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These were the favorite ventures; and that they were made very often is proved to everyone acquainted with the laws of chance by the circumstance that they not infrequently proved successful. For every time such a venture as a simple quaterne was won, it must have been lost some half a million times.
It appears that in France the Geneva system was adopted without any of the limitations we have mentioned, and with some additional chances for those who like fanciful ventures. Professor De Morgan, in his ' Budget of Paradoxes' says :--' In the French lottery five numbers out of ninety were drawn at a time: any person, in any part of the country, might stake any sum upon any event he pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a quine determine, if he chose, which is betting on five given numbers in a given order.' The chance of a successful guess, in this last case, is I in 5,274,7727160. Yet if every grown person in Europe made one guess a day,
venturing a penny on the guess, and receiving the just prize, or say 4,800,000,000 times his stake, on winning, it would be practically certain that in less than a year some one would win 20,000,000/. for a penny! It would be equally certain that though this were repeated dozens of times, the lottery-keepers would gain by the arrangement, even at the rate above stated. Nay, the oftener they had to pay 20,000,000/. for a penny the greater their gains would be. As the actual prize in such a case would be 10 million instead of merely 5,275 million times the stake, their real gains, if they had to pay such prizes often, would be enormous. For, in the long run, every prize of half a million pounds for a shilling stake would represent a clear profit of 250 million pounds. The successful ventures would be only I in about 5,000 millions of unsuccessful ones, while paid for only at the rate of 10 million stakes.
No instances are on record of a quine determine being won, but a simple quine, the odds against which, be it remembered, are nearly 44 millions to 1, has been won; and simple quaternes, against which the odds are more than half a million to 1, have often been won. In July 1821 a strange circumstance occurred. A gambler had selected the five numbers 8, 13, 16, 46, and 64, and for the same drawing another had selected the four numbers 8, 16, 46, and 64. The numbers actually drawn were
8 46 16 64 13
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