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e the wrath of losers (who would form a large part of the community if lottery operations were successful) might be roused in a dangerous way, unless it could be shown that the managers of public lotteries ran some chance, though it might be only a small chance, of losing, and even some chance of ruin as absolute as that which might befall individual gamblers.
It was to meet such difficulties as these that lottery systems like that sometimes called the Geneva system were invented. This system I propose now to describe, as illustrating these more speculative ventures, showing in particular how the buyers of chances were defrauded in the favorite methods of venturing.
In the Geneva lottery there are ninety numbers. At each drawing five are taken. The simplest venture is made on a single number. A sum is hazarded on a named number, and if this number is one of the five drawn, the speculator receives fifteen times the value of his stake. Such a venture is called a simple drawing. It is easy to see that in the long run the lottery-keeper must gain by this system. The chance that the number selected out of ninety will appear among five numbers drawn, is the same that a selected number out of eighteen would appear at a single drawing. It is one chance in eighteen. Now if a person bought a single ticket out of eighteen, each costing (say) 1l., his fair prize if he drew the winning ticket should be 18/. This is what he would have to pay to buy up all the eighteen tickets (so making sure of the prize). The position of the speculator who buys one number at Il. in the Geneva lottery, is precisely that of a purchaser of such a ticket, only that, instead of a prize being 181. if he wins, it is only 15/. The lottery-keeper's position on a single venture is not precisely that of one who should have sold eighteen tickets at 11. each, for a lottery having one prize only; for the latter would be certain to gain money if the prize were any sum short of 18/., whereas the Geneva lottery-keeper will lose on a single venture, supposing the winning number is drawn, though the prize is 15/. instead of 18/. But in the long run the Geneva lottery-keeper is certain to win at these odds. He is in the position of a man who continually wagers odds of 14 to I against the occurrence of an event the
real odds against which are 17 to 1. Or his position may be compared to that of a player who takes seventeen chances out of eighteen at (say) their just value, 1/. each or 17l. in all, his opponent taking the remaining chance at its value, 1l., but instead of the total stakes, 18/., being left in the pool, the purchaser of the larger number abstracts 3/. from the pool at each venture.
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