siyth hs. at the
first trial Taking tho mathematical value Of
the chance. Mr.. Ogden should. in fairness.
| have offered only q sixth part OF lOo1 guineas.
the amount OF the stakes to be let OF his wager.
| SO that his opponent accepted. In the FIRST In
stance. an utterly unfair OFFER and refused. in
| the second instance. n sum exceeding by more
than 800 guineas the real value Of his chance.
II.
| As another illustration OF the application Of
the gambling superstition regarding tho
maturity the chances" Mr.. Proctor cites
the case OF an Englshman once well Known at
foreign gaming tables. who had based q sys-
tenn on generalization Of this theory. 1t will
be recalled that the theory asserts that. when
there has been n run In favor Of any particular
event. the chances in favor Of the event are re-
duced. and. therefore. necessarily. the chances
In favor OF other events are increased. The
Englishmnn in question had watched the play
at n roulette table for two full hours. carefully
noting tho numbers which came up during
that time. Then. eschewing those numbers
which had como up often. he staked his money
on those which had come IN very seldom or not
at all. Here was an infallbe system. accord
ing to what gamblers deem tho most elemen-
tary OF the theories OF probability" The
tendency OF chance results to right themselves
so that events equally likely in the first in
stance will occur an equal number Of times in
the long run. was called into action to enrich
our gambler and to ruin the unlucky banker.
The result was that on tho first day the Eng
lishman won more than seven hundred pounds
In single hour His exultation was bound
less. He thought he had discovered the
philosophers stone. OF he few to his bank
ers and transmitted the greater portion OF his
winnings to London. The next day he played
and lost fifty pounds; on the third day he
achieved the same result. and had 10 write to
town for remittances. In fine. at tho
end Of a week he had lost all tho
money he had won at first with the
exception of fifty pounds. which he reserved
to take him home. and being thoroughly con-
WINGED Of the exceeding fckleness OF fortune.
he never staked a sixpence afterward On THIS
case Mr.. Proctor remarks that the gambler
took the very sound principle OF probabilities
as the supposed basis Of his system. but. in
reality. he entirely mistook the nature of the
principle. The principle is that. where tho
I'm nr har ~ fxyn lie
equal for each trial. and many trials are made.
the number Of events OF one kind will bear to
those OF the other kind a very nearly equal
ratio: the greater the number Of events. tho
more nearly will the ratio tend to abso-
Lutte equality. This is perfectly true. and
nothing could be safer than to wager
on this principle Mr.. Proctor himself
expresses In this book a willingness to wager
that, were man to toss a coin for an hour
neither would heads exceed tails or tails ex-
coed heads In a greater ratio than that OF p to
90 Let the man toss for day and Mr.. Proctor
would wager as confidently that the inequality
would not be greater than that represented by |
the ratio OF 1O1 to 100. Let the tossing be re-
peated day after day for a year. and Mr.. Proctor
declares his readiness to wager his life that |
the disproportion would be less than |
that represented b. the ratio OF 1.0O1 |
to 1000 Yet so little does this principle |
bear the Interpretation placed upon 1t |
by the inventor OF the gambling system
above described that II. on any occasion dur
ing this long-continued process Of tossing.
head" had been tossed no less than twenty
times In succession Mr.. Proctor. for his part
would not wager sixpence on the next tossing
giving tail" or trust a sixpence to the chance
OF tail appearing oftener than head in the next
five. ten. or twenty tossings. Not only should
reason show tho absurditv Of supposinR that
tossing. or set OF five. ten. or twenty tossinGs
can he affected one way or the other by past
tossngs. whether proximate or remote. but
the experiment has been tried and it
has appeared that after any number Of
cases IN which heads have appeared such and
such n number OF times in succession, the
next tossing has given head as often as +
it has given tail. To suppose that 1t would
be otherwise is utterly TO ignore the relation
between cause and effect. When any one as
serts that because such and such things have |.
happened. therefore such and such other
events will happen. he ought to be able to show
that the past events have some irectinfluepce
on those which are thus said to be affected by
them. But il one is going to toss a coin per-
fectly at random. In what possible way can the
result OF the experim ent be affected by the cir
cumstanoe that during ten or twelve minutes
before he tossed head only or tail onlya.
HI.
Among examples OF unfair wagers, the au.
thor OF this book mentions the case Of Lord
Marlborough. who used to offer freely FL 600 to
FL againstthe occurrence of a whist hand con-
tanning no card above nine. Odds of n thou
sand pounds are obviously tempting to the In
experienced. but as n matter OF fact. the offer
was most unfair one. Mr. Proctor shows the
mathematical certainty to be that in the long |
run, such bets will involve a loss to the taker
Of 81 1928 for each thousand pounds gained. or
, net loss Of fs2S 1t was in other words. as
certain as that two and two make four that a
arge number OF wagers laid on this plan
would assure to the layer OF the odds very
arge gain. Yet Lord Marlborough would prob
ably have been indignant II he had been told
hat In taking FL for each hand on which he
vagered which did not provo to be Yarbor-
,ugh. he was. in truth. defrauding the holder
II the hand Of upward OF nine shillngs notwith-
standing the preliminary agreem ent simply be-
ma prali m I'm n raa m nt >, |