Knave, Ten, and two others surely stops a suit, but Knave and three small is about as unreliable as Queen and two small. It, therefore, becomes evident that the Dealer, to count a suit as stopped, must have in it one of the following holdings:--

Ace.

King and one other.

Queen and three others.

Queen, Knave, and one other.

Knave and four others.

Knave, Ten, and two others.

Some experts, with three suits stopped, bid No-trump with exactly an average hand, but experience has shown that this is advisable only when supported by exceptional skill, and cannot be recommended to most players. The average holding of high cards is one Ace, one King, one Queen, and one Knave. From the average standpoint it is immaterial whether they are all in one suit or divided. Any hand containing a face card or Ace above this average is a No-trumper, whenever it complies with the other above-mentioned requirements. When the average is exceeded by holding two Aces, instead of an Ace and King, a No-trump should be called, but two Kings, instead of a King and Queen, or even a King and Knave, is a very slight margin, and the declaration is doubtful for any but the most expert. A hand with two Queens instead of one Queen and one Knave, while technically above the average, cannot be so considered when viewed from a trick-taking standpoint, and does not warrant a No-trump call.

In bidding No-trump with three guarded suits, it does not matter which is unprotected. For example, the minimum strength of a No-trumper composed of one face card more than the average is an Ace in one suit; King, Knave, in another; and Queen, Knave, in a third. This hand would be a No-trumper, regardless of whether the suit void of strength happened to be Hearts, Diamonds, Clubs, or Spades.

The above-described method of determining when the hand sizes up to the No-trump standard is generally known as the "average system," and has been found more simple and much safer than any of the other tests suggested. It avoids the necessity of taking the Ten into consideration, and does not involve the problems in mental arithmetic which become necessary when each honor is valued at a certain figure and a total fixed as requisite for a No-trump bid.

The theory upon which a player with possibly only three tricks declares to take seven, is that a hand containing three sure tricks, benefited by the advantage derived from having twenty-six cards played in unison, is apt to produce one more; and until the Dummy refuse to help, he may be figured on for average a.s.sistance. The Dealer is expecting to take four tricks with his own hand, and if the Dummy take three (one-third of the remaining nine), he will fulfil his contract. Even if the Dummy fail to render the amount of aid the doctrine of chances makes probable, the declaration is not likely to prove disastrous, as one No-trump is rarely doubled.

It is also conventional to declare one No-trump with a five-card or longer Club or Diamond suit,[2] headed by Ace, King, Queen, and one other Ace. This is the only hand containing strength in but two suits with which a No-trump should be called.

[2] With a similar suit in either Spades or Hearts, Royals or Hearts should be the bid.

As a rule a combination of high cards ma.s.sed into two suits does not produce a No-trumper, although the same cards, divided into three suits, may do so. For example, a hand containing Ace, Queen, Knave, in one suit; King, Queen, Knave, in another, and the two remaining suits unguarded, should not be bid No-trump, although the high cards are stronger than the example given above with strength in three suits.

Admitting all the advantage of the original No-trump, even the boldest bidders do not consider it a sound declaration with two defenseless suits, unless one of the strong suits be established and the other headed by an Ace. The reason for this is easily understood. When the adversaries have a long suit of which they have all the high cards, the chances are that it will be opened; but if not, it will soon be found unless the Declarer can at once run a suit of considerable length. When a suit is established by the adversaries, the Declarer is put in an embarra.s.sing position, and would probably have been better off playing a Trump declaration. It is a reasonable risk to trust the partner to stop one suit, but it is being much too sanguine to expect him to protect two. Should he fail to have either stopped, the Declarer's loss is so heavy that only with a long and apparently established suit and an additional Ace is the risk justified. It is realized that the case cited, namely, Ace, King, Queen, and two others, may not prove to be an established (or solid, as it is often called) suit. If however, the division be at all even, as it is in the vast majority of cases, the suit can be run, and it is cited as the minimum holding which may be treated as established.

With the present value of Clubs and Diamonds, either suit presents an effective original declaration. There is, therefore, much less excuse than formerly for a reckless No-trump bid, based upon five or six Club or Diamond tricks and one other suit stopped. When, however, an Ace of another suit accompanies the unusual Club or Diamond strength, the advantage of being the first to bid No-trump makes the chance worth taking.

The hands above cited as containing the minimum strength to warrant the call are all what are known as "weak No-trumpers." This kind of bidding may not be conservative, but experience has shown it to be effective as long as it is kept within the specified limits. A No-trump must, however, justify the partner in acting upon the a.s.sumption that the bidder has at least the stipulated strength, and it merely courts disaster to venture such a declaration with less than the conventional holding.

A few examples may possibly make the above somewhat more clear, as by that means the various "minimum-strength" or "border-line" No-trumpers, and also hands which fall just below the mark, can be accurately shown.

It will be understood that an effort is made to give the _weakest_ hands which justify the No-trump declaration, and also the hands which fall short by the smallest possible margin. In other words, the hands which puzzle the Declarer. With greater strength or greater weakness the correct bid is plainly indicated.

The suits are numbered, not designated by their respective names, in order to emphasize that it does not matter where the weakness is located.

HANDS IN WHICH THE NO-TRUMP DECLARATION IS DOUBTFUL

Suit 1 King, Knave, X Does not contain an Ace, but is " 2 King, X, X above the average and has four " 3 Queen, Knave, X suits stopped. It is a No-trump " 4 Knave, Ten, X, X bid.

Suit 1 Ace, Knave, X Has an Ace, three suits stopped, " 2 X, X, X and a Knave over the average. It " 3 King, X, X, X is a No-trump bid.

" 4 Queen, Knave, X

Suit 1 Ace, Queen, X Has an Ace and two face cards " 2 King, Queen, Knave more than the average, but, not " 3 X, X, X, X having three suits stopped, is " 4 Knave, X, X _not_ a No-trump bid.

Suit 1 King, Queen, X Has three suits stopped, but is " 2 King, Knave, X, X without an Ace, and is one King " 3 Queen, Knave, X short of three King suits all with " 4 X, X, X another face card. It is _not_ a No-trump bid.

Suit 1 King, Knave, X Has three King-Queen, or " 2 King, Queen, X King-Knave suits. It is a No-trump " 3 King, Knave, X bid.

" 4 X, X, X, X

Suit 1 Ace, X, X Has three suits stopped and is " 2 Ace, X, X, X above the average. It is a No-trump " 3 Queen, Knave, X bid.

" 4 X, X, X

Suit 1 Ace, X, X This is the border-line hand " 2 King, X, X mentioned above. It may be a " 3 X, X, X, X No-trump bid for an expert, but " 4 King, Knave, X the moderate player is hardly justified in risking it. The presence of one or two Tens would add materially to the strength of this hand and make it a No-trump.

Suit 1 Ace, X, X, X Only above the average to the " 2 King, Queen, X extent of a Queen in place of " 3 Queen, X, X, X a Knave. No-trump is not advised " 4 X, X unless Declarer is confident he can outplay his adversaries.

Suit 1 Ace, Knave, X An average hand. With this holding " 2 King, X, X only an expert is justified in " 3 Queen, X, X, X bidding No-trump.

" 4 X, X, X

Suit 1 Ace, X, X Below the average, and, therefore, " 2 King, X, X only "one Spade" should be bid.

" 3 Queen, X, X, X " 4 X, X, X

Clubs } Has the weakest "solid" suit or } Ace, King, Queen, X, X that with one other Ace warrants Diamonds } a No-trump bid.

Suit 2 Ace, X, X " 3 X, X, X " 4 X, X

Clubs } Ace, King, Knave, X, X Absence of Queen in one case, and or } or of King in the other, keeps the Diamonds } Ace, Queen, Knave, X, X suit from being established. Even } the presence of the additional Suit 2 Ace, Queen, X Queen in Suit 2 does not make this " 3 X, X, X a No-trumper.

" 4 X, X

Clubs } Absence of additional Ace makes or } Ace, King, Queen, X, X a No-trump inadvisable.

Diamonds } Suit 2 King, Queen, X " 3 X, X, X " 4 X, X

It is realized that in the last three cases cited the margin is unusually close; the last one, should the partner happen to have either Suit 3 or 4 stopped, and the Ace and some length of Suit 2, would be very much stronger than the example justifying the bid. It is also true that a fortunate drop of the King or Queen of the long suit, with a little help from the partner, would make the next to the last the strongest of the three. It is idle, however, to speculate on what the partner may have. In such close cases it is most important to invariably follow some fixed rule. The player who guesses each time may always be wrong, while the player who sticks to the sound bid is sure to be right most of the time. Experience has shown that, when only two suits are stopped, it is not wise to bid No-trump without both an Ace and a solid suit, and experience is the best teacher.

WHEN TO BID TWO NO-TRUMPS

An original bid of more than one No-trump is rarely advisable, as it is important that the partner be given the option of bidding two of a suit. With great strength such a call should never be made, as in that case there is no good reason for attempting to shut out the adversary.

The only character of hand which justifies starting with two No-trumps is the rare combination in which a long, solid suit of six or seven Clubs or Diamonds is held, accompanied by an Ace or guarded King in at least two of the remaining suits, the idea being to shut out adverse Royals or Hearts.

Some players believe in bidding two No-trumps with "every Ace and not a face," but that sort of an effort to "steal" the 100 is not justified as the partner's hand may make a game, which could not be won at No-trumps, obtainable in a suit declaration. A game with the incidental score is worth much more than "one hundred Aces" and only two odd tricks, or perchance an unfilled contract. It is also important that the bid be limited to the one case mentioned, as in that way it gives the most accurate information.

EXCEPTION TO THE NO-TRUMP RULE

There is one important exception to most of the No-trump bids above described, and that is when the hand, which otherwise would be a No-trumper, contains as its strong suit five or more Spades or Hearts.

It takes only one more Royal or Heart than it does No-trump to win the game, and with a suit unguarded, it is far safer and wiser, with such a holding, to bid the Heart or Royal than the No-trump. For example, with Ace, King, Knave, and two small Clubs; King, Queen, Knave, and one Diamond; Queen, Knave, and one Heart; and one Spade, the bid would unquestionably be No-trump. If, however, the Club and Spade holding be transposed, a Royal should be declared. When there is a score which places the Club or Diamond within four tricks of game, these suits become as valuable as the Heart or Royal, with the score at love, and should be treated accordingly.

The Declarer should bear in mind that as the game is the desideratum, the surest, not the most glorious or enjoyable, route of reaching it should be chosen. When No-trump is declared with a hand containing a defenceless suit, there is a grave chance that the adversaries may save game by making five tricks in that suit before the Declarer can obtain the lead. With five or more strong cards of a suit and two other suits stopped, four tricks are more probable with the suit declaration than three with No-trump, but three with the No-trump are more likely than five with the suit. It, therefore, depends upon which suit be held whether it or No-trump should be bid. The inclination which many players have for a No-trump bid should be firmly curbed, when the holding is of the character mentioned and the strength is in Spades or Hearts.

A very different case arises, however, when all the suits are stopped; the Dealer is then, the game being probable with either declaration, justified in bidding either the No-trump or the suit, as he may prefer, and the value of the honors he holds should be an important factor in guiding his decision. When he has more than five Spades or Hearts, the suit declaration is generally to be preferred, even with all suits stopped, unless the hand contain four Aces. A few examples follow:--

Spades Ace, King, Queen, X, X While this hand contains three Hearts Ace, Queen, X Aces, it is more apt to score Diamonds Ace, Knave, X, X game with Royals than without a Clubs X Trump. With the Spade and Club or Spade and Diamond suits transposed, it is a No-trumper.

Spades Ace, King, Queen, X Not having five Spades, this hand Hearts Ace, Queen, X, X is a No-trump bid. The fact that Diamonds Ace, Knave, X, X it contains a singleton is an Clubs X argument in favor of a suit declaration, but with only four Spades it is safer to risk the Clubs than long adverse Spades with one more trick required for game.

Spades Knave, Ten, X, X A No-trumper, as it has three Hearts Ace, Queen, Knave suits stopped and contains an Diamonds X Ace. A transposition of the Clubs Clubs King, Queen, Knave, X, X to Spades or Hearts would make it a Trump declaration.

Spades King, Queen, Knave, X, X Can be declared either Royals Hearts Ace, Queen or No-trump, as four suits are Diamonds Ace, X, X stopped and it has five strong Clubs Ace, Knave, X Spades. The 30 Aces as compared with 18 honors in Royals and the absence of a singleton make the No-trump more attractive. If, however, the Ten of Spades be subst.i.tuted for a small Spade, the 72 honors would make it a Royal.

Spades King, Knave, X While the four Suits are stopped, Hearts King, Queen, Ten, X, X, X the length in Hearts makes the Diamonds Ace, X suit call the more advisable.