ULTIMATE RESULTS OF PLAY. IX 



Hitherto all our results seem in favour of the hank ; 

 that is, tending to show that its advantage is not so 

 great as is commonly supposed. No person, granting 

 a bank permission to exist, would grudge it such an 

 advantage as would make it 49 to 1 against its being 

 ruined by the possible fluctuation attendant upon an 

 unlimited duration of play. This chance of being 

 ruined, namely *02, appears from the table to be ex- 

 ceeded, unless the bank possess 160 times the sum 

 risked at each game : if this were 100/., the bank would 

 need a capital of l6,000/. But I must now request 

 attention to the other side of the question ; first, con- 

 sidering the bank against the public; and, secondly, the 

 bank against an individual player. One of the most 

 important features in this game (which springs from 

 the old game of Faro, as did the last from the still older 

 game of Basset*) is, that the bank does not risk the 

 whole sum it lays down, but only the difference between 

 those sums which the caprice of the players obliges it 

 to stake on rouge and on noir. If 20 players have each 

 staked a guinea, 12 on rouge and 8 on noir, and if rouge 

 win, the bank loses 12 guineas and gains 8, and conse- 

 quently did not risk more than four guineas. It is im- 

 possible to say what chance there is of the bank having 

 to risk a given sum in such a case, as this depends on 

 the will of the players. When the cards have several 

 times decided for rouge, those players who think the 

 run is not finished will stake on that colour, while others 

 who think differently will stake on noir. I am wholly 

 without the means of saying what average exists, but I 

 should incline to think it very unlikely that the bank 

 really risks more than one fourth of its deposits, t But 

 the advantage which it derives from the refalt trente et 



* An assertion of the editor of Hoyle, which is true as to the principle of 

 the game namely, that besides equal chances for the bank and the 

 player, there are chances for a drawn game, and a case in which the bank 

 has a direct advantage amounting to half the stake but the details are 

 very different. Both games are described in De Moivre. 



f The bank is evidently (its chance of the apres excepted) merely the 

 means of equalising the sums staked on the two colours. 



