Now, if the playing of public games of hazard are on the decline from the interference of the State on moral grounds, the question arises: are there any considerations applying to Stock Exchange gambling, which, as a game, raises it above other games of chance, and entitles it to special privileges? Does the outside haphazard speculator stand a better chance as against the Stock Exchange, than a player at _Rouge et noir_ against the bank? The answer must be No. Exactly the same considerations apply to commercial speculations as to other games of chance in which no absolute certainty exists. Mathematicians lay it down as a law, that if any possible event which cannot frequently occur in a game of chance, but which is, nevertheless, a part of the nature of the game, if a bet or stake be made upon the recurrence of that event in a proportion to some large gain which it is agreed that event shall secure, then prudence demands that the game shall be often played; and if this be impossible it shall not be played at all. Here we come to the crux of the whole question of Stock Exchange speculation. Unless a speculator, handicapped as we shall show he is to start with, has enough means to enable him to hold out for the arrival of the event, the occurrence of which is absolutely necessary to his keeping above water, he should not speculate at all.[7] What is the one event constituting the benefit for which the speculator operates? it will be asked. The answer is, the greatest fluctuation in the direction favorable to him which may be caused by any one of the many influences that may spring into action at any time. This is part of the mystery which allures people on. If you tell persons who are throwing a die that the six will turn up once in six times in the long run, they can form some estimate of their chance of winning. But until a Stock Exchange speculator has been roughly undeceived, his understanding gets entangled so that what he sees clearly only at first, is what is in his favour, because his first interest is to discover that. What is against him, he disregards until he has discovered it has undermined him, and all goes together. In cases where the public play against a bank, it is so managed that the bank has a better chance than the players. It is so managed that a considerable succession of losses can be sustained against the good luck of any comer. One side always secures to itself the benefits of _the long run_. The haphazard speculator stands at the same disadvantage as the player against the bank. His position is always relatively inferior. When the balance is nothing, as worked out by the following rule as stated by De Morgan, then the play is equal:—“_Multiply each gain or loss by the probability of the event on which it depends; compare the total result of the gains with that of the losses: the balance is the average required, and is known by the name of the mathematical expectation._”