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£1. The chance of winning £4 is one. not know where the line could be drawn. quarter; so we set down a quarter of £4, The history of the Louisiana lottery shows or yet another £1. So we set down an that any number of idiotic persons would eighth of £8; a sixteenth of £16; and so pay £s for a ticket in a lottery where on continually. We thus have as the there was one prize of £1,048,576 and value of all the prizes put together, any only 1,048,576 tickets. Suppose our gamnumber of sums of £1. But even the bler to risk £i in such a venture as this; non-mathematician will admit that by add. having already risked £i on each of a ing sovereign to sovereign indefinitely series of wagers first and lottery chances you will get a sum larger than any that afterwards, for wagers ranging from £1, may be named.
£2, £,4, £8, and so on to prizes of £1,024, The proof is sound, the conclusion £2,048, etc., onwards to £524,288 and open to exception. The trouble is that £1,048,576. Such a gambler, if he dethe chances of the highest prizes are too pones his stakes, pays down in all £21 (it remote to be worth considering, in this will be found), and before the decision of world at any rate. Theoretically the any of the ventures, he is in the position chances of winning the prize resulting of a man who should have paid £21 for the from twenty successive heads, or more right to venture in the imagined lottery, than a million pounds, is one in rather wherein the tossing of a coin so long as more than a million, and therefore is fairly heads appeared' determined the prize. represented by £1. Yet who but an idiot Whatever difference there is, is of course would part with a sovereign for so minute in favor of the latter, who, besides correa chance of winning a sum which, when sponding chances of winning £1, or £2, or he had won it, would be more than he £4, or the rest, up to £1,048,576, has also would know what to do with ?
chances of winning £2,097,152 or £4,194Pause we here a moment, however. 304, or other monstrous sums, if only Perhaps this folly, which seems as thus heads run persistently enough. viewed so manifest, may not be quite so It may be said that there is a difference uncommon, or the foolish may be much between the two cases. One man has more uncommon, than the tone of that staked £21 for a number of prizes; and last question would seem to imply. there is nothing to prevent bis gaining all
Consider a typical gambling man, not of them. The other, who has equally necessarily professional. Let him be of- staked £21, can gain but one prize. It fered a wager of £l on some matter where might be answered that this is exactly the chances are even. Let him be offered balanced by the circumstance, that while a wager of two to one in pounds where the former may lose all he has staked, the the odds are really two to one ; a wager of latter must get back £1, and may get much four to one in pounds where the odds are more. But it may be better to devise a really four to one; a wager of eight to case more obviously identical, leaving the one (always in pounds) where the odds are one just considered to point our moral eight to one; and so on. Such wagers as the folly of gambling, even on „so-called these he would of course take. He would fair terms. be only too glad to take them when they Suppose, then, a lottery in which are rose to higher odds. But beyond a certain 2,097,151 tickets, each priced at £21 ; let point we may conveniently substitute the there be no blanks, one prize of £1,048,576, purchase of lottery tickets. Our gambler two of £524,288, four of £262,144, and would most willingly pay £1 for a ticket so on, till we come down to 524,288 prizes in a lottery where there was one prize of of £2 each, and 1,048,576 prizes of £1, £1,024, and 1,024 tickets. (So fair a making up the total number of 2,097,151 chance would be a novelty in lotteries.) prizes. In this case, any one who bought Then if he heard of another lottery where a ticket would be in precisely the position there were 2,048 tickets, and where one of one who paid £21 for a chance in the prize of £2,048 invited the venturesome, coin-tossing lottery, except that the latter he would assuredly jump at that. We do would have a chance of even higher prizes
than £1,048,576. The buyer of the ticket | because it seems so obviously certain in would be in a much better position than its action that no gaming“ bank" or gammen who, in former times, paid sums as bling opponent would allow it to be conlarge as £21 for chances in national lot. tinued for any length of time. It is the teries, or who pay such sums now for system of continued doubling. You stake chances in foreign swindles of the same & 1 at the rouge et noir table and lose. kind (we had nearly written “character,” | You then stake £2. If you lose yet once but there is an entire want of character in more, you stake 24; then (if you lose) £8, all such transactions). One who has thus £16, and so on. Whenever you win ventured is apt to consider himself rather and you cannot lose forever, you win clever than otherwise, especially if some enough to cover a!l your previous losses, dream, or other event entirely unconnected and £i over. At each trial you practiwith the lottery, has guided him in the cally make sure of winning £1. Patience, choice of his ticket's number. Yet such then, and you must win any number of a man has taken a venture far less favora- pounds. ble than that of a man (whom he would So far as we know, Hombourg and ridicule as an idiot) who should pay £21 Baden never set their face against this for the chance of a tossed coin coming system, which must have suited them well up heads often enough to bring him a enough. They set a limit, however, to the goodly prize, at the doubling rate above amount of stakes, and that would suffice to described.
kill the system. This may be shown very This case shows how little men appre- simply in any special case. Having in a ciate the real meaning of the large num- former example taken very large numbers, bers named in connection with lottery we will take smaller ones here, noting that chances. The same risk of loss which the principle is the same, let the numbers seems obvious when the question is of be large or small. tossing heads so often as ten times in suc. Suppose the gambler, anxious to make cession, seems trifling when compared more than £ i each time, begins with £10 with the chances against drawing the lucky stakes, and let the bank“ limit” be £640. ticket out of a thousand ; yet the risk in Imagine the gambler's ventures divided the latter case is greater than in the former into sets of sixty-four. Then from what in the same degree that 1,024 is greater Buffon and his three allies did in the way than 1,000.
of coin-tossing (where the chances for No particular harm follows, but rather head or tails are the same as the chances good, when the chance of winning a large for rouge et noir, omitting the bank's prize is mistakenly overlooked in consid- slight extra chances in the refait) we know ering this particular chance problem. The experimentally, apart from mathematical Russian government was foiled in a plan calculation, what the average result in any for getting large sums out of a lottery, by 64 trials will be. There will be 32 cases the recognition of men's unwillingness to favorable for our gambler at the first trial, risk anything like the sum which mathe- 16 at the second, 8 at the third, 4 at the maticians told them ought to be paid for fourth, 2 at the fifth, and i at the sixth, each chance in such a lottery. The prob- with one unfavorable trial; this last may lem has hence been long known to stu- occur anywhere in the series; but give dents of probabilities as the Petersburg our gambler the benefit of the doubt, and problem. But very serious loss has been put the run of six unfavorable tossings sustained because of men's blindness to last. Then the result of that set of 64 the converse truth, that very large sums trials will be to enrich our gambler by may be lost on this method of doubling £320, and £160, and £80, and £40, and stakes at each renewal of a particular 220, and £10. He will be £630 in pocket result.
out of those trials. Unfortunately the If there is one trap which has caught 64th trial will cost him £640. He cannot more gamblers, even of the professional go on doubling, because the bank limit sort, than any other, it is what may be forbids. The nearest thing he can do to called the “ martingale” trap; the belief, the working out of his system is to stake that is to say, in systems by which suc. 4,640 yet again. If he can and does do cess may be secured with absolute cer- this, trusting, perhaps, to what is called tainty, if only the gambler's pocket is long the maturity of the chances” (a most enough to enable him to keep on with his delusive doctrine), he has an equal chance systein against adverse runs of luck. of winning back £,640, or of losing that Among the systems thus devised, there is sum. If he is lucky, it will not be his one, which has only given way to others system that has brought him luck; if he
is unlucky, he exchanges small loss, all | events, and must therefore be utterly that the system fairly worked out would valueless in considering the chances for be apt to entail, for a large one. In any any particular event or series of events. case he gives up a tolerably slow way of Whatever happens, one or other law must parting with his money for a dangerously be justified; but gamblers rejoice at this bold venture.
as evidence in favor of the two laws, inThe system, then, which seems so ob- stead of seeing that it proves both to be viously to ensure slow but eady gain, worthless. Does a gambler who has been really ensures slow but steady loss. If lucky win afresh? then the gamblers this were the worst that could be said around see in the case an illustration of the against it, it would still be enough to " vein of luck.” Does the luck change? deter the gambling moth from this slowly then they proclaim, with equal wisdom, singeing fame. But another gambling their faith in the doctrine of the “maturity folly comes in to make ruin approach with of the chances.” They may not use these much more rapid strides on this line than precise words; on the contrary, their the fair progress of the system would words may be anything but precise; in ensure. To end a loser of only £10 on an one case they may say, "He has the average ron of sixty-four trials, our gam- devil's own luck," and in the other they bler must carefully bank all his gains. may swear lustily because, having backed Gamblers never do this. “Lightly come, his luck, they have lost money. But the lightly go,” is their motto. They even ideas are there all the same. And since fancy that bad luck is sure to follow any every single experience of every gambler attempt at hoarding idly acquired gains. is bound to confirm his belief that luck Hence the loss of £640 in the one un- will either change or continue unchanged, lucky run would probably find our gambler his faith in the fundamental idiocies of with not £20 of the previously won £630 gambling, the “vein of luck” and the to help in meeting it.
“maturity of the chances,” grows conBy diminishing the first stake in this stantly in strength and fervor. and similar cases, the gambler can ensure The belief that in the long run luck a much longer run for his money. But must run even is not quite so obviously he must take a correspondingly increased misleading as either of the two the combinumber of risks. Now Buffon's experi. nation of which it really represents. It is ments show that just as surely as there true, indeed, in a sense; but it is misleadwill, on the average, be one run of 6 unfa ing all the same. It means so much less vorable tossings in 64 trials, there will be than believers in it imagine ! one run of 7 unfavorable tossings in 128 Consider how little it really promises. trials; one run of 8 in 256 trials; and so on. If the gambler when he loses assures So that the gambler secures no escape from himself, on the strength of this law, that eventual disaster by diminishing his stake he must one day recover all he has lost, and increasing the number of trials. More. what an argument he should find in that over, he has to expend more time in get. against gambling! for what earthly use ting his smaller gains — so long as he can there be in continuing a process does get them - and even a gambler must, which, if continued long enough, is bound one would imagine, regard time as of to land you where you began? But the some value.
fatal trouble about this article of the gamThe doctrine of the “maturity of the bier's faith is that it says nothing about chances," combined with the doctrine of a beginning. It applies to every stage the “vein of luck," advanced by the de. of his progress, whether he is in pocket parted gambler (and rogue) Steinmetz, as or out of pocket. How little, then, it the two fundamental principles for suc promises can readily be shown. If the cessful gambling, curiously illustrate the gambler is a hundred pounds to the bad utter inability of the gambling mind to at any time, he ought to feel confident reason soundly. One doctrine really means that if he goes on long enough from that that the luck must change, not telling the stage, he will again find himself a hundred gambler whether it will change sooner or pounds to the bad - apart from all squan. later; the other really means that luck dered winnings in the mean time. may be trusted not to change for a while, Here, by the way, is an odd paradox, not telling the gambler how long that which is quite illusory, but it will do the “while" may be trusted to last. And the reader no harm to puzzle himself over it a poor simpleton, for even gambling rogues little :like Steinmetz are but simpletons at bot. If in the long run a gambler must come tom, cannot see that the two doctrines to the position from which he started, it necessarily fill the record for all possible follows that if at any time he is just even
with fortune he must come even again, or
From The Westminster Review. in a long enough time will have neither THE DISCOVERY OF THE SOLOMON gained or lost; if in the mean time he gets
ISLANDS. à certain sum ahead he will, in the long DESCRIPTIONS of newly discovered run, lose that sum; and if in the mean countries and their inhabitants are ex. time he gets certain sum in arrears he tremely attractive and interesting to almost will, in the long run, gain that sum (for no every one who is not exclusively preoccuotherwise can he get even). We may be pied with his own affairs, or with those sure, then, since he cannot be always just immediately around him. But of all the even, and must sometimes be ahead and habitable parts of our little globe few now sometimes in arrears, by a certain sum, be remain to be described, and still fewer to it what it may, that in the long run (1) he be discovered. Among those of which will gain that sum, (2) he will lose that the public knows next to nothing, and consum, and (3) he will come out even. Take cerning which geographers and ethnolo the second case, and let the sum be £10. gists knew but little until recently, are In the long run our gambler, starting even, the Solomon Islands. Happily, we are will lose £10. In another long run, from now enabled to become acquainted with what we have just proved, he will lose it this extensive and especially interesting again. Therefore, in a long enough run group of tropical islands; and, though the he will certainly lose £20; in another long knowledge of them which is as yet ren. enough run he will lose another £20; or dered accessible to us is partial, and is £40 in all. And so we go on, doubling at mainly restricted to a small number of the each stage, till we eventually show that in many islands constituting the group, that the long run, owing to the tendency of knowledge, owing to the scientific charac. luck to run even, the gambler must lose ter of the observer who has offered it to any sum that may be named, however the public, is, so far as it extends, ungreat it may be. Of course, we may doubtedly accurate. For this knowledge equally well show that in the long run the we are chiefly indebted to the two very gambler must find himself the winner of a interesting volumes recently published by sum greater than any that can be named. Dr. H. B. Guppy, which, though published
This result, though manifestly not to be simultaneously, form two separate works. trusted as it stands, yet indicates an im- One of them contains a description of the portant truth, viz., that in a sufficiently geological and general features of the isl. long series of gambling ventures the ranges ands; * the other gives a large amount of on either side of neutral fortunes may be information concerning their climate, their expected to be very wide indeed, while flora, their fauna, and, especially, concern. the general evenness of the balance in the ing their human inhabitants. This vol. long run shows that the widest ranges on ume is also enriched by a translation, made one side will be matched by ranges as by Dr. Guppy himself, from a Spanish wide on the other. Hence it follows that manuscript, of a most important and inno matter what the fortune may be with tensely interesting journal, extending to which a gambler starts, he is practically upwards of fifty octavo pages. This joursure, if he continue gambling long enough, nal, written by Hernando Gallego, one of to incur ruin. For whensoever the range the original discoverers of the islands, on the wrong side touches the amount of upwards of three hundred and twenty his means, there is for him no longer run. years ago, has not hitherto been published. It matters nothing, so far as his fortunes In the beginning of 1881, her Majesty's are concerned, that if he could go on in ship Lark was fitted out as a surveying definitely the score against him would be ship in the western Pacific,” and Dr. wiped off, or replaced by as large a score Guppy was selected by Sir John Watt in his favor. Other gamblers may come Reid, the medical director-general of the and others may go; his fate is sealed, his navy, to be appointed as surgeon. "For fortune gone forever.
this selection," Dr. Guppy tells us, he was Among all the certainties of chance | also “in some measure indebted to the this conclusion, that persistent gambling late Sir Frederick Evans, then hydrogra. means loss of fortune, that the run of luck pher, who was desirous that a person pos. is running blindly to ruin (run being simply ruin without an “i” or blind ruin), is Features, and Suitability for Colonization. By H. B.
• The Solomon Islands: their Geology, General the most certain of all. Never in the Guppy, M.B., F.G.S., late Surgeon R.N. London: whole history of gambling bas this law Swan Sonnenschein, Lowrey & Co 1887.
+ The Solomon Islands and the Natives. By H. B been observed to fail.
Guppy, M.B., F.G.S. London: Swan Sonnenscheid R. A. PROCTOR. Lowrey & Co. 1887.
sessing tastes for natural history should | 8,005 feet above the sea.” St. Christoval be chosen.” Certainly, the wisdom of the is over 70 miles in length; it is about 22 selection has been amply justified by its miles broad in its broadest part; but its results. Dr. Guppy not only made the average breadth is, probably, about 15 best possible use of the time and opportu- miles, and it reaches an elevation of about nity afforded him while the Lark was 4,100 feet. The remaining four of the occupied in her survey, but brought to his seven islands named are also of considerinteresting work a mind at once scientifi- able size; Isabel and Maleita appear to cally trained, stored with a large amount be each from 80 to 90 miles long; Choiof scientific knowledge, and imbued with seul and New Georgia are each somewhat an enthusiastic, as well as a genuine, love less extensive. Among the most notable of scientific investigation. Those results of the smaller islands we may mention are presented to us in the two excellently Fauro, which is 12 miles long; Alu, printed and handsomely bound volumes miles long, 7 broad, and 350 feet high; now before us. The extensive, varied, Treasury, 9 miles long, 5 and a half miles thoroughly interesting and trustworthy broad, and 1,150 feet high ; Ugi, 6 miles information they contain cannot fail to en- long, 2 and a half miles broad, and 500 sure for them a cordial welcome from every feet high; Simbo, 4 miles long; Savo, intelligent reader who becomes acquainted which is circular, and 3 miles in diamewith them. Availing ourselves of them, ter; Santa Anna, 2 and a half miles long, we shall now endeavor to give a brief and 2 broad; Piedu, 2 miles long; and the sketch of the Solomon Islands and of the two tiny groups — the Shortland Islands history of their discovery.
and the Florida Islands. The islands constituting the group called Though the Solomon Islands were disthe Solomon Islands are very numerous; covered as early as 1567, the knowledge there are seven principal islands, and then gained, and actually recorded, of many small ones, differing greatly from their position and character was each other in size, as well as in various afterwards lost, and the vague tradition of other respects. The seven large islands their existence and discovery was long are named, respectively, Bougainville, treated as a myth which itself became Choiseul, Isabel, New Georgia, Guadal- almost forgotten. And yet their Spanish canar, St. Christoval, and Maleita. The discoverers actually spent six months, whole group lies south of the equator in three hundred and twenty years ago, in the western part of the Pacific Ocean, examining them, and at that time took about a thousand miles from the north-east formal possession of them in the name of coast of Australia, and forms the eastern his Majesty the king of Spain. most part of the Indian Archipelago. The It appears that only in the second quarnorth end of the most westerly of the chief ter of the present century the existence of islands, Bougainville, is in latitude 5o the journal written by Hernando Gallego, south, and longitude 155° east. The south one of the officers of the expedition by end of the most easterly of the chief isl. which the Solomon Islands were discovands, St. Christoval, extends to the south. ered, became known to geographers. The ernmost part of latitude 10° south, and to original manuscript was, a few years since, the 162nd degree of east longitude. The in the possession of Mr. Amhurst. There islands form, collectively, a sort of chain is a copy of it in the library of the British extending along a line parallel with the Museum ; this copy was purchased of M. north-east coast of Australia, from the Fr. Michelena y Roiss in 1848. It is a northern extremity of the island of Bou- translation of this copy which is "given in gainville in a south-eastern direction to great part" by Dr. Guppy, and which the south-east point of the island of St. gives a detailed account of the discovery Christoval.
of the islands in question. Gallego exThe island of Bougainville is the largest plains why he wrote the journal, as foland loftiest of the group; it is about 10 lows:miles long, 30 miles broad, and “its lofti. est mountain peaks attain a height varying
It moved the mind of that most Christian between 7,000 and 10,000 feet above the and most Catholic monarch, Don Philip, to sea.” Guadalcanar, "the finest and most write to his Governor, the most illustrious interesting of the Solomon group,” is
Lope Garcia de Castro, that he should con
vert every infidel to Christ. Imbued with this about 80 miles long, and, on an average, is feeling, I have made it my first object, by about 25 miles broad. “Its eastern por means of this relation and of the additions tion rises in lofty mountain masses, which made by me to the sea-chart, to enable the attain, in Mount Lammas, an elevation of missionaries who are to guide the infidels into