December 1, 1886.] 



♦ KNO^WLEDGE ♦ 



31 



he requires but a single success to wipe out the losses result- 

 incr from any numbei°of failures. He is in that case sure to 

 succeed very much sooner (on the average of a great num- 

 ber of trials) than in the latter. 



But ^e remember that even in that case where success 

 .eems so assured, and where success in the long run- 

 t^anting the long run-is absolutely certain ^>e system 

 steadily followed out means not success but i"!^- JJ° 

 matter what the limit which the bank rules may assign to 

 the increase of the stakes, so long as there ^s a limit, and so I 

 on<^ as the bank has a practically limitless controlof money , 

 as compared with the player, he must eventually lose all j 



^'Hilcr^rSlnot assume that, because the methodwe | 

 are considering insures success in the long run, the gambler 

 can win to any extent when the long run is not assured to 

 him. Here lies tlie fallacy in this, as in all other methods 

 of binding fortune to the gambler's wheel. The player 

 finds that he must win in the long run, and he never .top. 

 to inquire what run is actually allowed him It maybe 

 a short run, or a fair run, or even a tolerably long run 

 but the question for him is, will it be long enough 1 And 

 note that it is not only the limitation which the bank may 

 assi.'n to the stakes which we have to consider : the gambler . 

 poss'essions assign a limit, even though the bank may assign 



"°llt us see, then, what prospect there is that in this, as in 

 the other case, a run of bad luck may ruin the PWer-or 

 rather, let us see whether it be the case that in this, as n 

 the other svstem, patient perseverance ui the system may 

 not mean certain ruin, which ruin may indeed arrive at the 

 very beginning ofthe confident gamblers career. _ 



Instead of all but certainty of success in each single trial 

 which exists in the simpler case, there is in tbe case we are 

 considering but a high degree of probability. It ly^ ^ 

 much more likely than not that in a given tr al the 

 gambler will clear the stake which he has set himself 

 to win. (This is why we so often hear strong expressions 

 of faith in these systems: again and again we are told 

 with open-mouthed expressions of wonder that a system of 

 this sort must be infallible, because, says the narrator, I saw 

 it tried over and over again, and always with successO 

 Granted that it is so; indeed, it would be a poor system 

 which did not give the gambler an excellent chance of 

 winning a small stake, in return for the risk, by no 

 means evanescent, that he may lose a very large one. 



Observe, now, how the chances for and against are balanced 

 between the two systems. Suppose such a run of fj^^^f 

 in the simpler system would mean absolute 'If f ' '*^^ f ^ 

 of the rapid increase (by doubling) of the sum staked by the 

 "ambler. Say, for instance, a bank allows no stake to ex- 

 ceed 1 000/., so that ten doublings of a stake of 1/., raising 

 the stake to 1,024?.. would compel the gambler to stop, and 

 leave him with all his accumulated losses, amounting to 

 1 0-^3/. Now. take the case of a gambler trying the other 

 svstem for a gain of 10?., divided into three sums, il, 61., 

 and 4/. under' column m, and suppose that after wmpmg a 

 number of times he unfortunately starts ten defeats in suc- 

 cession, his first loss ba^dng been 3?. ; then his second loss 

 was fi/ ; the third, 0/.; the fourth, ML, and so on, the 

 tenth being 30?. His total loss up to this point amounts 

 only to 165?., and is, therefore, much less serious than his 

 10S.S would have been had he begun by staking 1?., and 

 doubled that sum nine times, losing ten times in all. More- 

 over, his next stake, according to the system, is only dM 

 which is well within the supposed limit of the bank, lint 

 on the other hand, to carry on the system, he now has to go 

 on untU he has cleared ofl' all the thirteen sums m the 

 column under m. To do this he has to run the risk ot 



several further runs of ill-luck against him, and it is by no 

 means necessary that these should be long runs ot luck for 

 the score against him to become very heavy indeed. Be it 

 noticed that at every win he scores off only a small portion 

 of the balance against him, while every run ot luck agamst 

 him adds to that score heavily. And notice moreover that 

 ^hile on this system he does not quickly approach the 

 limit which the bank may assign to stakes, he much more 

 quickly encroaches on his own capital-a circumstance which 

 ?s iuite as seriouslv opposed to his chance of eventual suc- 

 cesTa the finality of the bank limit. So far as the carrying 

 out of his svstem is concerned, it matters little -bether he 

 °s obliged to stop the play on the system because his pockets 

 Lre emptied, or because the l>ank will not allow h.m further 



*°S:riS:rS%ply to the fblWng method which 

 has recently been suggested by another correspondent of 

 Knowledge as an improved system : 



.. Mv imDrovements," he writes, " consisted, 1st, in arranging that 



"''""nd" in .latino- the sum of the extreme figures in the gnidc- 

 column'onlvihen^thc number of figures in it was even ; when they 



1 

 were odd, c.ff.. I onlv the highest, 3, is staked. Thus the rise ot the 



4 

 stakes is considerably reduced, while the principle of the play is still 



"""s'rlt splitting up a game when a run of ill luck 

 has occurred into -two or more P™*^^. --^d ^.nnmg 

 these wriatim. Suppose, for instance, thai the 

 chances ofihe game 'bL-e brought the guide-column 

 into tbe form given in the margm. Ibe player nas 

 "ctual ly lost 30, and must win 36 to gam 6 He 

 mS stake 36. but this would be ra.h. He shou d 

 play more cautiously, and convert ibe column into 

 3 m^w columns, totalling 12 each, or even into 4, 

 totalling 0, 



-1 



_2 



-3 



3 



-4 



(> 



(; 



12 



3 of 



or 



1 of 2 

 3 

 3 



Fig. 3. 

 Tlic numeral-! 

 ■n-itli a mimi^ 

 sign are sup- 

 posed - to be 

 struck oat. 



Total 12 Total 



an. play out three - ^-r encoimte. with ^^^ J^^XJ^^S 

 rfi?rh%;anntirm::nwhilf raping the benefit of a run upon 

 ''lT!:S:;vetbat,allowingtheMnkitssmaUadv«the^h.^^ 



°^ribf;s^^ai^^^^u^^i^^^-^^^ 



and here, I have no doubt, the plan breaks down. 



The plan is only safer than the others in the sense that it 

 piJlongf ^be agon -. The introduction of two P-*-- ^^s 



rE;-Lftn;;s^^^^ 



that the bad elTects for one partner of '^ .'"^ °'^,.'' 'T „ 

 would be corrected by the good eflects for the other. A.s a 



be remembered that we not only bave to eonaeei i 

 loss when an unfavourable -l-^^P^^^^^Xo^raWe -a 

 the operation of the sys em Dunng - un avo^^^ ^^^^^^ 

 the Stakes are rising and the distance vo 



