Captain Weihe of Hamburg, of the German Marine Artillery, has published in German and Italian a brochure, entitled, in the former language, Das Falschspiel in Monte Carlo, in which he brings a charge of fraud against the company, based on his observation during three seasons of steady watching the play. Now the chances of the ball entering a given pocket are calculable. According to him, the number of times, say in a thousand, in which, by the law of chances, the ball ought to enter a given number is calculable, here, however, it does not obey the law of chances.

Further, he says that he noticed that wealthy players were encouraged to proceed, by winning stake after stake, and then, all at once, luck would declare against them. Why, he wonders, should such men be lucky at first and only unlucky afterwards?

Then, he asserts that the agents of the company occasionally encourage a timorous player by advice, given with all secrecy, to stake on a certain number, and that then, by some remarkable coincidence, this number will win. These observations, he says, led him to the conclusion that there existed some method whereby the ball could be directed to go where the croupiers desired that it should go. Then he asserts that he assured himself that a piece of steel was inserted in a certain number of the balls, and that these loaded balls could be drawn into any pocket desired, by the chef de partie, by means of an electro magnet manipulated by himself. He further asserts that by close observation during three seasons, he was able, by watching the fingers of the chef, to predicate with something approaching to certainty into which number the ball would run.

The pamphlet in question is not sold at Nice or Mentone, and it need not be said is not allowed to pass over the frontier of the principality of Monaco, but it can be procured at Bordighera.

However, it appears very improbable that the bank would run such a risk. It is true that detection of roguery is not easy, where the tables are in a principality under an absolute monarch, and where police and every authority are interested in the continuance of the gambling. There is, however, the risk of some croupier “giving away the show”; and there is also the risk of detection. But—is cheating necessary? Is it worth its salt? Let us look closer into the acknowledged system. While playing on the even chances gives 1·35 per cent. in favour of the bank, playing on any other gives the bank 2·70; and as many fools play on those chances that favour the bank most highly, it is probably safe to assume that the odds in favour of the bank will average 1·66 on all the tables, both trente-et-quarante and roulette. If individuals playing would take in all the money they could afford to lose, divide this into so many maximums (if one did not suffice) and stake the full maximum on each chance, and then retire, whether winners or losers, they would then have given the bank the least possible advantage, as they would have subjected themselves to the chances of the zero appearing the least possible number of times. As, however, almost every player wishes to have as long a run for his money as possible, almost all players, whether playing by a so-called system or not, divide their stakes, whether made on an increasing or on a decreasing scale, or haphazard, into a number of comparatively small stakes, so as to stay in the game as long as possible, with the result that the bank’s percentage is constantly working against them. The thinner they spread out their money, and the longer they stay in the game, the greater are the chances of their losing their money.

If you go into the stock-market and buy the first stock your eye happens to catch on the list, you at least stand an even chance of its going up or down, while your brokerage and stamp charges will not amount to the 1·66 per cent. charged as brokerage by the Casino; whereas in the stock market the action will be comparatively slow, at Monte Carlo the brokerage charge is approximately 1·66 per minute. If fifty coups are played per hour, it means that as brokerage the bank each hour absorbs 83 per cent. of all the money staked for one coup, while each day the bank takes for its commission for permitting you to play there, about ten times the average amount staked on the table at any one time. As Sir Hiram Maxim says, the martingale is the least defective of all the systems. Were there no limit and no zero, this system of 1, 2, 4, 8, 16, 32, etc. must infallibly win, as, whenever a gain is made, no matter how many previous losses there have been, it lands the player a winner of one unit. The defect, however, is that, starting with the minimum stake, the maximum is reached at the eleventh doubling, and a run of eleven is of by no means an infrequent occurrence. Against this the bank protects itself in its most vulnerable place; even then, were its limits removed, yet it would be steadily levying its 1·66 commission.

It is accordingly not necessary for the company to have recourse to underhand work as charged by Captain Weihe; the income of £1,245,008 realised without trickery, on an average stake per table would be 611·55 fr. Any one who has been at Monte Carlo will admit that this is probably very much below the average amount of money on the table at each spin of the wheel; and with such an income, where arises the occasion for illicitly supplementing it? The following is a table of stakes needed to realise the known profits of the company:

611·55 fr., average stake each of 14 tablesBank percentage,10.15 fr.
8,561·70 fr. total stakes at 14 tables, 50 coups per hour”———”142·69 fr.
428,085·00 fr., average stakes each 12 hours the Casino is open”———”7,134·75 fr.
5,137,020·00 fr., total daily stakes, 365 days a year Casino is open”———”85,617·00 fr.
1,875,012,300·00 fr., total yearly stakes”———”31,250,205·00 fr.
£75,000,492 sterling equivalent”———”£1,245,008

Thus enabling the bank on average stakes of 611·55 francs to realise £1,245,008. But it must be remembered that it is only during the winter season that considerable play takes place at Monte Carlo. Also that before profits are declared the prince has to pocket his share, all the officials have to be paid, the police, the lighting, the gardens have to be kept going, and the scores of unacknowledged dependents on the Casino have to receive enough to maintain them. Every season a little book appears, advocating an infallible system, and some of these cost twenty-five francs. Of course, every system is based on the assumption that there is no trickery. But if there be trickery, not one of these systems is worth the cost of the book that advocates it.