June i8, 1908] 



NATURE 



147 



ROULETTE AT MONTE CARLO. 

 La Loi lies pctits Nomhrcs. By M- Charles Henry. 

 Pp. xiv + 71. (Paris: Laboratoire d'Energetique 

 d'Ernest Solway, 1908.) Price 4 francs. 



THE question discussed by the author may be given 

 in his own words : — 



" Est-il possible de pri^-voir une loi de sequence plus 

 ou moins fragmentaire dans les phenomenes_ fortuits 

 comme les arrives de la rouge et de la noire h la 

 roulette? " 



He considers that the theory of probabilities 

 is only verified in practice when the number 

 of throws of the ball is indefinitely great, and 

 that new principles are required when the period 

 of play is short. He takes what he terms a psycho- 

 physical point of view, and bases his researches on the 

 ultimate vibrations of particles and the musical in- 

 terval, the fifth— the ratio 3:2. He adopts the latter 

 as governing the sequences at roulette without giving 

 ■anv scientific reason whatever. 



It is difiicult to take the author seriously, but as 

 he pretends in chapter iv. of the work to give rules 

 of play which will enable a plajer to win at Monte 

 Carlo, ft is necessary to inform the reader that the 

 system of M. Henry is not based upon scientific truth, 

 and can have no effect upon his winning or losing. 

 It still remains true that the construction of the Monte 

 Carlo roulette table gives an advantage to the bank, 

 which, roughly, may be stated to be 135 per cent, 

 on the even chances and 27 per cent, on the longer 

 chances. The percentage refers to all the money 

 placed upon the table that was originally in posses- 

 sion of one of the players. Should a player stake 

 five francs on one of the even chances, the piece 

 becomes immediately depreciated in value so as to be 

 only worth four francs ninety-three centimes. Placed 

 anvwhere else on the table it is worth but four francs 

 eighty-six centimes. If the stake be left upon the 

 table for another coup, with or without previous 

 winnings, a like depreciation takes place, and it is the 

 sum of all these depreciations which in the long run 

 constitutes the profit of the bank. 



Statistics show that each table earns about 400L 

 per diem on the average. This shows that the amount 

 staked at each table is about 20,oooJ. per diem. The 

 nine tables in use during the winter months thus 

 earn about 3600!. per diem, and the amount staked 

 probably reaches the large figure of iSo.oooZ. per 

 diem. It may be regarded as certain that a large 

 majority of the players leave off losers. Of these, 

 certain individuals lose a small sum which they con- 

 sider is sufficient to leave in the rooms ; others a sum 

 which they had previously determined not to exceed; 

 others sums which are in excess of what they wished 

 to lose. On the other hand, a minority of the players 

 will be winners, but this minority becomes smaller as 

 the average time during which the players remain 

 at the table becomes larger. 



Many of the players have probably been winners 

 at some time or other during the play. They deter- 

 mined to become larger winners, with the final result 



NO. 2016, VOL. 78] 



that they were losers. Few players know when to 

 stop the game and to hold their hands when a reason- 

 able sum, reasonable in proportion to the playing 

 capital, has been won. The consequence of a player 

 with a moderate capital thus settling down to play the 

 bank for immoderate winnings is in the long run 

 certain ruin, whether the bank has between one and 

 three per cent, in its favour or not. 



The large capital of the bank gives it an advan- 

 tage over the plaj'er, whose capital is relatively small, 

 which is quite separate from the advantage derived 

 from the design of the table. 



The influence of capital can be well seen in an 

 ordinary even .game of rouge et noire. We may sup- 

 pose Peter and Paul to be the players, and the stake 

 to be iL at each coup. It is quite certain, whatever 

 be the capital of each, that after a sufficient number 

 of coups one or other will lose all his capital. Which 

 of the two has the greatest chance of being ruined 

 depends upon the ratio between the capitals. It can 

 be shown that Peter's chance of ruining Paul bears 

 the same ratio to Paul's chance of ruining Peter that 

 Peter's capital bears to Paul's. If Peter's capital be 

 50;. and Paul's 40!., it is 5 to 4 that Peter ultimately 

 ruins Paul. The circumstance that the game, if con- 

 tinued long enough, will inevitably lead to the ruin 

 of one of the players may seem surprising to one 

 who has not given the subject special attention. There 

 is a popular fallacy that in the long run Peter and 

 Paul will win very nearly the same number of coups. 

 The fact is that in the result of a large number of 

 coups the ratio of the numbers of coups won by the 

 plavers approaches unity, but that the difference be- 

 tween these numbers has a tendency lo increase 

 beyond any limit. Great as is the advantage of a 

 large capital, it cannot be inferred that the bankers 

 at roulette could afford to play with tables not con- 

 structed to their advantage, because then there would 

 be nothing to hinder a combination of capitalists from 

 placing themselves on more than even terms with the 

 bank. So great is the advantage of the bankers due 

 to their large capital that, failing a combination 

 against them, they could afford to play with a table 

 constructed against themselves and in favour of the 

 players. 



If the respective capitals of the bank and of a player 

 be known, it is not difficult to design a table which 

 will place the two sides on an exact equality as 

 regards plav on the even chances for an unlimited 

 time. When the bank has practically an unlimited 

 number of stakes the solution is very simple, and 

 may be stated as follows :— If the player possess a 

 certain number of stakes, he should be able, from 

 the construction of the roulette, to win on the average 

 a majority out of four times that number of coups. 

 A player with fifty stakes should be able to win loi 

 coups out of 200. In this case the roulette should 

 have one zero and 100 numbers, and the zero should 

 be in favour of the player. On the existing roulette 

 tables a player with nineteen stakes and the zero in 

 his favour would be on even terms with the bank. 

 There would not be more than an even chance of his 

 final ruin. 



