The Pioche weekly record. [volume] (Pioche, Nev.) 1877-1900, 1885-03-14
ALL TRUNKS.
Mathematics of whist, showing the
Ratio of Certain Chances.

[R. A. Proctor, in Longman's Magazine
There are no less than 635, 0l3, $780,
600 ways Of which hand of whist can
be made. That all the cards in the hand
may be trumps (the dealers, of course,
must be taken) the chance is but one in
l5S, 1853, $3.50, 900 (one-fourth Of the num-
Der just mentioned). A few years ago
(see "Whist Whiting" in "How to
Play Whist" PIP. 100, l9l) two cases of
the kind were recorded, and many sup.
posed that there must be something
wrong in the mathematical computation
of the chance. For, they said, in 1885,
1853, 3S9, 900 cases only one would give
this particular hand, and yet two cases
occurred within few years of each other,
within which time SO many hands could
not possibly have been dealt. Now there
was here, at starting, the fallacy that,
because but one case in SO many is favor
able, so many trials must be made to
give an even chance of the event occur.
ring. As matter of fact, much smaller
number of trials is necessary to give an
even chance. Take a simple case-the
tossing of coin. Here there are two
possible results, but it does not take two
trials to give an even chance of tossing
head-one trial suffices for that; and the
chance of tossing head once at least in
Two trials instead of being one-half is
three fourths; the odds are not even but
three to one in favor of tossing head.
In like manner, if 1853, 1853, 3S9, 900 hands
we're dealt the odds we're not even, but
largely in favor of hand of l3 trumps
being among them. Moreover, if the
odds were shown to be ten or even twenty
to one against the event occurring in o
given much smaller number Of trials, YET
there is nothing very surprising in al
event occurring when the odds against il
are ten or twenty to one. But large
though the number just mentioned may
seem, the number of whist players il
also large. 1t would not be much out o
the way to suppose that among all thu
whist playing nations of the earth mil
lion whist parties play per diem, and t.
each we may fairly as ign 20 deals. o.
this assumption it would require onl,
| 1850 days, or not much more than q
years, to give l59, 1000, 900, 900 or mucl
more than an even chance of the remark
able hand in question. Then, too, Their
are cases where the trumps are NOR
likely to be distributed to one hand thai
il the distribution were absolutely a
random. Thus suppose cross ruff ha
been established in game and five o
six tricks taken that way; then it cal
readily happen that the five or six trump
which have thus fallen take the sam
position in each of the five or six trick
, gathered by the same player. Suppos
such thing to happen, with five trump
, only, once in thousand games. The
r it can be shown that the chance of til
, remaining cards of that suit all fallin
into the same hand is in 2, 500, 575, 0C
making the chance of both events comm
off and all Is cards falling into one han
} in 2, 629. 575, 900, or the odds only 2
500, 574, 999 to l INSTEAD of 1873. 1853
3S9, 800 to y against all Is trumps bein
in one hand. Large even as these odd
. are the real odds must be much large
, otherwise, with the great number I
whist hands constantly being dealt "
should hear of all-trump hands two {
three times a year at least