Ro. ON PROBABILITY. 43 
in which he introduced a treatise on the theory of games at dice, which he 
called Kubeia, from the Greek word signifying a die. At the end of it he 
printed the whole of Huyghens’s essay, professing to be ignorant whether it 
had been already published or not. Nicolas Bernoulli has characterised 
: Caramuel’s work as one continued blunder, and indeed this author has 
fallen into mistakes from which the reading of Huyghens’s treatise 
. ought to have preserved him. For instance, when proposing to determine 
this st the chances favourable to A and B; if the former (who is to begin) under- 
s edition i takes to throw six before the latter throws seven, upon two dice, his reason- 
und iy gh ing is as follows: A s chance of throwing six is -%, and therefore, if the stake 
bert (he be 36, the value of his throw may be taken to be five, leaving thirty-one to 
at oe B, whose chance of winning, if he have a throw, being equal to & his first 
ite] f, throw also may be bought, off for } of the remainder, or 5%, leaving 25%, 
it i, of still to be contended for. ; Caramuel’s reasoning is so far correct ; but 
of ou instead of continuing to divide this remainder in the proportion of the 
ally died chances of the two players, which would have led him to two infinite series, 
of half the sums of which would be the just proportions, he argued that the value 
it, 0d of the first throw of each player being compensated to him by the share 
hw thus allotted to each out of the stake, this second remainder ought to be 
hk bit rg equally divided between them. Hence he deduced the shares of A and B, 
ae if they were to leave the game unplayed, to be respectively 1715 and 184, 
Cb ese instead of 1743 and 181%, which Huyghens had already deduced by a 
i kiki different and more correct analysis. 
jis very far 69. The Journal des Scavaus for 1679 mentions an essay published in the 
wequainted, preceding November, by Sauveur, on the advantage of the banker at basset, 
 eatend bis a game of cards then much played in Paris, and celebrated for the duels it 
u1sy lien) occasioned, to such an extent that it became necessary, solely on that 
Tore direct, account, formally to prohibit it from being played. This treatise was com- 
me might be piled at the request of the Marquis Dangeau, and brought Sauveur into 
diag to the great favour at court, where he was admitted to explain his theory to 
ound. some {,ouis XIV.% 
ery ote, 70. It has been the misfortune of the science of probability, in conse- 
neous dist quence of the ready application made of its principles to games at cards and 
¢ aiempted dice, that a prejudice has from the first existed against it as if ministering 
pointed gu only to gambling and immorality, and available for no other purpose : accord- 
of Pascal § ingly the anonymous writer, who, in 1692, published the first English essay 
ast remarks “ Of the Laws of Chance,” thought it necessary to protest in his preface 
that the design of his book was ¢ not to teach the art of playing at dice, but 
s famed his to deal with them as with other epidemic distempers, and perhaps persuade 
fin treatise, a raw squire to keep his money in his pocket.” This essay, which was 
[638 at the edited, and is generally supposed to have been written, by Motte, the secre- 
st regular tary of the Royal Society, contains a translation of Huyghens’s treatise, and 
more and an application of his principles to the determination of the advantage of the 
in detail of banker at pharaon, hazard, and other games, and to some questions relating 
the general to lotteries. The body of the work does not contain any new principle, but 
aay plager there are some remarks in the preface, which, considering the time at which 
of gaining they were written, deserve attention, and show how justly the author had 
Poresented apprehended the nature of his subject. ¢ It is impossible,” says he, * for a 
die with such determined force and direction not to fall on such a deter- 
pl, mined side, only I do not know the force and direction which make it fall 
on such a determined side, and therefore I call that chance, which is nothing 
but want of art.”—¢ There are very few things which we know, which are 
ta HO first = 
pre + Histoire de I’Académie, 1716,