PART II. MIXED GAMES OF CHANCE AND SKILL. INTRODUCTION. WHEN chance reigns absolutely in a game, we can, as it has been shown 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 does 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. The 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 I of men, baffle all calculation; for oftentimes they are ignorant of their real interests, and even when they know them, are as frequently determined by caprice as by reason. The second cause of our ignorance of things which depend upon the future, arises from the limited power of the human intellect. Thus, to determine the value of the throw at back-gammon between two equal players-the value of the hand at piquet-which piece is the most advantageous at chess, the bishop or the knight-and in what ratio one is better than the others, are problems, the solution of which baffles all human analysis. All that a player has to do, therefore, is to content himself with seeking probability, and to endeavour to approach truth as nearly as possible. These reflections will be sufficient to satisfy my readers that there are problems which it is impossible to solve, while the few I have given in the following pages will make them acquainted with the nature of those, the solution of which may be attempted with hopes of success. WHIST. ODDS against and for the dealer's hand of trumps. 158753389899 338493367 to 1 to 1, that he don't hold 13 trumps. 12 .11 10 99965 7 to 5 that the dealer holds 4 or more. 12211799222 to 1, that he does not hold 12 trumps. ODDS against the dealer holding a certain exact quantity of trumps. 51 to 1, that he does not hold exactly 7 trumps. 39 to 1, against holding only the trump turned up. ODDS against any assigned non-dealer holding an exact quantity. 183 to 1, that he does not hold exactly 7) 32 to 1, or 23 to 7... 9 to 1, better than 9 to 1.. 57 to 1, that he is not without a trump. It is 27 to that the dealers have not the four honours. 23 to 1 nearly, that the eldest hands have not the four honours. 8 to 1 nearly, that neither one side nor the other have the four honours. 13 to 7 nearly, that the two dealers do not reckon honours. 20 to 7 nearly, that the two elder hands do not reckon honours; and 25 to 16 that the honours are not equally divided. |