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The Gaming Table by Andrew Steinmetz, Volume II

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The Doctrine Of Probabilities Applied To Gambling

The chances against holding seven trumps are 160 to 1; against
six, it is 26 to 1; against five, 6 to 1; and against four nearly
2 to 1. It is 8 to 1 against holding any two particular cards.

Similar calculations have been made respecting the probabilities
with dice. There are 36 chances upon two dice.

It is an even chance that you throw 8. It is 35 to 1 against
throwing any particular doublets, and 6 to 1 against any doublets
at all. It is 17 to 1 against throwing any two desired numbers.
It is 4 to 9 against throwing a single number with either of the
dice, so as to hit a blot and enter. Against hitting with the
amount of two dice, the chances against 7, 8, and 9 are 5 to 1;
against 10 are 11 to 1; against 11 are 17 to 1; and against
sixes, 35 to 1.

The probabilities of throwing required totals with two dice,
depend on the number of ways in which the totals can be made up
by the dice;--2, 3, 11, or 12 can only be made up one way each,
and therefore the chance is but 1/36;--4, 5, 9, 10 may be made up
two ways, or 1/8;--6, 7, 8 three ways, or 1/12. The chance of
doublets is 1/36, the chance of PARTICULAR doublets 1/216.

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