To James Logan
MS not found; reprinted from Sparks, Works, VII, 31–3.
Philadelphia, 27 January, 1748
I have not yet found the book,6 but suppose I shall to-morrow. The post goes out to-day, which allows me no time to look for it. We have a particular account from Boston of the guns there. They are in all thirty-nine, Spanish make and new; fifteen of them are twenty-eight pounders, and twenty-four are fourteen pounders. We offer by this post £1500, this currency, for them all, and suppose we shall get them.7
The insurers, in consideration of the premium of twenty per cent, engage thus; that, if the prizes arising against the tickets insured do not, one with another, make in the whole a sum equal to the first cost of the tickets, they will make up the deficiency. They now think it a disadvantageous agreement, and have left off insuring; for though they would gain, as you observe, £1000, if they insured the whole at that rate, in one lot, yet it will not be so when they insure a number of separate lots, as ten, twenty, or one hundred tickets in a lot; because the prizes, falling in one lot, do not help to make up the deficiencies in another. The person, that insured your one hundred and twenty-five, did the next day give the whole premium to another with six and a quarter per cent more, to be reinsured two thirds of them. I have not insured for anybody; so I shall neither lose nor gain that way. I will send the policy, that you may see it, with the book.8 I am, Sir, &c.
6. Probably Maittaire’s Stephanorum Historia. See above, p. 219 n.
7. The Sum offered was subscribed by the merchants. See above, p. 184.
8. Purchasers of lottery tickets sometimes insured their investments against loss. The premium on a single ticket or even a small number of tickets was prohibitively high. Sometimes, therefore, several subscribers, as the members of a fire company, forming a “club,” would insure their tickets, thus reducing their losses, but also their prizes.
Philip G. Nordell, Ambler, Pa., in a letter to the editors, analyzed the lottery in relation to Logan’s insurance of his tickets: the scheme consisted of 10,000 tickets at £2 each, or £20,000. From this sum £3000 was to be deducted for the use of the beneficiary, i.e., the Association and related defense needs, leaving £17,000 to be distributed in 2842 plus 2, or 2844 prizes.
Suppose that one adventurer bought all the tickets (£20,000) and paid a 20 per cent premium on them (£4000). He would then win all the £17,000. The insurer would have to pay the deficiency of £3000, leaving him a profit of £1000, as BF points out.
But suppose that each ticket was bought by a different person. Then, since there were 2844 prizes (two of which in two instances might be won by the same person), and since the lowest prize was greater than the cost of a ticket, the insurer would not have to pay anything to the holders of those tickets. But he would have to pay £2 to each of the adventurers who drew blanks, that is, 7156 persons, or £14,312. After deducting the 20 per cent premium paid him (£4000), the insurer would take a loss of £10,312.
Suppose that the 10,000 tickets were sold in 1000 lots of ten each and that all of the prizes fell to 700 of these 1000 lots. Even if the prize or prizes in each case reached the full cost of the lot, the insurer would have to pay the full cost of the 3000 tickets in the remaining 300 lots, or £6000. Since he received only £4000 in premiums, his loss would be £2000.
Logan’s 125 tickets cost him £250, but if his insurance premium was 20 per cent, he could not lose more than £50. Thus he took 125 tickets off the hands of the managers and at the same time limited the cost to himself to £50.