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PART II. |
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MIXED GAMES OF CHANCE AND SKILL. |
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INTRODUCTION.
When chance reigns absolutely in a game, we can, as it has been shewn in the first part of this work, always determine the advantage or disadvantage of the players.
But it is not the same with those games in which the skill of the player has a share in producing the result. Thus, the light which has guided us in our investigation of games of pure chance, fails us here in the solution of those questions, the result of which do not entirely depend upon chance.
The first rule of analysis is, that we cannot discover what is unknown, but by means of what is known; but in most of the questions which are proposed upon mixed games, what is known is not sufficient to discover what is to be found, and the reason is obvious :—1st. From our uncertainty of the measures to be taken by those, whose actions must necessarily exercise an influence over our undertakings. 1 he impulse given to a ball decides both its direction and its velocity, for the laws of impulse are fixed and invariable ; but the reason, the different motives which influence the conduct
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