_SHARPS AND FLATS_
Now that we have reached the final stage of our inquiry, the reader
having been put in possession of all the facts which are material and of
importance in connection with it, nothing more remains than to take a
brief review of our position, as it were, and see precisely how we
stand--to regard the question of gambling as a whole, in fact, and see
what conclusions we may arrive at with regard to it, when it is viewed
with the eye of common sense, and in the light of the knowledge we have
obtained. Every subject, of course, has many aspects, and gambling may
be regarded from many different standpoints. In this last chapter, then,
and with the reader's permission, I will take the liberty of regarding
it from my own; and, no objection being raised to the proposal, I should
prefer to regard these concluding remarks as being made confidentially,
so to speak, between the reader and myself. If, in delivering myself of
what remains to be said, I should appear to speak either egotistically
or dogmatically, I crave pardon beforehand, and beg the reader to
believe that, if I am inclined to emphasise any particular point
bearing upon the matter in hand, it is because I feel strongly with
reference to it, and not because I wish to pose in the eyes of the world
as a champion of right and an opponent of wrong.
Fear has been expressed, in some quarters, that the publication of the
secrets contained in this book will be the means of increasing the
number of sharps; that I am simply providing a manual for the
instruction of budding swindlers. This may appear very cogent reasoning
to some; but, for all that, it is very poor logic, in reality. In fact,
a more groundless fear could not be entertained. It would be as
reasonable to say that the manufacture of safes and strong-rooms, and
the increase of safeguards against thieves, will tend to augment the
number of burglars. Or, to come nearer to the point at issue, one may as
well assert that the exposure of spiritualistic frauds has increased the
number of 'mediums.' The subject of spiritualism affords a most striking
proof of the absurdity of such a contention. Contrast the state of
affairs twenty-five years ago, before the crusade against spiritualistic
humbug, with that of the present day. Then, dozens of impostors were
doing a thriving business. The medium was as much in demand as the most
popular society entertainer, and could command larger fees. Spiritualism
was a fashionable amusement; the drawing-rooms of the aristocracy were
constantly being darkened for séances. Now, only two or three miserable
rogues, without ability to earn a living in any other way, are dragging
out a wretched existence in the East End of London, giving séances in
back parlours, and charging a fee of a shilling a head. Even in America
things are not much brighter for the medium. Compare Dr. Slade's success
in London with his sad end in America, a few weeks ago. In fact, the
business is utterly ruined; those who have sufficient ability have
become conjurers and 'exposers of spiritualism'; others have become
gambling sharps and 'hypnotic subjects.' These facts constitute a
complete answer to the assertion that this book will tend to increase
the practice of sharping. I maintain that no young man's education
should be considered complete without some knowledge of the capabilities
of trickery; for, without it, he may be imposed upon by any charlatan.
Apart from the question of sharping, and with reference to the fallacies
indulged in by gamblers at large, there are, among a multiplicity of
others, three which demand our special attention, and with which I
particularly wish to deal. These three mistaken, though very commonly
entertained notions, constitute the very basis of what is called fair
gambling. They are these:--
1. That gambling is essentially honest.
2. That a bet may be fair to both parties.
3. That betting on fair odds, the chances of each bettor will,
in the long run, so equalise themselves that neither can win
nor lose, in an infinite number of bets.
Now, what I undertake to show may be summed up in three statements,
which can be put _per contra_ to the others, viz.:--
1. That gambling is essentially dishonest.
2. That a bet may be _unfair_ to both parties, but cannot
possibly be fair to more than one, and that only at the expense
of gross injustice to the other.
3. That a protracted run of betting gives the gambler no more
chance of winning, or of recouping his losses, than he has in
making a single bet.
Here, then, I bring the whole gambling fraternity--sharps and flats
alike--about my ears. But, having courage of my opinions, I stand to my
guns, and am prepared to hold my own against all comers. I will even go
so far as to back my opinion in 'the good old English way' (why
English?) to the extent of sixpence--beyond which I never go. Stay,
though, I am speaking hastily. I did once back a horse for the Derby to
the extent of a guinea. When I say that the horse was 'Maskelyne, by
Magic--Mystery' (I believe that was the formula given by the sporting
papers), perhaps I may be forgiven the extravagance for once. I have
less compunction in mentioning the circumstance because the horse was
'scratched.' 'Maskelyne' was a rank outsider, and I did not even have 'a
run for my money.'
But to return. I have said that gambling is essentially dishonest. This
is no new statement, I am aware; but it is one upon which too much
stress cannot be laid. A bet is almost universally considered to be a
fair bargain. But is it? A _fair_ bargain is one in which each person
receives something which is of more value to him than that with which he
has parted, or, at any rate, something which is of equal value. If
either receives less value than he gives, that person has been swindled,
and the fact of winning a bet signifies that one has deprived another of
money for which no due consideration has been given. The gambler, of
course, will argue that he _does_ give an equivalent return for what he
wins, in that he allows his opponent an equal chance of depriving him of
a similar amount; that is to say, he purchases the right to cheat
another by giving his opponent an equal chance of depriving him of a
similar amount. In short, a bet is simply a mutual agreement to compound
a felony. The fact that both parties to the transaction are equally in
the wrong cannot possibly justify either. But it may be argued that no
loser of a bet ever considers that he has been unjustly deprived of his
money. That again is quite a mistaken notion. No man ever lost a bet who
did not consider that he had every right to win it, otherwise he would
never have made it. Therefore he is just as much robbed as though he had
had his pocket picked. Because another will cheat me if he has the
chance, that does not justify me in cheating him if I can. If a man
seeks to take my life, I may be justified in killing him, as a last
resource, in order to protect myself; but, in a transaction involving
merely pounds, shillings and pence, there is no necessity to fight a man
with his own weapons. The act of cheating is not the weapon with which
to combat the desire to cheat; yet this is what actually takes place
even in so-called fair gambling.
It must be obvious to any one who will take the trouble to think over
the matter, that chances which are fair and equal are a question of
proportion rather than of actual amounts and odds. At first sight,
however, it would appear that if a man stands an equal chance of winning
or losing a certain amount, nothing fairer could possibly be imagined,
from whatever point of view one may regard it. I venture to say,
nevertheless, that this is not so. Suppose for the moment that you are a
poor man, and that you meet a rich acquaintance who insists upon your
spending the day with him, and having what the Americans call 'a large
time.' At the end of the day he says to you, 'I will toss you whether
you or I pay this day's expenses.' Such a proposition is by no means
uncommon, and suppose you win, what is the loss to him? Comparatively
nothing. He may never miss the amount he has to pay; but if you lose,
your day's outing may have to be purchased by many weeks of
inconvenience.
A bet of a hundred pounds is a mere bagatelle to a rich man, but it may
be everything to a poor one. In the one case the loss entails no
inconvenience, in the other it means absolute ruin. It must be granted,
then, in matters of this kind, that proportion is the chief factor, not
the actual figures. If you are with me so far, you are already a step
nearer to my way of thinking.
Let us proceed a step further, and see how it is that a bet is
necessarily unfair to both parties. The simple fact is that no two men
can make a wager, however seemingly fair, or however obviously unfair,
without at once reducing the actual value to them of their joint
possessions. This can be proved to a demonstration. We will take a case
in which the chances of winning are exactly equal, both in amount and in
proportion to the wealth of two bettors. Suppose that your possessions
are precisely equal in amount to those of a friend, and that your
circumstances are similar in every respect. There can be, then, no
disparity arising from the fact of a bet being made between you, where
the chances of winning or losing a certain amount are the same to each.
To present the problem in its simplest form, we will say that you each
stake one-half of your possessions upon the turn of a coin. If it turns
up head you win, if it falls 'tail up' your friend wins. Nothing could
possibly be fairer than this from a gambler's point of view. You have
each an equal chance of winning, you both stake an equal amount, you
both stand to lose as much as you can win, and, above all, the amount
staked bears the same value, proportionately, to the wealth of each
person. One cannot imagine a bet being made under fairer conditions, yet
how does it work out in actual fact? You may smile when you read the
words, but _you both stand to lose more than you can possibly win_! You
doubt it! Well, we shall see if it cannot be made clear to you.
Suppose the turn of the coin is against you, and therefore you lose half
your property; what is the result? To-morrow you will say, 'What a fool
I was to bet! I was a hundred per cent. better off yesterday than I am
to-day.' That is precisely the state of the case; you were exactly a
hundred per cent. better off. Now, the most feeble intellect will at
once perceive that a hundred per cent. can only be balanced by a hundred
per cent. If you stood a chance of being that much better off yesterday
than you are to-day, to make the chances equal you should have had an
equal probability of being a hundred per cent. better off to-day than
you were yesterday. That is obvious upon the face of it, since we agree
that these questions are, beyond dispute, matters of proportion, and not
of actual amounts.
Then we will suppose you win the toss, and thus acquire half your
friend's property; what happens then? When the morrow arrives you can
only say, 'I am fifty per cent. better off to-day than I was
yesterday.' That is just it. If you lose, your losses have amounted to
as much as you still possess, whilst, if you win, your gains amount only
to one-third of what you possess. The plain facts of the case, then, are
simply that the moment you and your friend have made the bet referred
to, you have considerably reduced the value of your joint possessions.
Not in actual amount, it is true, but in actual fact, nevertheless; for
whichever way the bet may go, the loss sustained by one represents a
future deprivation to that one far greater than the future proportional
advantage gained by the other. The mere fact of one having gained
precisely as much as the other has lost does not affect the ultimate
result in the least. The inconvenience arising from any loss is always
greater than the convenience resulting from an equal gain.
No man in his senses can be excused for making a bet of this kind, even
if one merely considers the injustice inflicted upon himself; whilst in
the case of a man who has others dependent upon him, such a proceeding
could be nothing short of criminal. If by this time you do not see that
gambling, in any form, means a possible loss of more than can be gained,
all I can say is that you should turn socialist, being totally unable to
protect or even recognise your individual interests. Civilisation is
wasted upon you. Properly speaking, if you gamble fairly you are a flat;
if you gamble unfairly you are a sharp: one or the other you must be.
To be a wise man, and an honest man, you cannot gamble at all.
Some of course will meet me half-way, and admitting the truth of all I
have put forward, will say, 'Yes, that is all very well, but no gambler
ever does stake half his possessions upon a single bet; therefore the
proportion which any individual wager bears to his entire property is
infinitesimal.' That, again, is perfectly true; but I cannot see nor
have I ever met with any one who could show me what difference can
possibly exist between a small number of bets for a large amount, and a
large number of bets for small amounts. Then comes in the third fallacy
I have mentioned. 'The chances,' some will say, 'are bound to equalise
themselves in the long run, and then one can neither win nor lose.'
Dear, good, simple-minded souls! The _proportion_ of gains to losses, I
grant, will become more equalised in an infinite number of bets where
the probabilities are always equal; but the amount which may be lost,
and the proportion it bears to the belongings of the bettor, may ever
_increase_ with the infinity of the bets.
Suppose, for instance, two men toss up a coin ten times, and stake a
pound upon the result of each toss. We will say that one of them loses
nine times, and wins only once. He has lost four-fifths of the amount he
has staked in the aggregate; but what does it amount to? Merely eight
pounds. But suppose they go on tossing for ten thousand times, and that
the same player loses only a hundredth part of the amount he has staked
during the whole time, he wins ninety-nine times for every hundred
losses. The proportion lost is infinitely less than in the former case,
yet the actual amount is one hundred pounds. Let the throws be continued
to a million times, and suppose the player loses only a thousandth part
of what he has staked from beginning to end, his losses will amount to
exactly _one thousand pounds_.
To talk of an infinite number of bets equalising the chances is sheer
nonsense; it simply equalises the _ratio_ of the gains to the losses.
The actual amounts won or lost may increase indefinitely. At the same
time the player's original wealth does not vary; and the man who
has a thousand pounds may as well lose it in one throw as in a
million--better, in fact, as he will waste less time over it.
I have tried to make this point somewhat clear, because it is one upon
which even the most scientific gamblers--if one may use the term--are
more or less befogged. They all think that, if they only keep on long
enough, they are sure to win, or at any rate to recoup their losses: but
the life of any man is too short to be certain of any such result, even
in fair gambling--and most gambling is not fair. The punter, of course,
after the manner of his kind, will differ from me in this last
statement. He is of opinion that the odds in ordinary betting _are_
fair. Well, if that is so, I should like to know who keeps the
bookmakers. I know _I_ don't, and I know the punter _does_. If he is
satisfied, so are the 'bookies'; and certainly other people have no
cause to complain. The bookmaker, above all people, makes an infinite
number of bets, and therefore, theoretically, he should neither win nor
lose; but somehow he contrives to 'live and move and have his being.'
Those who assist in maintaining him should best know how he manages it,
but they don't seem to realise it.
The absolute immorality of gambling--the desire to obtain money to which
one has no right--in any form is beyond dispute; and the sooner this
fact is generally recognised, the better it will be for the world at
large. There are some, of course, in whom the passion is ingrained, and
from whose natures it can never be wholly eradicated. But everyone
should clearly understand that the vice is as reprehensible in
proportion to its magnitude as that, for instance, of either lying or
stealing.
In an earlier chapter of this book I have said that directly a man
becomes a gambler he also becomes a person whose honesty is open to
suspicion. This may appear to be a somewhat harsh and sweeping
assertion, but I maintain that it is absolutely justified by the facts
which come under my notice almost daily. As an example of the laxity (to
use no stronger term) which gradually undermines the moral nature of the
gambler, however conscientious he may originally have been, I may quote
the following instance.
A few days ago a friend of mine, who belongs to a West End Club, was
discussing the subject of gambling with a fellow member. In course of
conversation he put the query, 'If you detected a man in cheating at the
Club, what should you do?' To this the other replied. 'I should back his
play; and then, after the game was over, I should make him give me half
his winnings.' This is what gambling had done for a presumably honest
'Club man.'
With reference to the numberless systems of which one hears now and
then, which are supposed to provide a certain means of enabling any
gambler to win, despite the chances and changes of fortune, it may be as
well to say a few words. These 'martingales,' as they are called, are
always intended for use, more especially in the great gambling-houses of
Monte Carlo and elsewhere.[12] Some of them, I should say, are as old as
gambling itself; others are of comparatively recent invention; but, one
and all, they are systems by means of which any amount of money may be
won, and any number of banks may be broken--on paper. There is the
trouble, they are useless in practice. They really look so promising,
however, that it is very difficult to convince some people of their
futility. But the fact remains that these systems have been in operation
for generations, and never yet has a gaming establishment been ruined by
their aid. This ounce of experimental proof is worth many pounds of
reasoning. Sometimes, of course, the martingale will answer its purpose
splendidly for a while; but, sooner or later, the inevitable crash
comes, when the system breaks down, and the gambler is ruined. The great
defect of all these devices is that, although they may promise a
constant succession of comparatively small gains, there is always the
chance of making a very heavy loss. This chance, of course, appears to
the gambler to be so remote as to be unworthy of consideration; but,
alas! that apparently remote chance is the rock upon which generations
of punters have split. It always turns up eventually, and then the bank
recovers all it has lost, and in all probability a great deal more.
The simplest form of martingale, and one which is typical of them all,
however much more complicated or 'improved' they may be, is the one
which consists of the practice of doubling the stake after every loss.
For instance, at rouge-et-noir the gambler may stake a sovereign and
lose it. The next time he stakes two sovereigns, and, if he loses, his
third stake will be four sovereigns. By pursuing this system it is
obvious that, whenever he does win, he will gain a sovereign over and
above his losses. Having won he will begin again with a sovereign and
double his bets each time, until he wins as before. It would seem, then,
that there must be a constant influx of sovereigns to the gambler; and
so there may be for a time, but it will not last. In fact, he may be
ruined at the very first sitting. This is how it happens. The success of
the system depends upon the assumption that the chances must, sooner or
later, turn in favour of the player; they cannot be against him for
ever, so he must win in the end. That is what he thinks. But what he
loses sight of is the fact that long spells of ill-luck are particularly
common. It is quite an ordinary thing for a player to lose twenty times
in succession; and meanwhile the amount of the stakes has been
increasing after the manner of the familiar problem in arithmetic,
wherein the nails in a horse's shoes play so prominent a part. The fact
is, if the player has lost eleven times, his twelfth stake will amount
to £2,048. Obviously, then, a very short run of bad fortune will either
cause the player to lose all his available money, or bring the stake up
to the amount beyond which the bank will not allow any single bet to be
made. What becomes of the martingale then? Ask of the winds.
And thus it is with all these systems. Their inventors fully believe in
them, until they learn from bitter experience that they have overlooked
the one weak point, the fallacy underlying the whole operation. Wherever
there is a chance of making a number of small gains, there is always a
chance of sustaining one great loss, which will swallow up many hundred
times the value of any single stake. From this unfortunate circumstance
there is no escape, no matter how ingenious the system may be, and
notwithstanding any amount of infallibility it may appear to possess. A
mathematician would demonstrate the folly of relying upon any
martingale, and lay his finger upon the weak points in a few minutes. In
short, these things one and all provide a means of winning which is just
about as reliable as the advice given by the 'Old Pard' in 'My
Sweetheart,' whose dying words were, 'Always copper the Queen on the
last turn.' This, of course, was intended to refer to the game of faro.
One may suppose that when the Queen remained in the dealing-box until
the last turn, his experience had been that it always turned up for the
bank, and hence his advice to 'copper.' Another person's experience
might have been just the opposite, and in that case the advice would be
quite the contrary. Everything of this kind hinges upon superstition,
and a belief in good and bad luck. When a 'lucky' gambler wins, his
acquaintances express no surprise; they consider his good-fortune to be
part and parcel of his nature. When he begins to lose, they suffer not a
whit more astonishment, because such luck as his could not possibly
last. The theories in each case are utterly at variance with one
another, but the absurdity of the position never seems to reveal itself
to the gambling intellect. The ultimate fate of the confirmed gambler,
however fortunate he may be for a time, has always been, without
exception, ruin and destitution. That is the only result ever achieved
by the punter in the end.
So much, then, for 'fair gambling.' As to the blacker side of the
question, as revealed in this book, what can be said of it, or what need
be said of it? The reader may draw his own conclusions, which will
doubtless vary according to the fact of his being either a sharp or a
flat. The sharps will, unquestionably, be among those who are most
anxious to see what disclosures are made herein; let us hope they will
be satisfied with the thoroughness of the revelations. It would be a
pity to disappoint them. On the other hand, the flats will find much
food for thought in these pages. They must not run away with the
impression that by mastering the details thus put before them they will
render themselves proof against sharping. If they imagine anything of
the kind they will become simply 'fly flats,' and that will not improve
their chances very much if they fall into the hands of an expert. Apart
from the impossibility of giving every device employed by all the sharps
in existence, it must be remembered that fresh trickeries are
continually being invented, though it may be many years before new means
of cheating can be devised which will prove so effective as those
enjoyed by the sharp at the present day. He is generally equal to the
occasion, however, and has his own individual methods of working; very
often methods of which even his brother-sharps are ignorant, and which
die with him. We can only hope that this book will be the means of
opening the eyes of his dupes, and of rendering the chances of success
in cheating less than they have been hitherto.
But we cannot hope that the sharp will find _no_ dupes in the future;
that is altogether too much to expect. As long as the world is
principally composed of rogues and fools, so long will there be 'sharps
and flats.' 'Surely the pleasure is as great in being cheated as to
cheat,' but the profit does not apportion itself in the same manner. The
sharp continually profits by his experience, but the flat--never.
At any rate, I have done the best I can to put forward a clear account
of the methods of swindling at games of chance and skill which are
adopted at the present day. At the same time I have tried to indicate
the best means of avoiding being cheated. It only remains for the reader
to make the best use of the information given. I have no fear that, in
writing what I have, I shall be accused by sensible people of assisting
those sharps who may not know all that is here published. The resources
of these men are always equal to their necessities; they can only cheat,
at the worst, and the sharp will always find means of cheating so long
as he can find dupes. Besides, this book will tend to make his dupes as
wise as himself, and should have the effect of rendering them scarce.
Having published such information as I have been able to acquire, I have
no intention of relaxing my vigilance in keeping a look-out for fresh
developments and new devices. Having put my hand to the plough I shall
not turn back; and, after me, I have every reason to believe that my son
will continue the work. He has taken the liveliest interest in the
production of this book; and, indeed, the whole of the illustrations are
by him, with the exception of the frontispiece, which is by my esteemed
and talented friend, Alfred Bryan.
Here, then, I will leave the work for the present, trusting that I have,
in some measure, succeeded in metaphorically flattening the 'sharps' and
sharpening the 'flats.'
FOOTNOTE:
[12] A friend of mine, who has just recently paid a visit to Monte
Carlo, describes a method of cheating the bank which came under his
notice during his stay in that hallowed spot. He observed, one evening,
a man standing by a roulette-table, who persistently put down a
five-franc piece upon the winning number, after it had been declared. Of
course, the 'croupier' never failed to detect the manoeuvre, and
removed the stake. The fact which passed unnoticed, however, was that a
gold coin, value twenty francs, lay hidden beneath the silver one as it
was put down. Being commanded to take up the five-franc piece, the man
did so without hesitation; but the gold piece remained on the table
among the other stakes. When the winnings were paid by the bank, that
particular coin was claimed by a confederate as being his stake, and was
paid accordingly. In roulette, the winning number receives 35 times the
amount staked; therefore the conspirators netted 700 francs each time
they succeeded in this little operation. I should think the bank would
not be long in discovering a robbery of this kind, if it were very
frequently perpetrated.
POSTSCRIPT
Whilst this book is still in the press, an article on 'Science and Monte
Carlo,' by Professor Karl Pearson, has appeared in the (monthly)
'Fortnightly Review.' This article deals with the game of roulette, and
is one which may be commended to the perusal of all who may have any pet
theories in connection with chance and luck. It constitutes, in fact, a
very serious impeachment of the validity of all accepted theories of
chance; so serious, indeed, that one stands amazed at the discrepancies
which are revealed, and their having remained so long unnoticed. There
appears to be no way out of the difficulty. Either roulette is not a
game of chance, or the doctrines of chance are utterly wrong.
It appears from Professor Pearson's investigations, that in a given
number of throws the results shown by the "even-money" chances are
fairly in accord with the theory as a whole. That is to say, the odd and
even numbers, the red and black, turn up respectively in very nearly
equal proportions. Also the 'runs' or sequences of odd or even are such
as would not give rise to any conflict between theory and practice. But
the astounding fact is that the 'runs' or successions of red or black
occur in a manner which is utterly at variance with theory. Why this
should be so, and why 'red and black' should thus prove to be an
exception to the theory, whilst 'odd and even' is not, passes the wit of
man to comprehend.
In one of the cases quoted by Professor Pearson, 8,178 throws of the
roulette-ball are compared with a similar number of tosses of a coin,
and both results are checked against the theoretical probabilities. In
tossing a coin or throwing a roulette-ball 8,178 times, theory demands
that the number of throws which do not result in sequences--that is to
say, throws in which head is followed by tail, or red by black-should be
2,044. Those are the probabilities of the case. But the actual results
were as follows:--
Theory 2,044
Roulette 2,462
Tossing 2,168
There are too many single throws in each case, but the results given by
tossing were much nearer the theoretical proportion than in the case of
the roulette. Proceeding a step further, we find that the sequences of
two work out thus:--
Theory 1,022
Roulette 945
Tossing 1,056
Here the figures given by roulette are far too small. This is found to
be the case with sequences of three and four also. When we come to
sequences of five, however, the numbers stand:--
Theory 128
Roulette 135
Tossing 120
In this case, the roulette is nearer the mark than the tossing; and from
this point onward through the higher sequences, roulette gives numbers
which are far too high. For instance, in sequences of eight, theory says
that there should be 16, but roulette gives 30. In sequences of eleven
theory says 2, but roulette gives 5. Arriving at sequences of twelve,
the figures are:--
Theory 1
Roulette 1
Tossing 1
Here all the results are in accord.
This is only one instance out of several recorded by Professor Pearson;
in every case the results being similar. That only one instance of such
abnormal variation should occur is, theoretically, well nigh impossible;
but that there should be three or four such cases in the course of a
single twelvemonth is nothing short of miraculous. The chances against
the occurrence of such events are enormous; and yet every case
investigated shows the same kind of result. Truly this must be another
example of the malignity of matter.
The practical outcome of these investigations is to emphasise the utter
futility of any scheme of winning at roulette based upon the law of
averages or the doctrines of chance. It is more than likely, in my
opinion, that further analysis of the records of Monte Carlo would
reveal similar discrepancies in other departments of the game.
Personally, I fail to see how the devotees of the 'Higher Statistics'
will contrive to meet the difficulty here presented. Why roulette should
obey the laws of chance in some respects and not in others, is
incomprehensible from any point of view whatever. One is driven to the
conclusion that human experience and human statistics are upon too
limited a scale to form a sufficient basis upon which to found either
the proof or disproof of any universal theory. The only refuge appears
to be that, given eternity, all events, however improbable, are
possible.
It is to be hoped that Professor Pearson will find an opportunity of
continuing his researches in this direction, for the subject promises to
be one of exceeding interest. Of course, it may be objected that the few
instances given are insufficient to affect the theory materially; but,
as the Professor says of one of his instances, had roulette been played
constantly on this earth, from the earliest geological times to the
present day, such an event might be expected to happen only once. Those
who believe that an infinite number of bets, where the chances are fair
and equal, can result in neither loss nor gain, should ponder this
carefully. If the doctrines of chance can fail in one case, they can
fail in others. At best, they are but a broken reed, and those who trust
to them should beware the risk that is thereby entailed. Above all, the
punter should bear in mind that, whatever theory may say or practice
apparently demonstrate, the fact that any given event has happened so
many times in succession makes not the slightest particle of difference
to its chances of happening again. If one tossed a coin a hundred times,
and it turned up 'head' every time, that would not in any way lessen its
chance of turning up the same way at the next throw. The figures given
in the article above referred to are neither more nor less than an
illustration of this very palpable truth, extraordinary as they
undoubtedly are when viewed in the light of theory.
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* * * * *
Transcriber's Notes:
Author quoted some pamphlets and deliberately kept their spelling and
punctuation errors; those have not been changed here.
Other punctuation, hyphenation, and spelling inconsistencies have been
standardized when a clear preference was used in this book, and left
unchanged otherwise.
End of Project Gutenberg's Sharps and Flats, by John Nevil Maskelyne