Suppose, then, that there were a precisely equal chance of success on the one hand and failure on the other in any enterprise, failure involving a complete loss of all the capital invested. Suppose, further, 6 per cent to be at the time a fair return on a perfectly secure investment. What would be the return which must be expected from the risky enterprise, in the event of its succeeding, before it will be undertaken? The reader may be tempted to answer, 12 per cent. But 12 per cent would not suffice. An equal chance of 12 per cent or nothing, as compared with a certainty of 6 per cent, does not mean that the risk in the former case is paid for to the tune of 6 per cent. It means that it is not paid for at all. In each case what a mathematician would call the _expectation_ is a return of 6 per cent. The odds are evenly balanced; in the long run, over a large number of cases, if the law of averages works as we assume it does, you would get just as much from the one type of investment as the other. Now, risky enterprises will not, as a rule, be undertaken on terms like these; investors and business men will not take risks with the odds precisely equal; they must have them, or believe that they have them, in their favor. §3. _Monte Carlo and Insurance_. To assert this is not to ignore the strength of the appeal which the gambling instinct makes to many, if not to most of us. The taste for gambling is, indeed, so deep and widespread that it would be foolish to leave it out of account in this connection. It is clear enough that at places like Monte Carlo people are prepared to have the odds unmistakably against them, apparently for the sheer pleasure and exhilaration of taking risks. Moreover, though for most people play at Monte Carlo represents a mere holiday indulgence, it would be unsafe to assume that what appeals to them there will not also appeal to them in their business affairs. But what exactly is the secret of the charm of Monte Carlo? It is the great attractive force of a small chance of a large gain, as compared with the deterrent force of a large chance of a small loss. People will readily pay $5 for one chance in a hundred of making no more, perhaps, than $400 or $450. And it is very likely that this holds good in the world of business. If, for example, we were to suppose that the promoters of a new enterprise were confronted with one chance in fifty of a profit of 50 per cent per annum on their capital, as against forty-nine chances of a profit of 5 per cent, this might well prove a more attractive prospect than a certain return of 6 per cent, although the strict _expectation_ of profit would be smaller in the former case. But the risks of business enterprise are not often of this type. They conform more usually to the opposite type of a large chance of a relatively small gain, balanced by a small chance of serious loss or entire failure. Now for almost everyone the possibility of a great