Bridge Hand Evaluation

Source: https://betbubbles.com/ Good bidding is not merely a matter of having a well-developed system and of knowing it. Far more important than having a good system is good judgement, and the basis of good judgement is intelligent hand evaluation. To a beginner and, alas to far too many experienced players, hand evaluation is a matter of counting points, mostly for high cards (HCP) but with some adjustment for holding a long or short suit. There is far more to it than that, as I hope to show over the next few months. Let’s start by listing the factors you should take into consideration when evaluating the strength of your hand.

1. 1. Shape

Even when intending to play in no trumps, holding a long suit can be a plus feature. Even 4-4-3-2 should be considered to be stronger than 4-3-3-3 as it gives two possible sources of an extra length trick rather than only one, while in a suit contract the doubleton may provide a trick by ruffing. A five card suit gives the possibility of two extra length card tricks, so a 5-3-3-2 shape would be considered to be better still.

1. 1. Honour Combinations

Two honours in combination in the same suit will tend to be more powerful than the same two honours split between two different suits. A holding such as Qxxx needs a lot of help from the partner’s hand before it will supply many tricks, whereas K-Qxx is a holding with some potential even opposite three low.

1. 1. Honours With Length

Honours in your long suits will tend to pull their weight better than honours in short suits. This is because it will make it easier to establish extra length tricks if you have high cards in the long suit. For example, K-Qxx in your long suit and xx in a sidesuit will be more useful than xxxx as a long suit and K-Q as a side suit.

1. 1. Intermediates

Intermediate cards such as nines and tens can make a big difference to a hand, particularly if they are backing up one or more higher honours. For example, try A-J-10-9 opposite xxx, then try A-Jxx opposite xxx. That should leave you in no doubt about the power of intermediate cards.

1. 1. Sidesuit Shape

Even when holding a long suit, your sidesuit shape is worth taking into consideration. When pre-empting, 7-2-2-2 is always considered to be the worst possible shape, while 7-3-2-1 is better and 7-3-3-0 or 7-4-2-0 better still in the long run. This is because 7-2-2-2 threatens to have losers in every suit, needing the partner to have a lot of strength if he is to cover them; also, you have no suit in which to establish tricks and are unlikely to be able to ruff anything in dummy. The more unbalanced your sidesuit shape becomes, the better the chance of just getting lucky with the position of partner’s high cards, and the greater the possibility that you will have an unpleasant surprise for the opposition should they come into the auction. All the above are factors to consider when taking a close decision whether to open a hand, or perhaps to look for game or slam after your partner has opened the bidding or responded. When you are not the first to bid a suit the position of your honours should also be taken into account bearing in mind the bidding to date.

1. 1. Partner’s Suit

Honours in partner’s suit(s) will tend to be more valuable than honours in unbid suits. This is because you are providing cards which may help to establish his long suit for extra tricks. If partner bids two suits, shortage in one of them can also be useful, but only if you have genuine support for the other one so that you can ruff any losers he may have in the first suit. You must have sufficient trumps to look after all his losers or the shortage may not be as useful as it looks at first glance.

1. 1. Opponents’ Suits

Honours in the opponents’ suits are generally less useful than in your sides’ suits in that, while they may be necessary as stoppers, they will rarely produce many length tricks. It is necessary, however, to distinguish between suits bid on your right and suits bid on your left. If RHO bids spades and your spades are A-Qx or K-Jxx, you could reasonably upgrade them as your strength rates to be sitting over the missing strength, increasing the chance of your high cards making tricks. Conversely, xxx would be a poor holding as any strength your side holds must be in the partner’s hand, under the missing high cards. If LHO bids a suit in which you hold A-Qx or K-Jxx, you should downgrade it; this time it looks as though their strength is sitting over your strength, making tricks hard to come by. On the other hand, three small becomes a reasonable holding as you have no wasted values and partner may have well-placed cards.

1. 1. Opposite Shortage

If the bidding makes it clear that partner is short in a suit, a holding such as xxx(x) is a very good one, assuming that you have a trump fit elsewhere, as it means that you have no wasted high cards and partner can easily ruff your losers in the suit. Conversely, K-Jxx would be a poor holding as the honours will provide few tricks if any compared to partner simply ruffing your losing cards. Better to have those honour cards in some other suit where they may combine well with high cards in partner’s hand to produce tricks. This is why so many regular tournament partnerships play Splinter Bids, as these help immediately to show whether the hands are fitting well, with no wasted values, or badly, with honours facing shortage. Having got the theory out of the way, in the next article we will start to look at some examples to illustrate what all this means when it comes to upgrading or downgrading hands from the strength given by the raw point count. The difference is not quite so great this time, but hand (iii) has an important edge over hand (iv) nonetheless. It is that all its honours are in useful combinations. Even without fitting honours in partner’s hand, this means that you have suits you can play on, while if partner does deliver a fitting honour any of the three suits could be a very useful source of tricks. Conversely, hand (iv) includes unsupported honours and less attractive honour combinations. The Q would be an excellent fitting card, but in most suits a single fitting honour will not create a suit on which you can play without running the risk of establishing extra defensive tricks.

(v)		63	(vi)		QJ
		K83			AQJ
		QJ84			K843
		AQJ5			8653

The same shape and the same honour cards, but hand (v) has the edge because there are more honour cards in the long suits where, not only might they make tricks in their own right, but where they might help to establish extra length tricks. Honours in a short suit may still win tricks themselves, but they are less likely to help to establish length tricks.

(vii)		98643	(vii)		AQ986
		AQ			43
		KQ			32
		J832			KQJ8

Again we see two hands with the same shape and honour cards, but I hope you can see that hand (viii) is much the stronger. The doubleton honours in hand (vii) are not pulling their weight at all. Consider that you hope to find a trump fit with partner and that the most likely place to find one is in one of your long suits. Either black suit in hand (vii) would require partner to hold a number of honours as well as length if you were not to have trump losers, while just one honour may be sufficient opposite one of hand (viii)’s black suits. Quite apart from anything else, the one suit in which you cannot avoid losing whatever tricks are due is the trump suit, in any other suit you have the prospect of discarding losers on winners in another suit. Again, if you play a very aggressive style, you might wish to open both of this pair of hands. Really, however, only hand (viii) looks like an opening bid to me. Hand (vii) has plenty of defensive values but has a lot of potential losers as declarer or dummy, so it makes more sense to Pass. You can always reevaluate your hand if partner opens the bidding but it is hard to see what you will miss if partner cannot open, and you certainly do not want to open 1and encourage him to lead a spade if you end up on defence.

(ix)		A84	(x)		A84
		K5			K65
		AJ1096			AJ109
		1095			1095

A long suit can be a useful source of extra tricks. Imagine that partner has three small cards opposite your AJ10; you have a good chance of taking two tricks; opposite AJ109, you are favourite to take three tricks; opposite AJ1096 you rate to make four tricks. On that basis, hand (ix) will often be a full trick better than hand (x). Though the difference will not be quite as great if partner holds only a small singleton or doubleton, the extra card may still prove useful so to count both hands as being worth 12 HCP can hardly be correct. Suppose that you opened each hand with a weak no trump and partner invited 3NT. Even with hand (x) you are close to being worth a game bid as, though you have only 12 HCP, the diamond intermediates are a significant plus feature (much better than AJxx), worth almost a full HCP. Hand (ix) should be an automatic 3NT bid. The combination of long suit plus intermediates makes this into a maximum, despite its mere 12 HCP. Though even the beginner is taught to add a point for a five card suit, this should not be considered to be an absolute rule.

(xi)		KQ8	(xii)		AQ8
		QJ5			QJ7
		KQ1092			107643
		85			A9

While the diamond suit in hand (xi) looks as though it may provide several tricks and so justifys upgrading the hand by at least a point, that in (xii) will require a lot of work to establish. While all the honours in (xii) are O.K. I would not consider the fifth diamond to be much of a plus feature at all and would value the hand at its basic 13 points . Once again , if we had opened with a weak no trump and heard partner make an invitational raise, hand (xi) would have an automatic acceptance while hand (xii) would be much closer, though I suppose that I would bid the game, I would not be at all surprised to find it going down. I hope that I am starting to convince you that there is more to judging a hand than just counting HCP When looking for a long suit on which to play, even a four card suit is better than nothing. Take these two hands:

(a)		A1094	(b)		A1094
		KJ3			KJ63
		A64			A4
		J105			J105

Hand (b) is stronger than hand (a) because it has two four card suits. This gives declarer two possible sources of a length trick as against only one with hand (a). Also, two four card suits doubles the chance of finding a 4-4 trump fit and, what is more, if you do find a trump fit you have a ruffing value courtesy of the doubleton diamond which may provide an extra trick. Which of this next pair would you rather hold?

(c)		AK76	(d)		A3
		K1094			1085
		A3			AK76
		1085			K1094

The correct answer is hand (c). Although the hands look identical, and indeed are identical in terms of playing strength in no trumps, this hand offers the possibility of finding a 4-4 fit in either major, which may be better than playing in no trumps. Hand (d) only offers the possibility of finding a fit in a minor suit, a less attractive option as it means playing game at the five level, and even a partscore will score less well. Let’s look at one more set of balanced hands, then we can move on to something a little more exciting.

(e)		Q865	(f)		AJ106	(g)		A865
		Q732			AJ93			AJ93
		AJ7			J4			Q87
		AJ			QJ8			QJ

It is good to have honours in your long suits, particularly ones which may eventually become trumps. It is also good to have honours in combination in the same suit, where they can back each other up. It is also good to have intermediates in suits where they can back up higher cards. All this means that hand (e) is the poorest as the two long suits are weak and there are too many loose honours. Even the two minor suits are not that wonderful as AJ combinations are only strong opposite some specific holdings in partner’s hand. Hand (f) is better than hand (g) because the two majors have better intermediates and the club suit is more promising than either of the minors in the other hand. Let’s just recap then on what features are plus features, things that might persuade you to upgrade your hand. 1) Many intermediates 2) Intermediates in the long suits 3) Having a five card suit or two four card suits 4) Honours in the long suits 5) Touching honour cards in combination 6) Length in the major suits 7) Holding aces Conversely, features which might make you downgrade your hand, i.e. minus features, would include: 1) Lack of intermediates 2) Suits headed by unsupported honours or two honours which are not touching 3) 4-3-3-3 distribution 4) Honours in short suits, particularly queens and jacks 5) Too many jacks Distributional Hands A distributional hand is any hand including a singleton, a void, or two doubletons. Occasionally, a 5-4-2-2 hand may be treated as balanced if much of the strength is in the short suits but, in principle, this is a hand with which you would like to bid both your suits and give partner a choice. With a distributional hand, it becomes even more important that you have high cards in your long suits rather than the short ones. If a trump fit can be found, that is the one suit in which you will have no choice but to concede however many losers you have, so to play 4 with a trump suit of Q863 opposite 10754 is not a very attractive proposition. Better to have high cards in the trump suit. While aces and, to a lesser extent, kings will always be useful, jacks and queens in your short suits will often fail to pull their weight. Consider this hand:

	AK1084
	KJ63
	Q5
	J2

If you find a fit in either major you will be reasonably happy with the quality of your trump suit. But consider the minors. Opposite many holdings partner might have these doubleton honours will prove to be no more effective than would a small doubleton. Consider that a queen gives you third round control of a suit, but so does a doubleton. Combining the two features leaves you with a case of overkill, two different kinds of third round control. That is not to say that the queen and jack will never be valuable, just not as often as they might be in a long suit. What you really look for in a distributional hand is trick taking capacity in the long suitsand controls in the short suits. In the long suits, high cards are important. In the short suits, an ace or king is very nice but can only be played once. A singleton, on the other hand, gives you repeated control of a suit, subject to your holding sufficient trumps. And, of course, not only does it give you control of the suit, it also gives you a source of extra tricks by ruffing partner’s losers in the suit. Just as a 4-4-3-2 hand is superior to a 4-3-3-3, so 5-4-3-1 is a more promising shape than 5-4-2-2. Similarly, 6-3-3-1 or even better 6-4-3-0 is stronger than 6-3 2 2. And once we get on to holding seven card suits, I would always prefer 7-3-3-0 or 7-4-2-0 to 7-3-2-1 and prefer that in turn to a 7-2-2-2 shape. I will leave you to think why that is the case. In the next article we will see why and look at some illustrative examples. We ended last article by saying that not only the distribution of a hand’s long suits but also its sidesuit shape affected its potential; the more unbalanced the distribution the better. So 5-4-3-1 distribution is better than 5-4-2-2 and 5-4-4-0 even better. Why is this? 5-4-2-2 shape basically offers two possible trump suits, while 5-4-3-1 offers two suits plus support for a third one if partner has five cards there. 5-4-4-0 is even better because it offers three possible trump suits. Also, when it comes to the play, the shortage offers a potential ruffing value which may provide extra tricks if your trump fit is good enough and, even if the ruffs would have to be taken with the longer trump holding, and so might not actually produce extra tricks, you have control in the suit and cannot lose quick tricks there. If you have two doubletons, you will usually need a lot of high cards in the suits between the two hands if you are to avoid losers. With 3-1 or 4-0 shape, you might get lucky that what high cards partner does hold are in the right suit, or he may have shortage opposite your three or four card suit. This applies with all shapely hands. If partner has three or four small cards opposite your three or four card suit, you will have losers there, but there is scope to get lucky and find his strength opposite your length and his weakness opposite your shortage, giving you fewer losers. The more balanced your own hand, the harder it is to get lucky in this way. Let’s look at a few examples to check that we are on the same wavelength. Which of these hands would you prefer to hold?

(i)		A K 7 3 2	(ii)		A K 7 3 2
		A Q J 4			A Q J 4
		7			7 5
		10 9 5			10 9

Both have 5-4 shape and all the honour strength in the long suits a positive feature but hand (i) is better because of the sidesuit shape. Imagine that partner holds something like:

	Q J 8 6
	K 7 3 2
	A 2
	A Q J

Holding hand (i), 6 is cold and you have the club finesse for the overtrick; holding hand (ii), a diamond lead leaves 6 needing the club finesse you still make an overtrick when it succeeds, but you go down if it fails. Of course, 6 might still be cold, subject to a 3-2 trump break, but are you sure you wouldn’t end up in spades?

(iii)		K 10 7 4	(iv)		A Q 10 8 5
		Q 8 6 5 3			K Q J 5 3
		A Q			7 4
		K J			8 6

Unless partner has a very suitable hand for you, (iii) leaves you needing all sorts of finesses and guesses, and losers in your long suits which will probably be unavoidable. Meanwhile, (iv) gives you solid holdings in the two important suits, no guesses, no finesses, and is a much more promising hand.

(v)		A Q 10 8 5	(vi)		A Q 10 8 5
		A K 6 4			A 10 6 4
		10 3			K 5 3
		8 5			8

Now the two main judgement factors are in conflict. Hand (v) has all its strength in the two main suits, but (vi) has the better distribution. As long as the position of the honours is reasonable, the distribution is more important, so in this case (vi) comes out on top, but if a 5-4-3-1 hand had very badly placed honours it would be possible for a 5-4-2-2 hand of the same HCP to be better. Here, for example, if (vi) was changed such that it had three small diamonds and a singletonK, it would be sufficiently weakened as to make (v) the more promising holding. It is possible to have too much strength in your long suit, such that some of it is likely to be wasted.

(vii)		J 6 3	(viii)		K J 3
		A K Q J 10 9			Q J 10 9 6 3
		Q 4			A Q
		8 3			8 4

Hand (vii) includes a beautiful suit which is guaranteed to provide six tricks. Unfortunately, it is not likely to produce much else. The minor heart honours are not really pulling their weight. Give partner three small hearts and the J might just as well be a small card, while the Q will also be unnecessary about half the time. Better then to have those high cards elsewhere. Hand (viii) does not have a solid suit, but it has one which will be solid once the ace and king are knocked out. Meanwhile, two of the side suits have useful honour combinations which could provide more than the two tricks we have given up in the heart suit. Of course, this idea can be overdone. We want a decent suit which will play O.K. opposite a small singleton or doubleton. So QJ10953 is fine but 1076432 would be a liability. Again, 6-3-3-1 is better than 6-3-2-2.

(ix)		K Q 4	(x)		K Q 4	(xi)		K J 9
		QJ10953			QJ10953			Q87543
		A 7			A 7 3			Q 10 3
		8 3			8			A

Hand (x) is clearly the best of the three, having a decent suit, good honours outside and the better shape. Hand (xi) has better shape than (ix) but the honours are less well placed, the bare ace in particular being a negative feature as you have no flexibility in deciding when to play it, and the main suit is poor. These negative factors are sufficient to outweigh the superior distribution of hand (xi) and I would say that (ix) is the second most promising of these three hands. So judgement is not a matter of applying blanket rules which will always rank with the same importance. Extra shape is generally more important than the position of high cards, but only within reasonable limits. Sufficiently good or bad honour dispersion can eventually outweigh differences in shape. We will continue our look at Hand Evaluation in the next article. We move along now to hands containing a seven card suit. How would you rate these three?

(a)		A J 10	(b)		K 7	(c)		K J 7
		J 6			J 6			A
		KQ108743			KQ108743			Q1098765
		6			Q 8			J 2

You are probably way ahead of me by now. Hand (a) is the best of the three. The main suit is good but also the 3-2-1 shape of the sidesuits is superior to 2-2-2 as in (b) for all the reasons we have seen before. And the honour combination in spades is also a big plus feature. (b) has the same main suit but two serious weaknesses; the poor sidesuit shape and the collection of unsupported honour cards. Though (b) has a better diamond suit, hand (c) is the better all round hand. It has better sidesuit shape and one useful honour combination. Give yourself even more extreme distribution such as 7-3-3-0 or 7-4-2-0 and the hand’s potential goes up even more though, as always, the degree of fit with partner will be crucial. The hands with the better sidesuit shape will not always produce extra tricks, they merely give you a better chance of getting lucky. Before we go on to look at a new area of bidding, let’s try a few examples, just to check that we are on the same wavelength.

(i)		A Q 4
		8 5 3
		A J 10 9 7
		10 2

Partner opens 1NT (12-14); what is your response?

(ii)		A J 10 8 6
		K Q 10 7 4
		8 6
		3

You are dealer at Love All; pass or bid?

(iii)		5
		Q 8 4 3
		K 6 5
		K J 5 4 2

Partner opens 1; your response?

(iv)		Q 6
		8 4 3 2
		9 7
		A Q J 8 3

Partner opens 1; your response?

(v)		J 8 6 4
		K 8 3
		A J 2
		Q 9 5

Partner opens 1NT (12-14); your bid?

(vi)		K Q J 9 7 6 5
		8 2
		J 10 9 8
		–

Your opening bid at Love All?

(vii)		K
		Q J 6 3
		A J 8 7 5
		Q 8 2

Your opening bid at Love All? (i) 3NT. True, you have only 11 HCP but imagine its potential opposite as little as three low cards in partner’s hand – and the spade honours are also working well in combination. No guarantees, but this hand is likely to be as useful as a flat 13 HCP and should raise to game. (ii) Open 1. Only 10 HCP but the shape is good and not only are all the high cards in the two long suits but they are backed up by the two tens. If you find any sort of a fit at all, the hand should play very well and produce far more tricks than the raw point count might suggest. (iii) Bid 1NT. 9 HCP and a five card suit qualifies for a two over one response in Acol but there are a number of negative signs which suggest downgrading this collection. The singleton spade is bad news, suggesting a possible misfit with partner, and note that she will frequently be obliged to rebid a five card spade suit over a 2 response yet be able to pass a 1NT bid from us (surely a better option). Also, there are no intermediates in any suit and both red suits feature an unsupported honour card. All in all, best to take a cautious view of what was always a borderline 2 bid at best. (iv) The same 9 HCP and five card suit as in (iii) but this hand is well worth a 2 response. The main suit is a good one and all the honours are well placed, the Q the only unsupported honour, being in partner’s suit where you can hope to find it combining well to establish tricks. (v) Pass. Yes, you have 11 HCP so there could be 25 between the two hands, but will game be such a bargain even then? You have the worst possible shape, no intermediates, and no good honour combinations. Unless partner has good suits on which to play, where will you find nine tricks when your own hand does not contain a single combination, would you be happy to attack? (vi) 4. The 7-4-2-0 shape makes this hand too good for a three level pre-empt. Consider that you would be very happy to open 3 if two of the diamonds were turned into clubs. Even without finding any help in partner’s hand, you can expect to make at least one extra trick from the diamonds, while on a good day a fitting honour could provide two or three tricks. It is winning bridge, in the long term, to pre-empt to the limit immediately. Under-pre-empting means the opposition have less pressure to overcome and so are more likely to judge correctly. (vii) Pass. 13 HCP but three of those are a singleton king which should be downgraded. Also, while there are two honour combinations in the long suits, there are no useful intermediates to back them up. For all that, some players would open this hand. It is unsound to do so and the crucial factor for me is the order of the suits. Say you had five hearts and four diamonds and the same hand; now you could open 1 and have a convenient 2 rebid to describe your distribution. With the actual hand, you must open 1 and frequently rebid 2, overstating the potential of the diamonds and leaving part of your story untold. Better to pass for now and judge whether to get involved later – you will hardly miss a game if there is no later. The Game Try. A bread and butter area of constructive bidding is the decision whether to try for game or settle for a safe partscorer finding a trump fit. There are two halves to this decision, firstly whether to make a game invitation and secondly, after finding a trump fit, whether to accept it. The bidding commences 1 – 2; with which of these hands would you try for game and what should you bid as your try?

(a)		J 3
		A Q J 7 4
		A Q 10 8 6
		5

(b)		5
		A Q J 8 6
		10 9 6
		A K Q 3

(c)		QJ6
		A K J 9
		K 3
		K J 7 3

(d)		Q 8 4
		A Q 8 3 2
		A 7 4
		K 5

(e)		K 5
		A Q J 10 8 6
		J 10 2
		9 7

In his excellent ‘Secrets of Success’, Tony Forrester suggests the rule that opener should try for game if he can give partner two specific cards totalling 6 HCP (i.e an ace and a queen or two kings), will make game a good bet. If two such cards would not be enough to make game a good bet, then do not invite game. The point is, of course, that the simple raise is a very limited bid and to ask for more than two ideal cards in partner’s hand is being a bit over-optimistic. Personally, I would be willing to relax Tony’s rule slightly and allow opener to hope for a specific ace and a king, but the basicprinciple is a sound one and I would not wish to argue too strongly that Tony’s rule was not more realistic than mine. Of course, if opener has a shapely hand, then not all high cards in partner’s hand the rule was not more realistic than mine. Of course, if opener has a shapely hand, then not all high cards are equal. Opener would like his partner’s honour cards to be facing his long suits, where they should be working well, rather than opposite shortage where they maybe less valuable. That being the case, it makes sense for opener’s game try to be as descriptive as possible to help responder to judge the value of his high cards. There are regular tournament pairs who agree that opener should bid his short suit in this situation, allowing responder to judge how much wastage he has, but the standard approach is the reverse of that; opener bids his length or, more accurately, bids the suit in which he has some length and needs help. So, here are the solutions, using the standard approach. (a) Here, game will be almost certain if responder has two of the missing aces and red kings so opener qualifies under the ‘two card rule’. The game try should be 3, focusing partner’s attention on the red suits. Knowing that opener is long in hearts and diamonds, responder will upgrade honours in those suits. But the reverse of that is that opener will be short in at least one of the black suits. Black aces and, to a lesser extent, black kings will be useful to opener but minor honours may play no part in the success or failure of the contract so should be down-valued. (b) You might think that 3 is the obvious game try, but stop and think a moment. You do not need partner to have any help in clubs and, indeed, you know that he cannot have fitting honours. If you bid 3, partner is all too likely to have a bad holding such as three small cards which will discourage him from bidding game. No, your game try should be 3. It is partner’s diamond holding which will decide whether 4 is a good bet or not so that is the suit to which you must draw his attention. He will consider three or more cards with no top honour to be a bad holding and will downgrade his hand – exactly as you would wish. But he will upgrade a shortage or any holding including a top honour, again just what you want him to do. It is true that a holding like Q will get upgraded yet will not actually make the play easy, but this is about the only problem holding and does not detract from the fact that 3will still help partner to judge correctly more often than will any other bid. It may seem strange to make the same bid on two such different holdings as in examples (a) and (b). True, partner will not know which type you have, but that doesn’t matter, all you want is for him to evaluate his own hand. (c) Bid 2NT. There is no particular suit you are concerned about, you just want as many high cards as possible from partner. 2NT tells him that all high cards should be valuable. He can pass or bid 3 with a minimum and bid 3NT or 4 with a maximum. And if he has raised to 2 with something like:

	7 5 4
	Q 6 3
	K 10 8 7 6 5
	4

he can bid 3, non-forcing and showing six diamonds and only three hearts – perfect. (d) Pass. Just try the ‘two card rule‘. Can you construct a hand for partner which makes game a good bet? No, so settle for a safe plus score. (e) Even giving partner two aces does not make game very likely so you should not offer an invitation. However, if you pass 2, it is almost certain that the next hand will protect. The opposition can certainly make a partscore and it is not too difficult to imagine them having a game if their fit is in spades. Make it a little more difficult by reraising to 3. For a beginner, the sequence 1 – 2 – 3 is invitational, indeed, it is the only way to invite game. But there are so many other ways in which to invite game that most regular tournament players prefer to use the reraise in a more pre-emptive fashion, not to invite game but to make life difficult for their opponents – just as here. Partner Makes a Game Try Last month we looked at opener’s requirements to make a game try after she hasopened one of a major and been raised to two of her suit. Now it is time to move round the table and look at responder’s decision whether or not to accept the try. (a) Firstly, let us assume that partner makes her try by rebidding 2NT. So the sequence might be 1 – 2 – 2NT. By bidding 2NT, opener has said that she has a fairly balanced hand and does not need help in one particular sidesuit. As she is balanced, all our high cards may be valuable, even queens and jacks, so really all we have to do is count points and decide whether we are in the top or bottom half of the range we promised with our initial response. With a maximum, we should bid game, while with a minimum we should settle for partscore. But it doesn’t end there. Sometimes we will have raised with only three cards. Partner has only promised a four card suit, indeed, the 2NT rebid will be based on precisely four cards far more often than not, so it is not clear that we want to play in the agreed major. Take these examples after the start 1 – 2 – 2NT:

(i)		J 6
		Q J 8 4
		A 7 6 5
		10 8 3

Bid 4. We have a maximum, four card trump support and a ruffing value. Though we are both balanced, there is no reason to think that 3NT will be a better spot than 4. dddd

(ii)		K 9 8
		K 10 4
		6 3
		Q 9 7 6 5

Bid 3NT. Again we are maximum so must accept the game try but this time we have only three trumps and cannot commit our side to game in a 4-3 fit. The 3NT bid tells partner that we have only three card support but it does not necessarily end the auction. Partner will remember that we started by raising her suit so can go back to 4 if that seems appropriate.

(iii)		Q 7 6
		K 9 8 3
		J 7
		9 8 7 4

Bid 3. We have four trumps so should want to play in hearts but the rest of the hand is quite poor with only 6 HCP and two unsupported minor honours so to bid game would be over-ambitious. Very occasionally, the fact that we promise the fourth trump will enable partner to go on to game herself.

(iv)		6 4
		K 8 3
		J 9 7 5
		Q 8 6 4

Pass. Though we have a small doubleton, the reason why we bid 2 rather than 1NT in the first place, we have only three trumps and would prefer not to commit our side to a 4-3 fit at the three level. Even if partner has five hearts, the long suit may prove helpful in the play of 2NT.

(v)		8
		Q 8 6
		Q J 9 6 4 3
		10 4 2

Bid 3. This is not some convoluted return game try showing values in diamonds. Rather it shows a long diamond suit, normally six cards, and only three hearts. We expect that partner will normally pass 3, though she may go back to a 5-3 heart fit or, with good enough diamonds to hope to run the suit, may gamble on 3NT. In either case, we will respect partner’s decision. (b) Now suppose that opener’s game try is in a second suit. She is saying that she wants us to evaluate our hand with particular reference to our holdings in her two suits. With a maximum, we should accept unless we have the worst possible holding in the second suit – three small cards. Don’t worry about only having three trumps. A good rule is to say that if opener’s game try is in a second suit she guarantees five trumps – that solves all the awkward problems about whether we can afford to jump to game with only three card support. With a minimum we need good cards to bid game. With a balanced hand we need two key cards in partner’s suits; with four trumps plus a singleton in the second suit we need one top honour in trumps or any ace or king; with four trumps and a doubleton any ace, the trump king, or another king plus the trump queen. With only three trumps plus a singleton in the second suit there is less chance of getting all the ruffs we need so we should be looking for an ace plus a trump honour or two kings; with three trumps and a doubleton we need an ace and a king or a king plus two trump honours. After 1 – 2 – 3:

(vi)		10 7 6
		Q 8 6 3
		J 9 4 3
		A 8

Bid 4. We have four trumps, the right ace plus a trump honour.

(vii)		Q 5 3
		Q 9 8 6
		Q 8 6 5
		8 3

Bid 3. We have four trumps, a doubleton club and a trump honour but it is unlikely that both side queens will be useful as partner rates to be short somewhere so we are well short of a game bid.

(viii)		9 7 5 3
		Q 10 6 4
		K 10 9 4
		7

Bid 4. Four trumps, a trump honour, a side king and a singleton club. Plenty to accept the try.

(ix)		6 5 3 2
		Q 10 2
		A 10 7 6 5
		9

Bid 4. Only three trumps this time but a side ace, a trump honour plus the right singleton. Were the A changed to the king, the lack of a fourth trump would suggest signing-off in 3. cccccc

(x)		8 7 5
		Q 9 6
		K Q 10 9 7
		J 2

Bid 3. This is a return game try. You are maximum but have only three trumps and a poor club holding. Show diamond values and let partner decide.

Responder Makes a Game Try

It is not always opener who has to decide whether to make a game try. In an auction such as 1 – 1 – 2, it is responder’s suit which has been agreed and accordingly it is her decision whether to make a move. It is not quite so easy to lay down hard and fast rules in this situation as it was after responder had raised opener’s suit to the two level. Although we know that opener’s simple raise is consistent with a near-minimum hand, that still covers a much wider range of handtypes than in the previous situation. It is worth bearing in mind that our basic bidding methods will have an effect on partner’s likely handtype and therefore on the odds of game being on. Say that we play Acol, or a similarfour card major system, with a weak no trump. Now the sequence 1 – 1 – 2 is entirely consistent with all these examples:

(i)		K 5 3
		Q 8 6 4
		8
		A Q 10 8 6

(ii)		8
		K 5 3
		Q 8 6 4
		A Q 10 8 6

(iii)		K 5 3
		J 8 6 4
		A 2
		A Q J 7

Opener will always have extra values in some form or another, either in high cards (iii) or in distribution (i) and (ii), but there is no guarantee of four card support. Examples (i) and (ii) are also entirely consistent with a strong no trump based system, whether playing four or five card majors. If we have to open one of a minor when holding a minimum balanced opening then even this is a possible hand for our auction:

(iv)		K Q 6
		J 10 7 3
		K 9 4
		K 10 9

Now you might say that you would not open that specific example due to its sterile shape and lack of aces, but the majority of players would. Anyway, you take my point, that in this type of system the 2 rebid may have extra values in terms of distribution but not in high cards and may be a very unattractive balanced minimum. Clearly, if opener’s average hand is significantly weaker in the second style, then responder needs to be that shade better before trying for game. So there will be some hands which will move over 2 in a weak no trump structure but not in a strong no trump structure. This should be considered any time that we think we have a borderline decision. When selecting our game try, we should again bear in mind that partner may have supported us with only three trumps and that at some point, we may want to clarify whether there is an eight card fit. While a 2NT game try, or going back to partner’s first suit, might be based on either four or five cards in our own suit, it simplifies things if a bid in a new suit promises five cards in the agreed trump suit. Forrester, who is assuming an Acol weak no trump base, suggests a ‘Rule of Nineteen’. Responder adds his high card points to the number of cards held in his two longest suits. If the total comes to nineteen or more the hand should at least try for game, if it does not then we should settle for a partscore. Of course, while this is a good basis on which to work, a certain amount of judgement is also required.

(v)		Q 8 3
		A 10 7 6 4
		Q 9 7
		K 4

Bid 2NT. Though we have at least eight trumps and a useful fitting club card, at least one of the queens will be of dubious value opposite an unbalanced hand so to bid game is too much. 2NT tells partner to look at her whole hand, not concentrate on one particular suit.

(vi)		10 3
		A J 10 8 6
		Q 8 6 4
		K 2

Bid 3. Nine cards in two suits plus 10 HCP qualifies under the Forrester rule and the K is a particularly good card. As partner’s diamond holding may be crucial, 3 is the best game try. Note that the strong no trumpers do not have the extra comfort of knowing that the K is well-placed, making things a little vaguer. It will be opposite an unbalanced hand but not necessarily if partner has a weak no trump type.

(vii)		K J
		Q 7 6 3 2
		Q 5 3 2
		Q 8

This hand also qualifies, but both suits are weak, we have no intermediates, and there arepoor honours in the short suits. Game may be on but we are more likely to end up in 3 or 4 going down if we make a try.

(viii)		A Q 4 3
		Q 9 8 7 6 3
		10
		5 4

Bid 2. The count only comes to eighteen but the big trump fit makes it far too easy for game to be on for us to feel comfortable passing. Change the Q to the king and we should bid 4. Making a game try when we need so little help puts too much strain on partner’s judgement.

(ix)		A 6
		K J 9 7 5
		10 4
		Q 8 7 6

Bid 3. The fact that clubs was partner’s first suit does not alter the meaning of 3. It is still a game try with hearts agreed. Some play this return to opener’s suit as constructive but non-forcing, allowing the partnership to get back to the better fit when opener has raised hearts on three cards, but mainstream style is for 3 to be forcing for one round, just like a bid in a new suit. As always, if partner makes a game try in a suit, she wants us to look in particular at our holdings in the bid suits. We will look at our decision over the game try next month. Last month we looked at game trys after the start: 1-1-2. Now it is time to look at opener’s decision opposite responder’s game try. When responder makes a game try in a new suit, opener will start by assuming that this shows around a 10 or 11-count with 5-4 in the two suits. If the game try is 2NT then about 11 HCP is expected in abalanced hand with either four or five trumps, while if responder goes back to opener’s first suit, she only guarantees eight cards in the two suits and a hand not really suitable for 2NT. 1-1-2-2NT-?

(i)		J 4
		Q 8 6 2
		K J
		A J 9 7 3

Bid 3. We have a minimum so should decine the game try but, with four trumps, should go back to the agreed suit.

(ii)		8
		K 9 8 6
		A 5 4
		A 10 9 8 6

Bid 4. Again we are minimum but we have three very good cards plus a singleton and a fourth trump. Game is not certain but it should have fair play.

(iii)		10
		A J 7
		K Q 7 2
		K J 9 5 3

Bid 3. We are maximum but have only three trumps and partner may have only four. The most helpful bid we can make is 3, completing the picture of our distribution and letting partner judge if any game is possible. It is better to play this bid of a third suit asconstructive, showing a maximum, rather than as the same hand without the K. With the weaker hand we have to decide between pass, dubious with a small singleton; 3 despite the lack of a fourth trump; and 3, which suggests a six card suit and only three hearts but is probably the best of a bad bunch as it at least gets us to the right partscore when partner has four hearts and three clubs.

(iv)		A 7
		Q 8 6 4
		K Q 9
		K J 10 5

Bid 3NT. You are both balanced but clearly have the values for game. Partner will usually go back to 4 but it costs nothing to let her know that you have this strong no trump type, just in case she also has weakish hearts and thinks 3NT may be safer. 1-1-2-2-?

(v)		8 7
		K J 6 3
		Q 5
		A Q 9 5 3

Bid 3. We are minimum and the spade holding is poor. Game rates to be poor if partner cannot bid it herself now that we have promised a fourth trump.

(vi)		K 3
		A J 5 4
		9 3
		A 6 5 3 2

Bid 4. Good honour cards and a good spade holding more than make up for the minimum and uninspiring shape. It would be disappointing if game did not have good play.

(vii)		8
		Q 7 6
		A J 8 6
		K Q 10 5 3

Bid 2NT. We have only three trumps and have no fitting honour in spades. 2NT suggests our minimum, our diamond values, and the lack of a fourth trump, leaving partner to judge our final resting place. 1-1-2-3-?

(viii)		Q J 6 2
		8 5
		K 8
		A Q 9 6 3

Bid 4. Another minimum but with a good diamond holding and all our other honours working.

(ix)		Q J
		K Q 10 9
		Q 8
		K J 4 3 2

Bid 3. True we are near maximum in high cards but we are dreadfully short of controls and partner will need to cover a lot of our top losers for game to be good. This has all the earmarks of a 25-point partscore. Opener’s Third Bid is a Game Try. Let’s look at one more game try situation. The bidding begins 1-1-2-2. When should opener make a move? Firstly, opener should bear in mind that the 2 bid will as often as not be based on a doubleton heart, responder even giving false preference with two hearts and three clubs quite often to keep the bidding alive. Responder is also limited to about a 9-count or so as with more she would have done more.

(x)		6
		A J 9 7 6
		K Q 4
		A J 8 6

Pass. We have some extras but opposite a typical responding hand 2 will be plenty high enough. We do not have the sort of hearts which will play comfortably in a 5-2 fit, we have a misfit with partner’s suit, and our own sidesuit will need help from partner to get it going.

(xi)		7
		K Q 10 8 4
		A Q 6
		K Q J 3

Bid 2NT. Partner could hold a small doubleton heart and a 6-count so don’t get carried away and jump to 4. 2NT shows about the values for a 2NT rebid on the previous round but we have gone more slowly to show our distribution. Partner knows pour strength, our approximate shape, and is well-placed to judge what to do.

(xii)		Q 5
		A K J 6 4
		9
		A Q 8 3 2

Bid 3. Again, remember that partner has not promised three hearts. Make a game try by repeating your second suit and she can pass, correct to 3, or if she likes her hand bid game in either suit. Responder Has Made a Game Try – Opener’s Third Bid By the time that both members of the partnership have bid twice and a trump suit has been agreed, a lot of information has been exchanged and the opener is usually in a position to decide whether to bid game or settle for a partscore. 1-1-2-2NT-?

(i)		7 4
		K Q 8
		J 7 5
		A K J 10 4

Bid 3NT. You have a good hand in terms of high cards but only three trumps. The maximumsuggests that you should accept the game try while the balanced nature of your hand and lack of a fourth trump suggests playing in no trump. partner has already heard you show heart support so can go back to 4 if he thinks it appropriate, though he will not often do so after himself suggesting no trump as a possible place to play.

(ii)		Q J
		9 7 6 5
		A Q
		K Q J 5 3

Bid 3NT. Again it is clear to bid game. Though you have four trumps this time, they are weak while both your doubletons are strong. 3NT doesn’t have to be the right spot but with partner suggesting all round strength and a fairly balanced hand you would not be surprised to find 3NT making on sheer weight of high cards while 4 failed due to having two or three trump losers.

(iii)		K J 4
		J 6 3 2
		Q 10 7
		A J 8

Pass. Obviously, you can only hold this handtype if playing a strong no trump. Equally clearly, you must decline the game try as you are completely minimum both in terms of high cards and distribution. Despite the four card heart support, your hand looks right for no trump. You have weak hearts and strength in every other suit with not even a doubleton as a ruffing value.

(iv)		Q J 5
		Q J 7 5
		7
		K Q J 8 2

Bid 3. With a small singleton in an unbid suit plus four respectable trumps, you should insist on playing in hearts. Superficially, your hand is not too bad, 12 HCP plus a singleton, but the lack of aces and kings means that partner will need perfect cards to allow game to make. Consider that he is limited to invitational values and you have only one king and no ace. He can have at most three of the missing key cards and it would be very fortunate if there was no wastage in diamonds.

(v)		9
		K J 8 5
		A 8 7
		K Q 9 7 4

Bid 4. You have reasonable trumps, a good sidesuit and excellent controls with no unsupported minor honours. Much more and you would have raised to 3 on the previous round so it is clear to accept the invitation this time around. 1-1-2-3-?

(vi)		A 4
		K J 7 6
		7 6 5
		A Q 9 7

Bid 4. Again, it is clear that you could only hold this hand if playing a strong no trump based system. If you are doing so, then partner will expect that 1-1-2 will frequently be based on a weak no trump type and will allow for this when deciding whether to try for game. In the context of a weak no trump, your hand is excellent. You have good hearts, a ruffing value, and all your honours are working well. Note that had partner’s game try been in diamonds you would have been significantly less enthusiastic about your hand because of the worst possible diamond holding.

(vii)		A Q
		Q 9 6 4
		K J
		J 9 6 4 2

Bid 3. Had partner’s game try been made in either spades or diamonds, you might have been tempted. But he has length in clubs and hearts, two suits in which you also have length but little strength. Your high cards are not pulling their weight and game will be an uphill struggle.

(viii)		K Q 6
		J 10 8 4
		A K
		Q 10 9 5

Bid 3NT. Given that partner knows that you both have length in hearts and clubs, he may well over-rule this decision, however, that does not mean you should not make it. Your 15 HCP are enough to make you want to try a game contract, yet most of your high cards are in yourshort suits. It may be that 3NT will be safer than 4 and is costs nothing to suggest it. If partner is really unbalanced he will go back to 4 and no harm is done, 1-1-2-2-?

(ix)		8 4
		A K Q 2
		Q 5
		J 8 6 4 3

Bid 3. Wonderful hearts but if anything they are too good, leaving you with little outside. The rest of the hand is pretty uninspiring and the spade holding only moderate. Partner may occasionally be able to bid game when it is correct to do so simply because your 3 bid has confirmed the fourth trump.

(x)		6 2
		A Q 4
		K Q 9
		A 10 5 4 3

Bid 3NT. You only rebid 2 rather than 1NT because of the spade weakness. If partner has spade length then you need no longer worry about the suit for play in no trump. With yourmaximum in high cards, good diamond stopper and only three hearts, 3NT looks the best chance of making game. As always, partner can go back to 4 if he is shapely. But 3NT gives him an option and describes your hand nicely.

Natural Slam Trys

If, after the auction begins: 1 – 2, it is appropriate to play natural game trys, opener describing his hand further to help responder to judge whether to bid game, it seems clear that the same sort of scheme should apply when slam is in the picture after the start 1 – 3 or 2 (Acol) – 3. While opener will clearly have a stronger hand in the latter situation, the degree of fit between the two hands will still be crucial on many deals. Yet most players start to cuebid as soon as they are commited to game and interested in slam. So: 1 – 3 – 4 merely shows a club control plus slam interest and asks partner if he feels like cuebidding in turn. This is one of those rare situations where, at a very small cost, you can ‘have your cake and eat it‘. Some hands lend themselves to natural slam trys, and I suggest that a new suit bid should be exactly that, just as it would be a natural game try if a level lower. Other hands are better suited to the simple cuebidding approach. The solution is to play 3NT as an artificial bid – hardly a terrible loss when you have a guaranteed fit in a major. So: 1 – 3 – 3NT and 2 – 3 – 3NT both say, ‘I am interested in slam, please start cuebidding‘. Of course, this also applies when hearts is the agreed suit. 1 – 3 – ?

(i)		K Q 10 6 5
		7
		K J 4 3
		A K Q

  The traditional approach is to cuebid 4. Partner will cooperate by also cuebidding with all of these hands:

(a)		A J 7 4
		A Q 8
		8 6 2
		J 4 3

(b)		A J 7 4
		8 6 2
		A Q 8
		J 4 3

(c)		A J 7 4
		A 8 2
		Q 8 6
		J 4 3

Facing examples (b) and (c), opener wants to be in slam, which is almost solid. Facing example (a), he wants to stay out of slam as six needs both diamond honours onside, roughly a 25% proposition. Yet in all three cases, facing a 4 cuebid, responder will cuebid either 4or 4. Opener will be sufficiently encouraged to cuebid again, or even launch into Blackwood, and as responder has no way of knowing that the Q is waste paper and the Q gold-dust, slam will be reached. Two times out of three that will be fine, but wouldn’t it be nice if you could stay out of slam the third time? Now imagine that instead of cuebidding opener makes a natural slam try of 4, focussing responder’s attention on his diamond holding as well as just his controls in all suits.

(a)	Opener	Responder
	1	3
	4	4
	5	5
	Pass

Holding two aces, responder is worth a return cuebid below game but when opener cuebids a second time he signs off, realising that his diamond holding is very poor. 5 is not quite safe but it is difficult to stop at the four-level, even when playing natural slam trys.

(b)	Opener	Responder
	1	3
	4	5
	6	Pass

With a superb diamond holding, responder can cuebid above game. 6 is an alternative over 4, suggesting good spades and diamonds but nothing else to cuebid. Slam can hardly be bad if partner can invite it and you have such great holdings in both his suits.

(c)	Opener	Responder
	1	3
	4	4
	5	6
	Pass

Again responder cuebids and opener is encouraged to try again. Unlike example (a), however, responder is willing to bid the slam this time as he has the valuable Q. There can hardly be two aces missing if partner is bidding so strongly. 2 – 3 – ?

(ii)		A K Q 10 5
		K 3
		A Q 7 6 4
		5

The key to this hand will be partner’s diamond holding (he is already known to hold an ace for the 3 response). Make a 4 natural slam try.

(d)		J 8 4 3
		J 10 5
		8 5 2
		A K 7

Responder bids 4. With a bad diamond holding, do not go beyond game to cuebid. Opener will pass 4, knowing there is at least an ace and the K missing to explain the sign-off.

(e)		J 8 4 3
		A J 10
		8 5 2
		K 7 6

Bid 4. A cuebid below game does not promise the earth. Opener should now bid only 4, trusting responder to bid on with the K. With the actual hand, responder passes 4.

(f)		J 8 4 3
		A J 10
		K 5 2
		7 6 3

Bid 4 but this time continue with 5 over partner’s 4 sign-off. Opener can now bid the slam.

(g)		J 8 4 3
		J 10 5
		K 5 2
		A 7 6

With a good diamond holding you can afford to cuebid above game. As you have bypassed 4, denying the ace, it should be clear that you hold the K, so opener will bid 6.