Hoyle's Games, Improved And Enlarged - online book

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From the foregoing problems it appears that, when A wants but one game of a set, and B two, the odds in favour of the former are 3 to 1. The accuracy of this calculation, however, has been questioned by the celebrated d'Alembert, who il­lustrates his position by the game of Croix ou Pile (Heads or Tail), which is too well known to need a definition.
In these four combinations there is only one by which the thrower loses; the odds are then 3 to 1 in his favour. If he betted in three coups, he would find eight combinations, seven in his favour, and one against him ; the odds would be, therefore, 7 to 1 ; but, says d'Alembert, is this correct ? For to consider only the two coups, must we not reduce to one the two combinations,
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