|
r a very long time, his gains and losses will eventually be very nearly equal; assuming always, of course, that he is not swindled-which, as we are dealing with gambling men, is perhaps a sufficiently bold assumption. Yet it by no means follows that, if he starts with considerable losses, he will ever recover the sum he has thus had to part with, or that his losses may not be considerably increased. This sounds like a paradox; but in reality
the real paradox lies in the opposite view.
This may be readily shown.
The idea to be controverted is this: that if a gambler plays long enough there must come a time when his gains and his losses are exactly balanced. Of course, if this were true, it would be a very strong argument against gambling; for what but loss of time can be the result of following a course which must inevitably lead you, if you go on long enough, to the place from which you started ? But it is not true. If it were true, of course it involves the inference that, no matter when you enter on a course of gambling, you are bound after a certain time to find yourself where you were at that beginning. It follows that if (which is certainly possible) you lose considerably in the first few weeks or months of your gambling career, then, if you only play long enough you must inevitably find yourself as great a loser, on the whole, as you were when you were thus in arrears through gambling losses; for your play may be quite as properly considered to have begun when those losses had just been incurred, as to
have begun at any other time. Hence this idea that, in the long run, the luck must run even, involves the conclusion that, if you are a loser or a gainer in the beginning of your play, you must at some time or other be equally a gainer or loser. This is manifestly inconsistent with the idea that long-continued play will inevitably leave you neither a loser nor a gainer. If, starting from a certain point when you are a thousand pounds in arrears, you are certain some time or other, if you only play long enough, to have gained back that thousand pounds, it is obvious that you are equally certain some time or other (from that same starting-point) to be yet another thousand pounds in arrears. For there is no line of argument to prove you must regain it, which will not equally prove that some time or other you must be a loser by that same amount, over and above what you had already lost when beginning the games which were to put you right. If, then, you are to come straight, you must be able certainly to recover two thousand pounds, and by parity of reasoning four thousand, and again twice that; and so on ad infinitum: which is manifestly absurd.
|
