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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FOOTNOTES
[1] Quotation from the late Earl Fitz-Hardinge, a most ardent sportsman.
[2] Vide Chapter VI., 'Manipulation.'