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The Doctrine Of Probabilities Applied To Gambling

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The Doctrine Of Probabilities Applied To Gambling

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In horse-racing the expectation of an event is considered as the
present value, or worth, of whatsoever sum or thing is depending
on the happening of that event. Therefore if the expectation on
an event be divided by the value of the thing expected, on the
happening of that event, the quotient will be the probability of
happening.

Example I. Suppose two horses, A and B, to start for L50, and
there are even bets on both sides; it is evident that the present
value or worth of each of their expectations will be L25, and the
probabilities 25/50 or 1/2. For, if they had agreed to divide
the prize between them, according as the bets should be at the
time of their starting, they would each of them be entitled to
L25; but if A had been thought so much superior to B that the
bets had been 3 to 2 in his favour, then the real value of A's
expectation would have been L30, and that of B's only L20, and
their several probabilities 30/50 and 20/50.

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