TOSSING THE COIN

Evening Star, Issue 18919, 18 April 1925, Page 10

TOSSING THE COIN

I IS THERE A LAW OF AVERAGES? ROULETTE WHEELS AT MONTE CARLO . ! jßv P. L. Gonioravk, in the Melbourne ; ' ‘Argus.’) 1 Whatever opinion Gilligan. the captain - of the English cricket team, Inn - have hart ; concerning the relative merits of the Eng- ■ | lish and Australian elevens, lie must have ; felt in the earlier stages of the- testmat cites thul. the mem hers of his team had ' exceptionally had Inch. Not only were ; several plavers injured, hut it seemed almost impossible for Gilligan to call rightly 1 when (he, coin was tossed at (hr beginning of each game. It was not until the fourth match, after England had failed to regain flic ashes, that flilligan won the loss. The ; feature of his calling was that ho cried “ heads ” each time. In four tosses “ tails ’’ fell upright three times, and “ heads ’’ once. There are many people who will say that (he fall of the coin one way or (he other cannot lie accounted for, and that it was to all intents and purposes “ accidental.” They would probably admit that the force behind the spin might have something to do with the matter, but they would not admit that any kind of law could govern it. Probably they would bo right. Vet long treatises have been written on the calculus of probability, and great pains have been taken to work in algebraic formula the chances of any particular event occurring in given circumstances. The working of the calculus forms a definite branch of mathematics. It is well known that, if a person takes a com and spins it a number of times steadily, ho will gradually acquire the ability to make the coin fall heads or tails as he wishes. Thi' matter is merely one of gauging the. distance and strength of the spin. It is not suggested that the captains of the teams sinrepiit ionsly pram | (ised the spinning of coins when they were not- playing cricket. They were lon busily engaged in other direct ions, even it they wanted to practise, which is not likely, and in any case (hey could gauge dm force and distance necessary tor any desiied result only by several preliminary tosses at the time of the deeidirg tm... The opportunity to do this would mil. of eourse. he presented. The spinning of eoins in a series of cricket matches floes not provide a. perfectly apt illustration of the working of the calculus of probability, because I each of (he spins is made with a different j coin, and usually hi places widely separated. It raises the ipicstion, however, j wild her there is such a tiling as a law of j averages, or a law coni rolling the ire- j I qnency of any defined happening, j SYSTEMATIC KECOKDS AT CASINO, j No better instruments for testing (Ins ' question could be suggested tlian (lie , roulette wheels used at .Monte Carlo. The j wheels are divided into thirty-seven j snares, colored alternately red and black, j with the exception of the. spaces numbered 26 and 0. If is not- surprising that there have been created at .Monte Carlo ■ superstitions among vasions people con-', I corning the luck of certain numbers and ■ (lie ill fortune which follows the, calling of other numbers. Neither is it surpris- ■ ing that the management of the. Casino j should have been interested to learn i whether the balls on the. wheels rolled' into any pnnicular compartment with | more frequency than into the others, j Most careful and systematic records of i the results of ilje. spinning of the wheels are-kept by (he proprietors, and these are I published in the weekly ‘ Revue de Monte | Carlo,’ which is sold to (he public, at, a I small charge. The result.-, are shown in various forms, (he daily records of each color on the wheels being presented, together with the records ol each number. These are furl her analysed, and a general calculation of the number of limes I (hat the ball falls into each number for I each day of the week is made. The total i ■number during the whole week is also j shown. Thus it is possible, by consult ing 1 the review, to ascertain how many limes | the hall rolled into division 7. 2d, 42. or . anv other number of any particular wheel j on which the gambler may wish to wager j his money. In addition to giving the total | results, the review gives the sequence of : the numbers and the colors into which the ball fell. It even takes Hole of the changes of (lie croupiers, who are changed frequently. s-- Iha I there is no chance of . their becoming accustomed lo the “lay' ; of the wheel, and consciously or mi- i consciously spinning for a particular color j or number. A person reading the review ! can learn after which of each spins tlm - croupier is changed to another (aide. The . review also gives the results of the falls j : of various combinations of numbers in j several different, games that are played, . SEQUENCE OK FALLS. (

A rcTni. xi!! m I if’ r of (lie ' Revue ’ giving the results i'll the spinning of the wheel on table Xo. 2 shows (!i;it. in the fir.-t three spins the. winning number was red. Tim next three numbers were black. Therealt-er the numbers worn red, ml. 1 ilai'k. led five Hines. black, red, and black. Later the ball dropped into black nine, limes in succession. Of (lie firs! twenty spins nn Mint, day red won fourteen times and black six, The most informative guide to the, turning of the numbers is gained, however, no! from flic study of a small number of spins, billifom a study of (hose mafic during (he whole week. If is found lhaf there is a remarkable evenness in the manner in which the individual numbers '‘turn up.’’ During one day, for ini-dance, (he ball fell inlo the red division 308 times, and into the black 328. The colors for tile following davs, with tin* number for rod shown first were; 326, 306; 386, 331; 363, 366; 321. 32b; 388, 342: and 320, 320. The total milliners for (he second week were ; Red, 2.326: black. 2.308. Selecting numbers at rajidom on the first day. it is found that 0 turned up .14 times; 4, 26 times: 19, 18 limes: 27, 21 times; and 32, 25 times. Five, 9, and 21 turned up onlv 9 times, and 24 only 8 limes. In (lie aggregate number of times for the wee!;, however, tin' numbers are. in close proximity to each oilnn- in jhe results. It is not necessary to lake the whole of Ihe thirty-seven divisions, but the numbers from 0 io 10 won, during the week, the following I huesl2l. 117. 108, 161. 1.26, 120. 132, 140, 157. 107. and 122. Among t!u' games played is passe et iiiampm, in which file playin’ wagers I hat the ball will fall mampir (1 to 18) or passe (10 to 36), For the week the ball felt ‘‘passe” 2,334 times, and “manque”

j 2,300 limes. There is n'so another game, in which the plnyor selects one nf three columns of fi^iires. and if any of (he figures in that, column turn up he wins his wager. For the week the first, second, and third column figures won 1.542, 1.582, and 1,510 times respectively. SYSTEMS FOR SALE. Tl is only to he expected that malliematiciiuis and oilier stmlenb; of these (inures would try to invent- systems to “heal,-' : the wheel, and acquire wealth quickly. I The visitor to Monte Carlo will find little difficulty in obtaining a system if he wants to buy one. The. review cadi wick con tains a large number of advertisements for publications which have hoen issued. The systems am advertised at from 1 franc upwards. Notwithstanding the sale of these systems, the management of (lie Casino still flourishes, and, although large i sums are won by visitors on occasions, large sums are also lost. It might he of some use to know that a certain number or color will turn np so many times a week, if it were possible to know just when it would do so. Visitors find, however ,that the numbers have a tantalising habit of turning up at the wrong time, and (hat an annoying fate seems to impel them to call the number nr color one spin too early. Having found that red has turned nn (wife, they will wager on it for the. third spin, only to find that (lie ball rolls into black. Nevertheless, thousands of pleasure-seekers and gamblers frequent the Casino every year, and will probably continue to do so. From a close study of the figures on the ‘ Revue ’ there does appear to be some ground for stating that there is a law of averages controlling the wheels, but (lie greift diflicnlty for gamblers is to persuade the law to operate in a sequence favorable to : Ilicmselyos.