A wager is fairly laid when the odds are proportional to the proba bilities of the event happening or failing. Thus if it be four to one against tho happening of an event, the better who beta that it will not happen should offer four to one. In the long run such an event will fail four times where it happens once, and the better will receive a pound four times for every occasion on which he pays four pounds once. But suppose a person should continually offer only three to oue upon a contingency on which it is four to one he wins. In the long run lie will, upon every five bets, receive one pound four times, and pay three pounds once : he will therefore win one pound on every five bets. Algebraically thus :—let the odds for his winning be a to b, while these which he offers are m to n; in a + b trials, one set with another, he will win n pounds a times, or £na, while he will lose re pounds b times, or £mb. If na equals mb, the wager is fair on both sides; if nu be greater than mb, it is unduly favourable to the better ; if na be less than mb, it is unduly against him.
There are many cases in which doubt may arise as to whether a wager is fair, and also as to how it is to be interpreted. With respect to the latter it is or ought to be clear, that if both parties understood the wager in one sense, that one sense is the fair interpretation but that if either of the parties uudcrstood the wager in one certain sense, and the other party knew that he understood it in that sense, no sub sequent attempt at a different interpretation should be admitted ou the part of that other party. We are told that this rule is widely departed from ; and that under cover of adherence to literal significa tion of words, interpretations are permitted which offer inducements to what we must call attempts at fraud. Thus, it is said, that when the better undertook to run across a bridge in an incredibly small time, and had his bet accepted, he was permitted to win by running from one parapet to the other, which was held to be crossing the bridge, in the same manner as going from one footpath to the other is held to be crossing a street. Here it is clear that the party accepting the bet understood that the other was to cross the water upon the bridge, which is the true meaning of going across a bridge; and it is also clear that the better knew he was taken iu that ammo. An adherence to the literal meaning of a wager is, of course, necessary in all cases of doubtful meaning, but there is no language in which the literal meaning of a sentence is always made up of those of the words put together.
A wager is not fair unless the point in doubt be clearly the same to both parties, and unless there be no concealed knowledge in the pos session of either. The latter is included in the former, as an instance will show. John beta Thomas that the ship Hope 18 arrived in dock from Jamaica before the time at which the bet is laid ; his manner implies that he has formed the conclusion from his knowledge of the time at which the Hope was to sail, of the properties of the vessel, of the prevailing weather, ito. : if his manner tell truth, the wager is fair Or Ids manner implies that ho may be in possasaion of particular In formation, that he may have seen the captain, &c. ; it says, " Mind, I do not tell you what my reasons are, all I tell you is the fact : " still the wager is fair. If Thomas dispute, he knows in either case what he disputes, be it the question of the Hope's rate of sailing, or the good ness of John's inference from his particular knowledge. But if John, actually knowing of the If opo's arrival, should lead Thomas into a wager on the probabilities of the ship having arrived, when he that it actually has arrived, the wager is unfair. In all matters o
skill, indeed, the mere offer of the wager is an assertion of skill, am the acceptance of the wager is the denial of this assertion : this i understood, so that there is no occasion for the party who offers th, wager to make any declaration of skill, other than is implied in tin wager itself.
There is one case, and that a common one, in which the immoralit; of the wager is not easy to expose, though it is, we think, aufficientl; certain ; it is where a person, by offering different wagers to differed people, secures himself a certainty of gain, let the event happen whicl way it will. Thus one of three things must happen, A, B, C ; a persoi bets 4 to 4 against A, 5 to 4 against B, 6 to 4 against C, with three different persons; he must win 8, for two of his opponents must lose he cannot pay more than 6, for one only can win; he is therefore, el the most unfavourable supposition, a gainer of 2. As against each o his opponents the wager may be fair : these may not be known to eacl other, and each one may consider that he has the best of the wager Whom then does he injure / If it be admitted that a man has a nigh to lay any bet which he can get taken provided the event betted of be perfectly understood, he can then injure no one, and no exception can be taken to the proceeding. But if it be not allowed that a man has a right to lay any odds, except those which, to the best of hu knowledge and belief, represent the state of the chances, he must that offer a bet which he believes to be unfair, to some one or other of tin preceding persons. By betting 4 to 4 against A, he declares his belie that the chance of A's arrival is d : similarly by betting 5 to 4 against B, he declares his belief that the chance of B'a arrival is a. Cense quently he implies a declaration that his belief of the chance of arrival is— Consequently he ought to lay 17 to 1 against the arrival of C, whereas he lays 3 to 2, or 6 to 4. He is then telling contradictory stories to different people, and is saved from conviction only by the fact of each party not knowing what he has stated to others. If there were a possible mode of fighting in 'which the weapon of each opponent should be armour against those of the rest, we imagine it would not be con. sidered either brave or honest that a man should provoke the combat with several enemies, in such a manner that he should be sure to kill, and sure not to be killed; and we suppose that if wagering be per. knitted at all among men of honour, it is under the idea that be whc makes another risk his money also risks his own.
This possibility of securing certain gain by betting against belief (for against belief it must be) seems to us toabe enough, were there no other reason, to show that a wager is not right, unless the. odds really represent the opinion of the better : for to maintain that such a wager is a fair one, is also to maintain that it is fair to make other', meet risk without sharing it.
It may indeed be asserted that each better has his own book, which lie endeavours to make up in such a way as to win In every event: so that the whole is an admitted trial of skill. But this excuse breaks down when it ie remembered that it is impossible a society of gamblers can make a set of books which will give a balance of gain to all, with out taking in a number of persons who de not belong to the society : and the question is whether the words in italics have not two real meanings.