Valuation and fit in suit contracts Larry Hammick larry@hammick.com 2001.07.31 Contents ;The meaning of fit ;Duplication ;Picture bidding ;Game tries ;Slam tries ;Quacks in competition ;Support for a good suit ;Volatile values ;Choice of suit with a misfit ;Other notes on the choice of suit ;Freaks of valuation ;Fit implies fit ;Point count and losing trick count ;The meaning of fit The term "fit" has a couple of different meanings. It sometimes refers to a trump fit: "We had a fit in hearts." We are concerned here with the other meaning of "fit": the degree to which our side's two hands are working in combination. What fits with what? It's simple: I: Length fits with strength. II: Shortness fits with losers. Among good bidders, these factors seriously influence decisions on games and slams. On other occasions, in competitive auctions, they sway a decision whether to defend or bid on. To prove that fit makes a difference, consider this pair of imaginary deals: AKxx AKxx QJxx xxxx xxx Qxx xx Jx xxx xx Qxx Jx xx xxx Jx Qxx AKxx QJxx AKxx xxxx QJxx AKxx xxxx AKxx QJxx xxxx AKxx AKxx xx Jx xxx Qx At left, either side readily makes 9 tricks in either of its fits. At right, the distribution and the gross high-card strength of each hand is unchanged, but now only 7 tricks will go to the declaring side. (The defence can cash 4 and wait for 2 more. Or West, say, can cash his AK and exit with a third diamond.) Another illustration: KQxx xxx AKQx Ax AJxx xxx x KJxxx You have 3 top losers. But interchange South's (or North's) red suits and you have a very good chance for 6S. From the above illustrations emerge two principles about how the value of a hand changes with the appearance of a trump fit: Pictures in that suit increase in value. Queens and jacks elsewhere depreciate considerably. Both notions may be thought of as corollaries of (I) and (II). To keep a constant total on the value of high cards, we need to revalue side aces upwards, and the ace of trumps downwards. Kings are intermediate cases and change little in value either inside or outside the long suit. There are limits to the validity of (I) and (II). As for (I), it would be more accurate to say that _trump length plus_ shortness fits with partner's losers, for the value of the shortness runs out when the ruffers run out. And for (II), if a trump suit is as strong as AJxxx KQxxx the Q is very probably, and the J almost certainly, a duplicated value -- you would rather have Axxxx/Kxxxx and another 3 HCP somewhere else. ;Duplication Poorly fitting hands display the opposite of (I) or (II) or both: shortness facing strength, or losers facing length. AKQx facing a singleton, above, was a very bad case. How many points (other than the ace) which face a singleton make the fit "bad" is relative to your overall strength. If, for example, you have 13 HCP and 3 cards opposite a singleton, you will average to have about 3 points in that suit. More than 3 would be a relatively poor fit. Another variety of poor fit is shortness facing shortness, called "collision" or "duplication of distribution". One hand, irrespective of the other, may be defective by reason of having strength and shortness in the same one suit, such as a stiff K or Qx. Even a singleton ace or doubleton AK is a defect. When strong short suits appear in both hands, one sees the worst kind of duplication, e.g. the doubleton KQ facing the doubleton AJ or the singleton A, or two singleton honours colliding. There is some duplication even in strong colliding trebletons, such as AQx/Kxx: 9 HCP normally do more than just take 3 tricks. When you reach a poor contract, try to see if there was unlucky duplication between the two hands before you blame your bidding. ;Picture bidding In the section following this one, we will look at bids which serve specifically to evaluate fit. In this section we just mention some general bidding policies. Try not to bid weak suits on strong hands. xxxx AKQJ Axx Ax Depending on system, I might open 1H, pretending to be 4-5 or 3-4 in the majors. Jxxx AJx KQx AQx If I open 1NT and partner uses Stayman, I will say 2D, concealing the spades. Systems which emphasize distribution irrespective of suit quality can get into difficulty with evaluation, without always avoiding the wrong denomination. A notrump bid suggests scattered strength. It should sometimes be avoided on strength which is relatively concentrated. For example, the traditional opening 1NT on 16-18 suggests stoppers in 3 suits. In competitive auctions, don't get too busy on primarily defensive hands. Many players seem to think that if a hand has the values for a bid, then a pass cannot possibly be better. It can. In the same vein is this principle: In competition, it is usually right to raise partner as soon as possible, but not always. Say it goes S:1D W:1H N:1S and you, East, hold QJxx xxx Qxxx Ax. Your quacks are worth a lot more on defence than offence. Valued at hearts, you are not worth a raise. 1NT is better than 2H in that 2H may still be available later. A pass might be best: when the adverse bidding peters out, partner will know approximately your gross strength and distribution, and the opponents won't. Occasions for a well-timed pass over a forcing enemy bid or takeout double are fairly frequent. When you back into the auction on the next round, partner should place you with a largely defensive hand and the values for a probable plus score. For slam ventures, three small cards in partner's side suit are a very bad sign. AJxxx Qxxx Ax Kx xxx AKJx KQJx Ax North opens 1S and the heart fit comes to light later. Twelve tricks are highly unlikely despite 32 HCP and a double fit. ;Game tries A game try is an invitation to game which, at the same time, helps partner to evaluate the fit. The well-known short-suit game try is a direct application of (II). The traditional long-suit try is not as simple. 1H 2H 3D ? Responder looks at his diamonds to evaluate the fit. A singleton is good, doubleton is so-so, 3 small is bad, 3 with 2 pictures is good, Kx is ideal. But it is something of a guess how these cards will be used: whether to develop partner's length or just to take care of some losers. Opener may have: KJ KQxxx AQxx xx or KJ KQxxx AJxxx x He should not have: Kx Qxxxx AKQx Qx On this last hand, using long-suit game tries, it is better to say 3H or 2NT. For suit play, partner will then revalue his aces and kings upwards, quacks downwards. A third type of game try is feasible: bidding a side suit which contains "honours of uncertain value", such as KJx. For this type, a singleton fit is bad, length or strength is good, xxx is average. This type of game try is already in use, in an indirect way: Qxxx xx Axxx KJx Partner opens 1S. In the traditional Goren method, this hand is too strong for 2S or 1NT, and not strong enough for 3S or 2NT, both of which are forcing. So you must bid a side suit, planning to support spades on the second round. To help your side evaluate the fit, you should say 2C rather than 2D. ;Slam tries Evaluation of slams, too, can apply the basic principles (I) and (II). The splinter bid is a short-suit slam try. If you show 13 HCP and a singleton, there is a probable slam if partner has 14 HCP outside the suit of the singleton. Pictures facing the singleton are, as a rule, duplicated values. Even an ace opposite a singleton might be of more value somewhere else, protecting some losers or speeding up the development of some length. A double fit can produce a slam on 26 points or so. Such slams are not terribly frequent and are usually missed by average players. Axxxx KQxx AKx xx x Ax QTxx KJxxx The "delayed game raise" of Acol might find this slam. 1S 2C 3C 4S Now opener can see that slam values are present. The delayed game raise shows a real side suit and a 6-loser hand with opening values. But many pairs, who play mostly at match-points, would fail to diagnose the secondary fit in clubs because they would not take each other's club bids seriously. For them, the very mention of a minor suit can only be: -- a suggestion of 3 NT -- a demand for 3-card support for one's 5-card major -- a demand that partner show any 4-card major! The revaluation of side honours -- aces up and quacks down -- is especially sharp in double-fit deals. ;Quacks in competition As we said, quacks improve in value when they become trumps. This applies whichever side holds those quacks. Look again at the two imaginary deals above. They make this point: in competition, you should tend to bid on when your quacks are in your side's suit(s), but to defend when they are in the enemy's. There is a secondary reason to do so: it is a lot easier to score unprotected honours as a defender than as declarer. ;Support for a good suit In suggesting a suit as trumps, length is more important than strength. That is because, although high cards improve a little when they become trumps, small cards improve a great deal. But when partner has shown a _good_ suit of some length, a fitting honour is sure to be of real value. When partner has rebid a suit, or has come in with an overcall which must be based on a good suit, a singleton J is as good support as xx, and a singleton Q almost as good as xxx. Axxxx xx AKJTxxx Q x KQJxx -- QJTxx 1H 2D 2S 3C 4H Pass. Do not be tempted to take a preference. ;Volatile values The tendancy of picture cards to go up or down in value has a corollary of which few players are aware: If your pictures are all in two suits, the value of your hand is volatile. If partner has length in both, your offensive value will sharply increase; if length in the other two, sharply decrease. Your defensive value will go sharply down or up, respectively, at the same time. Now if partner has two suits, only about once in six times will he hold both of yours (less, actually), and once in six will he hold neither. On the other two-thirds of the deals, he will hold one of yours and one of the others, in which case your net value will change relatively little, either for offence or defence. Still, for those one in three on which the difference is great, it would be well to be able to show where the pictures are. AQxxx KJx AKx xxx Axxx KQJ x xxx We have given East only twelve cards. If his thirteenth is a spade, 6S is pretty cold. If a heart, it has little play. If a diamond, 6D is good but not 6S. If a club, 6S has some play on a dummy reversal. The point is that East is 4-3-3-3 in all 4 cases. East has a "volatile" hand, and this deal seems to be one on which an honours-of-uncertain- value slam try would serve well. ;Choice of suit with a misfit Any misfitting pair of hands lies somewhere within a spectrum of which the following cases are typical. North South 1-suiter facing 1-suiter 7-3-3-0 0-3-3-7 1-suiter facing 3-suiter 7-2-2-2 0-4-4-5 2-suiter facing 2-suiter 5-5-2-1 1-2-5-5 The first type has a strong tendancy to play better in the long suit of the _weaker hand_. The stronger hand will have entries, but the weaker hand will not unless its suit is trumps. In the second type the long suit should be trumps. It will take some tricks even if it cannot keep trump control. The worst type of misfit is that of mismatched 2-suiters, the more so as such hands are deadly on defence. The hand with the better suits is less likely to lose trump control. But if the hands are not strong, the sooner you get out of the auction the better. Players who like to get busy on weak 2-suiters sometimes go for 800 or more even with a 5-3 plus a 5-2 fit, and even against normal breaks. ;Other notes on the choice of suit One suit may be better than another by reason of the scoring. For instance, the chance of game might be better in a 4-3 major fit than in a 4-4 minor. At match-point scoring there are various other such cases, but we are concerned here only with how one fit can take more tricks than another. A side-suit shortage in the short trump hand is better than one in the long trump hand. In particular, 4-3 fits usually play well enough provided that the 4-card holding is safe from a force. If North is 5-4-3-1 and South 2-3-4-4, diamonds are better than hearts, and may be better than spades, for a partial. If trump control is shaky, a 6-2 is better than a 5-3, and a 5-2 is better than a 4-3, as a general principle. At higher levels, one fit can be better than another which is equally long, or even longer. The reason has to do with controls in the other two suits and discards from them. AJxx Axxx KQxxx KQxxx x x Axx xxx KQxxx KQxx AJxx AJxx Ax xx xx KT9 At left, 7H has practically no chance, but in 7S a club can be discarded on hearts. To look at it another way, in 7S a ruff can be had in the _short_ trump hand, gaining a trick. At right, similarly, 4S is better than 4H. This phenomenon about discards has an important special case: the choice between a 5-3 and a 4-4 for a slam. The 4-4 is preferable, unless it is too weak and there are tricks in the other two suits. But you will frequently see pairs in slam in a 5-3 major rather than a 4-4 minor because of deficiencies in their bidding system. When there are two fits of equal size, it can happen that the _weaker_ suit makes the better trumps. The reason is that it costs nothing to leave an isolated high trump at large, but if that card is a stopper in a needed side suit, declarer needs to expend a tempo to drive it out. E.g. Axx Axx xxx KQxx Kxxxx KQJTx Q xx 4S needs trumps 3-2 but very little else. 4H could lose control against diamond leads, even if both majors are 3-2. Because this phenomenon is not common, bidding systems cannot afford to make much allowance for it. ;Freaks of valuation We will just mention two rare and exceptional types of superfit: The 3NT hand based on what appear to be suit-type values, and the suit contract with a solid 4-3 or 4-2 side suit and controls. KQxxxx AJx Ax xx xxx Axxx Ax xxxx 3NT is cold on only 22 HCP. (Such a pair of hands can be constructed containing as few as 15 HCP.) Don't worry about how to reach it, because the opponents have at least a save in hearts. This pair of hands appears to contradict these notions about the 4-3-2-1 valuation scheme: 1. Minor honours are undervalued for NT and overvalued for a suit. 2. For aces, the opposite. But the fact is that the above hands _are_ worth more at spades than at NT: you have a chance of 10 tricks in spades but not in NT. You would prefer to be in NT only because game is cheaper there. (Off the topic, on those rare deals in which the par result is a sacrifice in NT, the sacrificing side's hands are of this type.) Now the second type. -- xxxx AJxx KQx AJxxxxx KQxx Ax xx 7D is cold, barring only a ruff of the opening lead. The J of hearts is a sure trick and it provides a club discard. It is worth more than the KQJT of spades. But if we move one of East's spades to clubs, the grand slam has almost no chance. How can one hope to evaluate fit down to the level of a fourth-round discard on a J? Maybe it's not altogether hopeless. If West shows his spade void (and maybe also his extra trump length) EW can evaluate their hands as if there were only 3 suits in the deck. In a 3-suit game, each suit would be led 4 and one-third times, on average, rather than just 3 and one-quarter times. Jacks, therefore, would have relatively greater importance. Maybe we should experiment with a 3-suit point count, e.g. 5-4-3-2-1 for A-K-Q-J-T. ;Fit implies fit Below are a few facts about fit-implies-fit. All are easily proved by simple arithmetic. If NS's best fit is: then EW have one of these, or better: 7/7 8 or 7/7 8 8 or 7/7/7 9 9 or 8/8 or 8/7/7 10 10 or 9/8 or 9/7/7 or 8/8/7 11 11 or 10/8 or 10/7/7 or 9/9 or 9/8/7 or 8/8/8 12 12 or 11/8 or 11/7/7 or 10/9 or 10/8/7 or 9/9/7 or 9/8/8 On any deal NS have at least one 8-card or better fit or at least two 7-card fits; likewise for EW. If both sides have a fit of the same length, anything from 7 to 13 cards, then each side has a secondary fit of at least 7 cards, and these secondary fits are also of the same length. ;Point count and losing trick count The following two notions about the accuracy of the point count are well known: 1. The point count is very accurate for fairly balanced hands, but becomes less and less accurate as the hands become more unbalanced. 2. Relative to the minor honours, aces are somewhat overvalued for play at NT and undervalued for play at a suit. 1: The point count is "additive" or "linear", as a mathematician might say. Your side's point count in a suit, or in the whole deal, is the sum of your hand's and partner's hand's. This sum is fairly reflective of their combined trick-taking potential, so long as the high cards cover losers opposite, which for balanced hands is generally the case. But the linearity breaks down on unbalanced hands; then the value of a high card is more dependant on its location. In some parts of the world, notably Italy, unbalanced hands are evaluated by means of a loser-count, or losing-trick count. A "loser" is any card less than a queen, except the fourth highest or any smaller card in that suit. E.g. AQx 1 loser Kxxxx 2 KQxxx 1 x 1, for a total of 5 losers A refinement of the loser-count goes like this: count the fourth card in a suit (except the case AKQJ) as one-half loser, and for each card beyond four, deduct one-quarter loser. Given a satisfactory trump suit, if one partner has X losers and the other has Y, that side can expect to make 24-X-Y tricks. Two six-loser hands, for example, add up to a small slam. AQx 1 loser Kxxxx 2 KQxxx 1 x 1, for a total of 5 losers Given a satisfactory trump suit, if one partner has X losers and the other has Y, that side can expect to make 24-X-Y tricks. Two six- loser hands, for example, add up to a small slam. 2: The high cards in a hand may be worth more for NT than for a trump contract, or they may be worth less. The reason for the difference is very simple: long cards take more tricks at NT than at a suit, since ruffs take none. Even on a flat hand, you might accept an invitation to 4S holding holding three aces when you would not accept an invitation to 3NT. Conversely, despite a known 5-4 or 6-3 major fit, a handful of minor honours might bid 3NT but not 4 of the major. The 4-3-2-1 count may be thought of as a compromise between a more accurate "suit count" (such as 6-4-2-1, which has been used) and a more accurate "NT count" (such as 5-4-3-2-1). It is up to the bidder to adjust his count according to the nature of his points and whether he is suggesting NT or a suit.