Even the ordinary newspaper reader is
accustomed to look on the national death-rate or birth-rate as a thing
capable of being stated with accuracy to one or two places of decimals,
and he knows that the annual number of suicides is practically constant.
If a man played whist often and kept a record of the number of trumps n
each hand, he would find fortune treated him quite fairly; in a year's
play the average number would deviate very little from the theoretical
average, _i.e._, one-quarter of thirteen. And a knowledge of this truth
is useful, and that not merely in keeping ejaculations in due restraint.
But every good player knows more than this: he has a sense of what
variations in the number of trumps may reasonably be expected. For
example, he will be prepared to risk something on neither of his
opponents having more than five trumps, and will accept it as a
practical certainty that no one has more than eight. Much of what is
known as good judgment is based on a proper estimate of deviations from
the average. The question has an important bearing on sampling, as may
be seen from the fact that shuffling and dealing at cards are but
modifications of the well-known mixing and quartering of the sampler.
Because of this bearing on sampling and for other reasons, I became many
years ago much interested in the question, and gave to its solution
perhaps more labour than it was worth.
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