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This is a game that
used to be (and may be to this
day, for
aught I know)
a favourite means of swindling employed by card-sharpers at racecourses
and in railway carriages.
As, on its own
merits, however, the game is
particularly
interesting, I
will make no apology for presenting it to my readers.
The cardsharper
lays down the twenty-four cards
shown in the
illustration, and invites the innocent wayfarer to try his luck or
skill
by seeing which of them can first score thirty-one, or drive his
opponent
beyond, in the following manner:
One player turns
down a card, say a 2, and counts
"two"; the
second
player turns down a card, say a 5, and, adding this to the score,
counts
"seven"; the first player turns down another card, say a 1, and counts
"eight"; and so the play proceeds alternately until one of them scores
the "thirty-one," and so wins.
Now, the question
is, in order to win, should you
turn down
the first
card, or courteously request your opponent to do so?
And how should you
conduct your play?
The reader will perhaps say: "Oh, that is easy
enough.
You must play first, and turn down a 3; then, whatever your opponent
does, he cannot stop your making
ten, or stop your making seventeen,
twenty-four, and the winning thirty-one.
You have only to secure these
numbers to win."
But this is just
that little knowledge which is
such a
dangerous thing,
and it places you in the hands of the sharper.
You play 3, and the
sharper plays 4 and counts
"seven"; you
play 3 and
count "ten"; the sharper turns down 3 and scores "thirteen"; you play 4
and count "seventeen"; the sharper plays a 4 and counts "twenty-one";
you
play 3 and make your "twenty-four."
Now the sharper
plays the last 4 and scores
"twenty-eight."
You look in
vain for another 3 with which to win, for they are all turned
down!
So
you are compelled either to let him make the "thirty-one" or to go
yourself beyond, and so lose the game.
You thus see that
your method of certainly winning
breaks down
utterly,
by what may be called the "method of exhaustion."
I will give the key to
the game, showing how you may always win; but I will not here say
whether
you must play first or second: you may like to find it out for yourself.
See answer
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