Thus, 'supposing I play with
an adversary who allows me the odds of 43 to 40, and agrees with
me to play till 100 stakes are won or lost on either side, on
condition that I give him an equivalent for the gain I am
entitled to by the advantage of my odds;--the question is, what I
am to give him, supposing we play at a guinea a stake? The
answer is 99 guineas and above 18 shillings,[52] which will seem
almost incredible, considering the smallness of the odds--43 to
40. Now let the odds be in any proportion, and let the number of
stakes played for be never so great, yet one general conclusion
will include all the possible cases, and the application of it to
numbers may be worked out in less than a minute's time.'[53]
[52] The guinea was worth 21s. 6d. when the work quoted was
written.
[53] De Moivre, Doctrine of Chances.
The possible combinations of cards in a hand as dealt out by
chance are truly wonderful. It has been established by
calculation that a player at Whist may hold above 635 thousand
millions of various hands! So that, continually varied, at 50
deals per evening, for 313 evenings, or 15,650 hands per annum,
he might be above 40 millions of years before he would have the
same hand again!
The chance is equal, in dealing cards, that every hand will have
seven trumps in two deals, or seven trumps between two partners,
and also four court cards in every deal.
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