aration."

Although doubles are made under widely divergent conditions, they may
be subdivided into two classes:--

1. The double of a declaration which, if successful, will result in
game, regardless of the double, such as four Hearts, with a love score.

2. The double which, if unsuccessful, puts the Declarer out, although
if undoubled, he would not secure the game by fulfilling his contract,
such as two or three Hearts, with a love score.

In the first instance, the doubler has nothing to lose except the
difference in points which the Declarer may make as a result of the
double. When, for example, a bid of four Hearts is doubled and the
Declarer fulfils his contract, the double costs exactly 82 points. If
the Declarer fall one trick short, the double gains 50 points. When,
however, there is a redouble, the loss is increased 114 points, the
gain 100 points. The doubler is, therefore, betting the Declarer 82 to
50 that he will not make his contract, and giving the Declarer the
option of increasing the bet, so that the odds become 196 to 150. It is
evident, therefore, that even when the Declarer will go out in any
event, it is not a particularly advantageous proposition for the
doubler to give odds of 8 to 5 or 20 to 15, if the chances be even.
When the declaration is Royals or No-trumps, the odds against the
double are increased. If four No-trumps be doubled, the figures are 90
to 50 with the option given to the Declarer to increase them to 220 to
150.

The explanatory remark so often heard after an unsuccessful double, "It
could not cost anything, as they were out anyhow," is not an absolutely
accurate statement. It may be worth while to consider one ordinary
illustration of how many points may be lost by a foolish double of this
character. A bid of four Hearts is doubled and redoubled. The Declarer
takes eleven tricks, as he is able to ruff one or two high cards which
the doubler hoped would prove winners. This is an every-day case, but
the figures are rarely brought home. Without a double, the Declarer
would have scored 40 points; with the redouble, he scores 160 points
and 200 bonus, or 360, presented by an adversary, who hoped at most to
gain 50 and thought his effort "could not cost anything."

A doubtful double should not be made when the partner has another bid,
as, for example, when the adversary to the right has called four
Hearts, over three Royals declared by the partner. Under these
circumstances, t