others, and that therefore any particular gambler can only be cautioned beforehand that his conduct is not to be recommended, by appealing to some such suppositions as those already mentioned in a former section.
§ 14. As an additional justification of this view the reader may observe that the state of things in the last example is one which, expressed in somewhat different language and with a slight alteration of circumstances, is being incessantly carried on upon a gigantic scale upon every side of us. Call it the competition of merchants and traders in a commercial country, and the general results are familiar enough. It is true that in so far as skill comes into the question, they are not properly gamblers; but in so far as chance and risk do, they may be fairly so termed, and in many branches of business this must necessarily be the case to a very considerable extent. Whenever business is carried on in a reckless way, the comparison is on general grounds fair enough. In each case alike we find some retiring ruined, and some making their fortunes; and in each case alike also the chances, cœteris paribus, lie with those who have the largest fortunes. Every one is, in a sense, struggling against the collective commercial world, but since each of his competitors is doing the same, we clearly could not caution any of them (except indeed the poorer ones) that their efforts must finally end in disadvantage.
§ 15. If we wish to see this result displayed in its most decisive form we may find a good analogy in a very different class of events, viz.[ TN: space] in the fate of surnames. We are all gamblers in this respect, and the game is carried out to the last farthing with a rigour unknown at Newmarket or Monte Carlo. In its complete treatment the subject is a very intricate one,[8] but a simple example will serve to display the general tendency. Suppose a colony comprising 1000 couples of different surnames, and suppose that each of these has four children who grow up to marry. Approximately, one in 16 of these families will consist of girls only; and therefore, under ordinary conventions, about 62 of the names will have disappeared for ever after the next generation. Four again out of 16 will have but one boy, each of whom will of course be in the same position as his father, viz.[ TN: space] the sole representative of his name. Accordingly in the next generation one in 16 of these names will again drop out, and so the process continues. The number which disappears in each successive generation becomes smaller, as the stability of the survivors becomes greater owing to their larger numbers. But there is no check to the process.
§ 16. The analogy here is a very close one, the names which thus disappear corresponding to the gamblers who retire ruined and those which increase in number corresponding to the lucky winners. The ultimate goal in each case alike,—of course an exceedingly remote one,—is the exclusive survival of one at the expense of all the others. That one surname does thus drop out after another must have struck every one who has made any enquiry into family
genealogy, and various fanciful accounts have been given by those unfamiliar with the theory of probability. What is often apt to be overlooked is the extreme slightness of what may be termed the “turn of the tables” in favour of the survival at each generation. In the above numerical example we have made an extravagantly favourable supposition, by assuming that the population doubles at every generation. In an old and thickly populated country where the numbers increase very slowly, we should be much nearer the mark in assuming that the average effective family,—that is, the average number of children who live to marry,—was only two. In this case every family which was represented at any time by but a single male would have but three chances in four of surviving extinction, and of course the process of thinning out would be a more rapid one.