The Hazards of Gambling

A recent item on the ACM RISKS Forum by Martin Ward argues that all gambling necessarily involves the destruction of value. This is a convincing, purely economic argument, even leaving aside the moral argument, that gambling is essentially theft.

Martin quotes chapter 14 of John Nevil Maskelyne's 1894 book Sharps and Flats:

It must be obvious to any one who will take the trouble to think over the matter, that chances which are fair and equal are a question of proportion rather than of actual amounts and odds. At first sight, however, it would appear that if a man stands an equal chance of winning or losing a certain amount, nothing fairer could possibly be imagined, from whatever point of view one may regard it. I venture to say, nevertheless, that this is not so.

Suppose for the moment that you are a poor man, and that you meet a rich acquaintance who insists upon your spending the day with him, and having what the Americans call 'a large time.' At the end of the day he says to you, 'I will toss you whether you or I pay this day's expenses.' Such a proposition is by no means uncommon, and suppose you win, what is the loss to him? Comparatively nothing. He may never miss the amount he has to pay; but if you lose, your day's outing may have to be purchased by many weeks of inconvenience.

A bet of a hundred pounds is a mere bagatelle to a rich man, but it may be everything to a poor one. In the one case the loss entails no inconvenience, in the other it means absolute ruin. It must be granted, then, in matters of this kind, that proportion is the chief factor, not the actual figures. If you are with me so far, you are already a step nearer to my way of thinking.

Let us proceed a step further, and see how it is that a bet is necessarily unfair to both parties. The simple fact is that no two men can make a wager, however seemingly fair, or however obviously unfair, without at once reducing the actual value to them of their joint possessions.

This can be proved to a demonstration. We will take a case in which the chances of winning are exactly equal, both in amount and in proportion to the wealth of two bettors. Suppose that your possessions are precisely equal in amount to those of a friend, and that your circumstances are similar in every respect. There can be, then, no disparity arising from the fact of a bet being made between you, where the chances of winning or losing a certain amount are the same to each.

To present the problem in its simplest form, we will say that you each stake one-half of your possessions upon the turn of a coin. If it turns up head you win, if it falls 'tail up' your friend wins. Nothing could possibly be fairer than this from a gambler's point of view. You have each an equal chance of winning, you both stake an equal amount, you both stand to lose as much as you can win, and, above all, the amount staked bears the same value, proportionately, to the wealth of each person. One cannot imagine a bet being made under fairer conditions, yet how does it work out in actual fact? You may smile when you read the words, but you both stand to lose more than you can possibly win! You doubt it! Well, we shall see if it cannot be made clear to you.

Suppose the turn of the coin is against you, and therefore you lose half your property; what is the result? To-morrow you will say, 'What a fool I was to bet! I was 100% better off yesterday than I am to-day.' That is precisely the state of the case; you were exactly 100% better off. Now, the most feeble intellect will at once perceive that 100% can only be balanced by 100%. If you stood a chance of being that much better off yesterday than you are to-day, to make the chances equal you should have had an equal probability of being 100% better off to-day than you were yesterday. That is obvious upon the face of it, since we agree that these questions are, beyond dispute, matters of proportion, and not of actual amounts.

Then we will suppose you win the toss, and thus acquire half your friend's property; what happens then? When the morrow arrives you can only say, 'I am 50% better off to-day than I was yesterday.' That is just it. If you lose, your losses have amounted to as much as you still possess, whilst, if you win, your gains amount only to one-third of what you possess.

The plain facts of the case, then, are simply that the moment you and your friend have made the bet referred to, you have considerably reduced the value of your joint possessions. Not in actual amount, it is true, but in actual fact, nevertheless; for whichever way the bet may go, the loss sustained by one represents a future deprivation to that one far greater than the future proportional advantage gained by the other. The mere fact of one having gained precisely as much as the other has lost does not affect the ultimate result in the least. The inconvenience arising from any loss is always greater than the convenience resulting from an equal gain.

Maskelyne also covers the moral argument:

The absolute immorality of gambling — the desire to obtain money to which one has no right — in any form is beyond dispute; and the sooner this fact is generally recognised, the better it will be for the world at large. There are some, of course, in whom the passion is ingrained, and from whose natures it can never be wholly eradicated. But everyone should clearly understand that the vice is as reprehensible in proportion to its magnitude as that, for instance, of either lying or stealing.