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d by the chance of such enormous gains; and it was thought that the gains of Government would be proportionately heavy. All that was necessary was that the just value of a chance in this lottery should be ascertained by mathematicians, and the price properly raised.
Mathematicians very readily solved the problem, though one or two of the most distinguished (D'Alembert, for instance) rejected the solution as incomprehensible and paradoxical. Let the reader who takes interest enough in such matters pause .for a moment here to inquire what would be a natural and probable value for a chance in the suggested lottery. Few, we believe, would give 10/. for a chance. No one, we are sure--not even one who thoroughly recognized the validity of the mathematical solution of the problem-would offer 100/. Yet the just value of a chance is greater than 10/., greater than 100/., greater than any sum which can be named. A Government, indeed, which would offer to sell these chances at say 50/. would most probably gain, even if many accepted the risk and bought chances--which would be very unlikely, however. The fewer bought chances the greater would be the Government's chance of gain, or rather their chance of escaping loss. But this, of course, is precisely the contrary to what is required in a lottery system. What is wanted is that many should be encouraged to buy chances, and that the mere chances are bought the
greater should be the security of those keeping the lottery. In the Petersburg plan, a high and practically prohibitory price must first be set on each chance, and even then the lottery-keepers could only escape loss by restricting the number of purchases. The scheme was therefore abandoned.
The result of the mathematical inquiry seems on the face of it absurd. It seems altogether monstrous, as De Morgan admits, to say that an infinite amount of money should in reality be given for each chance, to cover its true mathematical value. And to all intents and purposes any very great value would far exceed the probable average value of any possible number of ventures. If a million million ventures were made, first and last, 50/. per venture would probably bring in several millions of millions of pounds clear profit to the lottery-keepers; while 80/. per venture would as probably involve them in correspondingly heavy losses: 40/. per venture would probably bring them safe, though with- out any great percentage of profit. If a thousand million ventures were made, 30l. per venture would probably make the lottery safe, while 35l. would bring great gain in all probability, and 25l. would as probably involve serious loss. If all the human beings who have ever lived on this earth, during every day in their lives had been taking chances in such a lottery, the average price of all the sums gained would be quite unlikely to approach 100l. Yet still the mathematical proposition is sound, that if the number of speculators in the
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