foreword to the online edition
preface
I. introductory
II. common sharpers and their tricks
III. marked cards and the manner
of their employment
IV. reflectors
V. holdouts
VI. manipulation
VII. collusion and conspiracy
VIII. the game of faro
IX. prepared cards
X. dice
XI. high ball poker
XII. roulette and allied games
XIII. sporting houses
XIV. sharps and flats
postscript


SHARPS AND FLATS
CHAPTER XIV
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 "evenmoney" 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 rouletteball 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 rouletteball 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 emphasize 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.
