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."
[Illustration:
[1] [1] [1] [1]
[2] [2] [2] [2]
[3] [3] [3] [3]
[4] [4] [4] [4]
[5] [5] [5] [5]
[6] [6] [6] [6] ]
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.