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The Doctrine Of Probabilities Applied To Gambling

Volume I

The Gaming Table by Andrew Steinmetz, Volume II

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The Doctrine Of Probabilities Applied To Gambling

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Casino Gambling in history

Among the many mistakes that are committed about chances, one of
the most common and least suspected was that which related to
lotteries. Thus,supposing a lottery wherein the proportion of
the blanks to the prizes was as five to one, it was very natural
to conclude that, therefore, five tickets were requisite for the
chance of a prize; and yet it is demonstrable that four tickets
were more than sufficient for that purpose. In like manner,
supposing a lottery in which the proportion of the blanks to the
prize is as thirty-nine to one (as was the lottery of 1710), it
may be proved that in twenty-eight tickets a prize is as likely
to be taken as not, which, though it may contradict the common
notions, is nevertheless grounded upon infallible demonstrations.

When the Play of the Royal Oak was in use, some persons who lost
considerably by it, had their losses chiefly occasioned by an
argument of which they could not perceive the fallacy. The odds
against any particular point of the ball were one and thirty to
one, which entitled the adventurers, in case they were winners,
to have thirty-two stakes returned, including their own; instead
of which, as they had but twenty-eight, it was very plain that,
on the single account of the disadvantage of the play, they lost
one-eighth part of all the money played for. But the master of
the ball maintained that they had no reason to complain, since he
would undertake that any particular point of the ball should come
up in two and twenty throws; of this he would offer to lay a
wager, and actually laid it when required. The seeming
contradiction between the odds of one and thirty to one, and
twenty-two throws for any chance to come up, so perplexed the
adventurers that they began to think the advantage was on their
side, and so they went on playing and continued to lose.

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