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The Gaming Table by Andrew Steinmetz, Volume II

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The Doctrine Of Probabilities Applied To Gambling

These examples may suffice to show the working of the system;
regular tables exist adapted to all cases; and there can be no
doubt that those who have realized large fortunes by horse-racing
managed to do so by uniformly acting on some such principles, as
well as by availing themselves of such 'valuable information' as
may be secured, before events come off, by those who make

The same system was applied, and with still greater precision, to
Cock-fighting, to Lotteries, Raffles, Backgammon, Cribbage, Put,
All Fours, and Whist, showing all the chances of holding any
particular card or cards. Thus, it is 2 to 1 that your partner
has not one certain card; 17 to 2 that he has not two certain
cards; 31 to 26 that he has not one of them only; and 32 to 25
(or 5 to 4) that he has one or both--that is, when two cards are
in question. It is 31 to 1 that he has three certain cards; 7 to
2 that he has not two; 7 to 6 that he has not one; 13 to 6 that
he has either one or two; 5 to 2 that he has one, two, or three
cards; that is, when three cards are in question.

With regard to the dealer and his partner, it is 57,798 to 7176
(better than 8 to 1) that they are not four by honours; it is
32,527 to 32,448 (or about an even bet) that they are not two by
honours; it is 36,924 to 25,350 (or 11 to 7 nearly) that the
honours count; it is 42,237 to 22,737 (or 15 to 8 nearly) that
the dealer is nothing by honours.[55]

[55] Proctor, The Sportsman's Sure Guide. Lond. A.D. 1733.

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