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unt of which they are in reality defrauded at each venture is easily calculated. Suppose the speculator to venture 1l. Now the actual value of one chance in eighteen of any prize is one-eighteenth of that prize, which in this case should therefore be 18/. If, then, the prize really played for has but fifteen-eighteenths of its true value, or is in this case 15/., the value of a single chance amounts only to one-eighteenth of 15/., or to 16s. Sd. Thus at each venture of 11. the speculator is cheated out of 3s. 4d., or one-sixth of his stake.
This, however, is a mere trifle. In the old-fashioned English system of lotteries, the purchaser of a 10/. ticket often paid more than 20/., so that he was defrauded by more than half his stake; and though less than half the robbery went into the hands of the contractor who actually sold the ticket, the rest of the robbery went to the State.
In other ventures, by the Geneva system, the
old-fashioned English system of robbery was far surpassed.
Instead of naming one number for a drawing (in which five numbers are taken) the speculator may say in what position among the five his number is to come. If he is successful, he receives seventy times his stake. This is, in effect, exactly the same as though but one number was drawn. The speculator has only one chance out of ninety instead of one chance out of five. He ought then, in strict justice, to receive ninety times his stake, if he wins. Supposing his venture 1/., the prize for success should be 90/. By reducing it to 70/. the lottery-keeper reduces the real value of the ticket from 11. to one-nineteenth part of 701., or to 15s. 6 2/3d., defrauding the speculator of two-ninths of his stake. Such a venture as this is called a determinate drawing.
The next venture allowed in the Geneva system is called simple ambe. Two numbers are chosen. If both these appear among the five drawn, the prize is 270 times the stake. Now among the 90 numbers the player can select two, in 8,010 different ways; for he can first take any one of the 90 numbers, and then he can take for his second number any one of the 89 numbers left; that is, he may make 90 different first selections, each leaving him a choice of 89 different second selections; so that there are 90 times 89 (or 8,010) possible selections in all. But in any set of five numbers there are, treating them in the same way, only 20 (or 5 times 4) different arrangements of two numbers. So that out of 8,010 possible selections only 20 appear in each
drawing of five numbers. The speculator's chance then is only 20 in 8,010 or 2 in 801; and he ought, if he wins, to have for prize his stake increased in the ratio of 801 to 2, or 400 1/2 times. Instead of this it is increased only 270 times. At each venture he receives in return for his stake a chance worth less than his stake, in the same degree that 270 is less than 400 1/2; he is, in fact, defrauded of nearly one-third the value of his stake.
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