ON THE BISKS OF LOSS OR GAIN. Ill 



that the permanency of each had 100 to 1 in its favour, 

 we are entitled to conclude that (the tenth root of 101 

 being 1*59) the games played were each not less than 

 3 to 2 in favour of the bank, if they staked the 10th 

 of their resources at each throw, or 11 to 10 if they 

 stake one fiftieth. 



PROBLEM. The odds in favour of the bank being b 

 to a, required the greatest proportion of the fund which 

 may be staked at one game, in order to insure the chance 

 A; to 1 for the permanency of the establishment. 



RULE. Divide the logarithm of one more than A: by 

 the excess of the logarithm of b over that of a : the 

 quotient is the denominator of the fraction required, 1 

 being the numerator. Suppose, for instance, that the 

 odds for the bank, on single games, are 30 to 29, then, 

 if 99 to 1 be required to be the chance that the bank 

 shall continue to exist, divide the logarithm of 99 + 1 

 (which is 2) by the excess of the logarithm of 30 (or 

 1-47712) over the logarithm of 29 (or 1-46240), and 

 2 -7- "01472 gives a fraction more than 135 ; whence 

 the 135th part of the capital is the highest which 

 should be staked. 



A merchant, who engages in speculations which must 

 produce a fixed loss or a fixed gain, and who offers td 

 deal with any one in such a manner, is precisely in the 

 position of a bank such as is above described. The reason 

 why neither party need be ruined in this instance is 

 that the produce of the earth and sea is an unlimited fund, 

 upon which the merchant draws. Trade by itself would 

 tend to ruin the many, and accumulate all the stakes in 

 the hands of a few, and the theory of probabilities would 

 enable us to foretell that continual approximation to- 

 wards the extremes of wealth and poverty which com- 

 mercial countries always present. We have seen that 

 the poorer player must, to maintain his ground, have a 



protection and encouragement which legal regulation of gambling-houses 

 would appear to give to gambling in general, is a good reason for the state 

 of our own law : otherwise, there can be no doubt that much particular evil 

 would be prevented. by allowing a regulated system. 



