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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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Example IV. There are four horses to start for a sweepstake,
namely, A, B, C, D, and they are supposed to be as equally
matched as possible. Now, Mr Sly has laid 10 guineas A against
C, and also 10 guineas A against D. Likewise Mr Rider has laid
10 guineas A against C, and also 10 guineas B against D. After
which Mr Dice laid Mr Sly 10 guineas to 4 that he will not win
both his bets. Secondly, he laid Mr Rider 10 guineas to 4 that
he will not win both his bets.

Now, we wish to know what Mr Dice's advantage or disadvantage is,
in laying these two last-mentioned wagers.

First, the probability of Mr Sly's winning both his bets is 1/3
of 14 guineas; and Mr Dice's expectation is 2/3 of 14 guineas, or
L9 16s., which being deducted from his own stake (10 guineas),
there remains 14s., which is his disadvantage in that bet.

Secondly, Mr Rider's expectation of winning his two bets is 1/4,
and, therefore, Mr Dice's expectation of the 14 guineas, is 3/4,
or L11 0s. 6d., from which deduct 10 guineas (his own stake), and
there remains 10s. 6d., his advantage in this bet,--which being
deducted from 14s. (his disadvantage in the other), there remains
3s 6d., his disadvantage in paying both these bets.

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