which the long Club holding of
the Third Hand is headed by King and Queen, and is it not much more
probable, when the Third Hand has _long_ Clubs, that the No-trump
maker has the suit stopped with the Ace than with _four_ headed by
Knave, Ten?

It must be remembered that the three Club take-out with Ace, King,
Queen, at the head of five or more, is only advantageous when the
No-trump has been called with a hand in which only three suits are
stopped, of which the Club is one. If the Club be the suit unstopped,
the call merely forces an advance in the No-trump.

If, however, the convention be to use three Clubs to overbid the
partner's No-trump only when holding an otherwise trickless hand which
contains either at least five Clubs headed by King, Queen, Knave, or at
least six headed by King, Queen, would not the number of instances in
which the call proves of benefit appreciably increase, and would not
every reason applicable in the former case be even more forceful in the
latter?

It cannot be questioned that the partner having called No-trump, the
Third Hand is more likely to hold either five Clubs headed by King,
Queen, Knave, or six headed by King, Queen, than five or more headed by
Ace, King, Queen. The greater probability that the Dealer will have the
Ace than four headed by Knave, Ten, is just as obvious.

Take such a No-trump declaration as

Spades Ace, King, Knave
Hearts X, X
Diamonds Ace, King, Knave, X, X
Clubs Ace, X, X

and the advantage of the proposed system becomes apparent. The game,
which is almost sure to be lost by the Heart lead in No-trump, becomes
almost a certainty with Clubs Trump. When this plan is used and the
Dealer has the other suits stopped but has not the Ace of Clubs, he can
easily decide whether to go to two No-trumps, as he can estimate from
the length of his Club holding whether he can establish the long Clubs
or the adverse Ace will block the suit. When the latter is the case, he
should not bid two No-trumps unless his own hand justify it, as the
Third Hand has announced the absence of a reentry.

Take such a No-trump declaration as

Spades Ace
Hearts Ace, King, X
Diamonds Ace, King, X, X, X, X
Clubs X, X, X

and suppose the Third Hand hold one or two small Diamonds; six Clubs,
headed by King, Queen, Knave, and no other face card.

In such a case Clubs is the call most likely to produce game.

Another and possibly