Why No-Trumpers Fail

Not the Original Call but The Partner's Answer is Really Important

R. F. FOSTER

PROBLEM LXXII

Hearts are trumps and Z leads. Y and Z want all the tricks. How do they get them? Solution in the July number.

BRIDGE is peculiarly a bidding game, and the big "swings" in results are due more to the character of the contract upon which the hand is played that! upon the way it is played.

The secret of success at the bridge table is now pretty generally admitted to be what is called "team bidding". That is, the partners must work together as a team, and not as individuals. The object is to arrive at the best final declaration for the combined hands, whether with a view to playing the hand in an effort to win the game; or to playing it at a deliberate loss to save the game; or letting the other side play it.

These final declarations fall naturally into two classes: suit bids and no-trumpers. In team bidding, the partner's duties with regard to suit bids are now thoroughly well understood by all good players, but when it comes to notrumpers it seems to be all guess work.

THE SUIT RIDS

THE usual rule for suit bids is based on the quick-trick and double valuation system, the partner denying the suit with less than three small, or as good as queen and one, and

refusing to assist with less than four tricks, these tricks being counted at double their face value.

An analysis of a thousand deals in which this system was consistently followed, shows that in 37 per cent, the play produced exactly the number of tricks predicted by the bidding estimate of the combined hands; in 39 per cent, more than their estimated value; while in 24 per cent, they failed to produce the predicted number of tricks. In many of these it was manifestly impossible to reach the estimate, because the value of the combined hands exceeded thirteen tricks.

But in spite of including these impossibilities in the estimate, the system won an average of half a trick a deal more than the bidding estimate predicted, and if any person can produce a better system, bridge players will be glad to examine it.

THE NO-TRUMPERS

When this system of quick-trick valuation comes to be applied to no-trumpers, it is a complete failure.

I have, spent nearly two years in searching for the reason. In doing so I have tested out a thousand deals, with every known system of valuing the hands, but without finding anything better than the quick-trick system. The trouble with the Robertson rule and its congeners is that they cannot be applied to the partner's hand for purposes of assisting, denying, or shifting.

Starting with the rule that the dealer should have a minimum of five tricks for his original no-trump bid, it was found that he averaged seven. All hands in which the dealer had a choice between no-trumps and a good majorsuit bid, even on four cards, were rejected. All deals in which third hand held a suit of more than five cards, or two five-card suits, or any of the generally accepted take-outs, were rejected, and also all deals in which anything would disclose the situation to the third hand, such as a bid or double by second hand.

In these 1,000 deals, the value of the combined hands predicted the ability to win 9,338 tricks; but the best they could do, with perfect play and with the assistance of the take-outs, was 6,913, if left to play either the no-trumpers or the take-outs. This would seem to show that the quick-trick system overestimates the playing value of no-trumpers by about 25 per cent.

The most careful analysis failed to show anything wrong with the principles upon which the original or dealer's no-trump bid was based, so I turned my whole attention to the dealer's partner.

THE PARTNER

IN COMPARING the two great classes of declarations, suit bids and no-trumpers, I came to the conclusion that the success or failure of the suit bids depended entirely upon the partner's having a precise scale of values upon which to base his assisting or denying the suit named by the dealer.

I could not find any such accurate and well defined system to guide the partner when the original call was one no-trump.

W. C. Whitehead gives six rules for taking out no-trumpers, but they are merely statements of his opinion, with no facts or figures to back them up. He says to take out with any six cards of a minor suit and a trickless hand, but not with five. What is the difference between five and six? I think it can be shown that the number has nothing to do with it.

In studying the method of bidding and denying suits, which seems to work so perfectly, I came to the conclusion that it should be possible to discover an equally serviceable and invariable rule for no-trumpers.

As there is no such rule, one had to be invented or discovered, and the only way to accomplish this was to try out several methods; but the first thing to do was to discover the precise type of hands in which no-trumpers failed, and to segregate them, as it were.

The dealer's hand being admitted to be uniformly a minimum of five tricks, and to average seven, it is unnecessary to pay any further attention to that side of the table.

ON EXAMINING the partner's hands, it was found that 710 of them contained anywhere from three tricks to nothing, and 290 of them four tricks or more. In the 710 cases, the no-trumper, if left in, failed to fulfil the contract 280 times, at a cost of 20,950 points in penalties (without doubling); won the game only 149 times, and was left with a partial score 281 times; but still had a net profit of 3,925 points. This is about 5 1/2 points a deal.

In the 290 cases in which the partner held four tricks or more, there was a net profit of 36,215 points, which is an average of about 125 points a deal. The danger line seemed to be that below four tricks.

THE DENIAL

The solution of the problem seemed to be how to warn the dealer that his partner is below average on high cards, and to do so just as effectively and unambiguously as he is warned that his partner is shy of the suit, when the dealer names one.

I have already twice demonstrated the value of the invariable take-out with any five cards of a major suit, regardless of its strength, or the rest of the hand, and have published the results of the analysis in this magazine, showing that the take-out would win an average of about fifty points a deal, as against leaving the no-trumper alone.

The only objection to this take-out that has ever been brought forward is that the bidding does not stop there, and that the dealer is always in doubt as to whether the take-out is from strength or weakness, and is in a quandary as to what he shall do.

If that objection can be removed, absolutely and completely, it must be admitted that there is nothing to be said against the take-out. I have the following rule to offer as the solution of the problem, and, so that no "authority" need be blamed for it, I shall call it

THE FOSTER TAKE-OUT

With three tricks or less, counted at bidding values, always take your partner out of a notrumper with any five-card suit, major or minor. With more than three tricks, leave him alone unless you have a singleton, or two five-card suits, or a hand that you are perfectly willing to rebid.

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This rule is based on the fact that with three tricks or less, the take-out is a big winner, and that with four tricks or more it does not make the slightest difference, in the long run, whether the hand is played at the take-out or at no-trumps.

With three tricks or less in the partner's hand, the net profit of the no-trumper, if left in, is only 5 1/2 points a deal. If taken out it is 67 for the take-out, a difference of 61 1/2. The full details are worked out in "Modern Bridge Tactics", published by Dodd, Mead and Co., and are epitomised here by their permission.

When the partner has four tricks or more, we get the following table of results, the left-hand column showing the partner's trick holding. These figures have been reduced to percentages, so as to show the average values, without having to allow for the varying number of cases in which the partner held a different number of tricks.

At No-trumps Games Tricks

At Suit Bids Games Tricks

4 65936 63 1,054 5 79 1,042 79 1,052 6 100 1,078 100 1,054 244 3,056 242 3,160

When the dealer is taken out of his no-trumper, he knows exactly what to do. If he has the proper suit distribution for a no-trump bid, he will have normal support for the take-out and need never deny it. If it is overcalled, he need not say anything, because if the take-out is strong, it is strong enough to rebid the hand, and is ready to do so, and it is a hand in which the suit distribution is not favorable to the success of a no-trumper.

It has taken about two years to go into all the details of this problem, just for the five-card-suit take-outs. Whether I shall ever find time to carry it out for the four-card take-outs depends on circumstances. Perhaps some man of leisure who can devote about a year to the problem may do it for us.

ANSWER TO THE MAY PROHLEM

This was the distribution in Problem LXXI, which is a good example of forcing discards from an opponent before discarding yourself.

Hearts are trumps and Z leads. Y and Z want six tricks. This is how they get them:

Z leads diamond queen, which Y trumps with the jack of hearts. Y then leads the six of trumps and Z picks up both B's trumps. On these three tricks A must make three discards.

Supposing A's first discard to be a club, he must finally get down to one club and three spades, or to two of each suit. If A keeps three spades and a club, Y will keep two of each suit, and Z will lead a small club for the fourth trick, putting A in. A now loses two spade tricks to Y, and Z makes the jack of clubs at the end.

If A keeps two clubs and two spades, Y keeps three spades and one club. Now Z leads the losing diamond, putting B in, and avoiding A's hand, while Y discards the remaining club, so as to make all three of his spades when B is compelled to lead that suit.