THE DOCTRINE OF CHANCES. 13
which give croix the first coup; for head once thrown, the game is over; thus, then, there are really only three combinations possible, viz.
Croix............... first coup.
Pile and Croix............... 1 and 2 coup.
Pile et Pile.................. 1 and 2 coup.
The odds are, therefore, only 2 to 1. Again, in three coups we shall find,
Pile. Pile. Croix.
Pile. Pile. Pile.
The odds are, therefore, in this case, only 3 to 1.
We invite the attention of our readers to this problem, which, in the opinion of the celebrated mathematician alluded to, would go far to reform many of the methods pursued in the analysis of games of chance.
To find in how many trials an event will probably
Example 1.—Required in how many throws one may undertake, vnth an equality of chance, to throw two aces with two dice.
Now the number of chances upon two dice being 36, out of which there is but one chance for two aces, it follows that the number of chances against it is 35 ; multiply therefore 35 by the log. 0*7, and the product, 24*5, will show that the number of throws requisite to that effect will be between 24 and 25.
Example 2. — In a lottery whereof the number of blanks is to the number of prizes as 39 to 1, to find