%images;]> lchtml-006202 Science of betting. ...: a machine readable transcription. Lewis Carroll Scrapbook, Library of Congress Selected and converted. American Memory, Library of Congress.

Washington, DC, 2003.

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 2004/05/18
0001

The Science of Betting.—Mr. Charles Dodgson, Mathematical Lecturer at Christ Church, Oxford, writes to the Pall-Mall Gazette that the rule of betting may be stated thus:—“Write all the possible events in a column, placing opposite to each the odds offered against it: this will give two columns of figures. For the third column add together the odds in each case, and find the least common multiple of all the numbers in this column. For the fourth column divide this least common multiple by the several numbers in the third column. For the fifth and sixth columns multiply the original odds by the several numbers in the fourth column. These odds are to be given or taken, according as the sum total of the sixth column is greater or less than the least common multiple.” The last two columns give the relative amounts to be invested in each bet:—

1 2 3 4 5 6 A 2 to 3 5 12 24 to 36 B 4 to 1 5 12 48 to 12 C 5 to 1 6 10 50 to 10 D 9 to 1 10 6 54 to 6 The Field 14 to 1 15 4 56 to 4

An example will make this clear:—Suppose that in a race about to be run there are four horses in the betting, the odds being 3 to 2 on the favourite, which is equivalent to 2 to 3 against. The least common multiple of the third column is 60, and the sum total of the last 68, and as this is greater than 60, the odds in this case are all to be given in the relative amounts given in the fifth and six columns. Suppose, for example, that I multiply these columns by 10, and make the bets in pounds—that is, I take 360l. to 240l. on A, I give 480l. to 120l. against B, and so on. Now, suppose C to win the race; in this case I lose 500l., and win 360l. + 120l. + 60l. + 40l. = 580l. It will be found on trial that I win the same sum, 80l., in each of the five events. If all betting men tried to work this system, they would either be all offering odds or all taking odds on each event, and so no bets could be made. But the fact that this system of winning is ever possible arises from the odds being unevenly adjusted, so that they do not represent the real chances of the several events. Supposing this system to be applied only in cases where the odds were evenly adjusted, the sum total of the sixth column would always be equal to the least common multiple, and thus, whether the odds were given or taken, the concluding entry in every betting-book would be ‘Gain = Loss = Nil—a most desirable result.”