and very cautiously between the outward-bound herring boats dropping down with the tide, not forgetting to pitch a few couple of ducks on board for men on whose goodwill so much of the wildfowler's sport depends, our 'scuppers' full of beautiful and dainty birds, and the broadening sunlight flashing at every dip from our paddles, we felt that, after all, the fun had been worth while turning out into the grey morning for, and well! if our hostess could by any manner of means be induced to suggest a second breakfast when we got in, we were not the men to say no to it.

A GREAT change is gradually coming over the world. Adventure, sport, enterprise, are giving way to caution and the calculation of averages. Men do not take the risks they used to do. The modern man is surrounded by police constables, sanitary inspectors, and insurance agents. It was to escape this burglarproof life that Louis Stevenson fled to a romantic island in the Pacific, there to assist the cause of a handsome, eloquent, barbarian pretender and rebel. Adventure,' as we read in the 'New Arabian Nights,' 'was dear to his heart.' So he abandoned Piccadilly for Samoa and Tongatabu.

There are still some habitable countries-for Samoa is not habitable-where the counting up of percentages has not yet begun. Africa and Australia, for instance, produce cattle plagues, rebellions, droughts, bank smashes, and similar temporary catastrophes with a heartiness which startles more settled countries. It was an exile to Australia, Lindsay Gordon, who said:

No game was ever yet worth a rap

For a rational man to play
In which no disaster, no mishap
Could possibly find its way.

But the modern, civilised, European tendency is to avoid all disasters, and to insure against those which cannot be avoided. This spirit has even invaded gambling. Straight bets over single events are losing their popularity in favour of 'systems.'

A system is a kind of patent safety insurance policy. It promises a clever and easy method of suddenly becoming rich.

It appeals both to cupidity and to vanity. The desire for wealth is hardly greater than the desire to outwit other men. The possession of a large income would not prevent many persons from laboriously concocting a system by which they could win a few shillings from their neighbours. It is said that a prince of one of the great reigning families of Europe once committed a petty theft at a gambling table, so upset was he at the trumpery losses which a system of his own invention had brought upon him. Money was not in question. But vanity was. The system inventor is always ready to boast of his cleverness. He will not say exactly what his plan is. It is too precious to be given away. But he takes care that all the world shall know that he could an if he would.'

The research and ingenuity which some of these schemes exhibit are astonishing. But the main types of systems have now for many years past been fully examined. All new inventions are mere varieties in detail containing no novel principle, and therefore no greater probability of success than those which have already been discarded. And it is notorious that the 'professionals' themselves, the croupiers and the bookmakers, whose experience is worth considering, have never invented any punting system of any value whatever. Considerations such as these, however, have little weight with the system inventor, who is always confident that he has done what no other human being in the history of the world has ever done before.

The general principle which governs all games of chance, such, for instance, as roulette, is that the past does not affect the future. Whether red has turned up once, ten times, a hundred, or a thousand times in succession, in each case the next result, the second, eleventh, hundred and first, or thousand and first, is as likely to show another red as a black. All systems, whatever their nature, are based upon the opposite idea, for they all direct the gambler to regulate his bets by the results which have already been obtained. Therefore they are all based upon a fallacy.

If the past really affected the future, then it would follow that the machinery of the roulette table, and the croupier who sets it in motion, would be physically affected by a series of ten reds in succession, so as to become less capable at the eleventh trial of producing red again. Even if the machine were changed and a fresh croupier were introduced, the same physical disability would attach to them. And a croupier at one table would suddenly find that he and his machine were physically affected by a run of ten reds at another table. So whenever the wheel and ball are set in

motion at roulette, they must feel the influence of all past results since the creation of man, compared with which ten reds in succession cannot be of any interest whatever.

In order to establish the complete independence of each venture as shown by actual experience, I have examined the large number of 44,025 consecutive results at Monte Carlo at roulette, as published in a newspaper called Le Monaco.' The series of 7, or more, consecutive appearances of a colour were as follows:

Of the 467 series, 220 or about one-half stopped at 7, while the remaining 247 went further; the eighth venture showed a change of the colour 220 times, and a repetition of it 247 times. Of these 247, about one-half, 121, stopped after the sequence of 8, while the remaining 126 went on to sequences of more than 8; after 8 reds the next result was black 121 times and red 126 times. These figures show, beyond possibility of doubt, that even when a colour has appeared an unusual number of times in succession the next result does, in fact, give another appearance of the same colour as often as a change. It is thus clearly proved by actual experience that the past does not affect the future in such games as roulette. Thus no system of watching the past before betting on the future can be of any value.

The gambler may say that his system is based upon the fact that, on the average, red appears once in every two ventures, and-quite inconsequently-declare that this law of average points to a bet on red after black, and black after red. He is mistaken in supposing that this would be betting on the average of results. He would really be betting on red black and black red, as against red red and black black. No law of average

supports such a bet. Experience shows that the sequences red red and black black are as common as the sequences red black and black red. If, for greater security, he decides to bet on only one red in three ventures, again he is not, as he fancies, betting on an average, but he is betting on black black being followed by red, while we know, both from logic and experience, that black black black is just as common as black black red. In short, he is betting against red appearing at a particular point in a series, which has nothing to do with the average total of the appearances of red and black, but does depend upon the fallacy that the past affects the future.

The system-monger is apt to derive encouragement from the fact that long runs on a colour are rare, the longest known at Monte Carlo being a series of 28 reds. When once 28 turns have been made, every additional turn creates a fresh series of 29. Add 1 red to a series of 28 reds and it makes a series of 29 reds. Then add a black at the end, and take away a red at the beginning, and you have a series of 28 reds and 1 black. Add another black, and take away another red, and you have a series of 27 reds and 2 blacks, and so on. Now every series of 29 is equally improbable. A series which is all one colour is no more improbable than any other possible arrangement of red and black, such as 15 reds followed by 14 blacks, or any other conceivable series. There are about 3,028 turns at each table every week at Monte Carlo. These make 3,000 different series of 29, each of which was before it appeared as improbable as 29 reds. What, then, can be interesting in the fact that 29 reds have never appeared at Monte Carlo, when we know that equally improbable results do actually occur every week, every day, even every hour?

For those who pin their faith upon the improbability of any particular result, such as 29 reds in succession, perhaps the following calculation may be of interest. Since the inauguration of the gambling establishment at Monte Carlo about 25,000,000 turns of wheel and ball have been made there. The odds against the first 20,000,000 of the results which have already been obtained are so great as to run into six million figures. The Editor has refused me the space required to state the actual figures. In 25,000,000 turns, there are 5,000,001 distinct series of 20,000,000, so that Monte Carlo has already produced 5,000,001 results, the odds against each of which run into six million figures, and would cover, if stated, more than 2,000 pages of the 'Badminton Magazine.' The fact that 29 reds in succession have not yet appeared is utterly unworthy of attention when we know that results which are unthinkably more unlikely have already made their appearance more than 5,000,000 times.

The errors which are made in this matter arise from a confusion of series with units. If a gambler wishes to bet against a long series ci reds, he can only do so by betting on black from the beginning, and doubling his stake after each loss. This would be an infallible system if his wealth were unlimited and the bank allowed unlimited stakes. But the bank does not allow the gambler who begins with the lowest stake to double it

NO. XVII. VOL. III.

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