The problem here is that you don't know what your RHO is doing. Is she bidding 4♥ because she has a strong hand and thinks she can make it?  Or is she bidding 4♥ with a weakish hand and, say, 4 hearts, in order to extend the original preempt? 

Sitting North, I would be paranoid that it was the latter, and we were being stolen from. But what can one do about that? If you do decide to act, then the only sensible move would be to make a takeout double (if you've agreed with your partner that such a double would be for takeout).  You could hardly try 5♣ with such a moth-eaten suit.

John Robertson was the only North player to be presented with this problem, and he coolly passed, which was very wise, once you see all the hands. (A double would land you in 4♠ doubled, which will go down 800 on good defence.)  He did better than I would have!  Susan Hammond (East) and Maria Christensen (West) were the only E/W pair to present North with the problem. They didn't land their fish, but they did earn a fine score anyway, as only half the field got to the cold 4♥ contract.  All I can say is that 2♥ was a good bid, and so was 4♥.

If you pass 1♣, a very bad thing could happen. Partner could end up declaring 1♣ holding just 3 clubs himself. In your 3-2 fit, you're surely going to go several down, vulnerable to boot.

On the other hand, it might not be a disaster. Partner might actually have real clubs, and 1♣ becomes your best possible contract. Or maybe your LHO will rescue you with a bid of his own.

Marg Ferguson passed 1♣ and that became the final contract. Partner had 4 clubs, so it was still a non-fit, nevertheless she managed to scramble 6 tricks, for a score of -100 and a 70% board for Marg. Not so bad!

Dawn Braham did even better with her pass. North bid something, and her opponents then proceeded to have a misunderstanding and go down in a contract. That was a top for Dawn. Praise be!

Now let's look at the 1♥ response. How could that work out well? Heaven would be for partner to rebid 1♠, which you could pass with relief.  But that's not very likely. If partner supports your hearts (which is what would happen here), then you still go down in 2♥.

And those are the good outcomes from responding!  What if partner rebids the clubs? Now you regret not playing 1♣.  Or jumps to 2NT? Or jump-raises hearts? Or reverses with 2♦? Bottom. Bottom. Bottom.

I'm happy to try a response to 1♣ with 4 or 5 HCP and short clubs, in the hope that the situation won't get out of hand. But responding with two jacks pretty much guarantees that the situation will  get out of hand. I don't think much of the commonly given advice: "never leave your partner in 1♣".

7 of the 9 Norths bid spades (3♠ over 3♣ or 2♠ over 2♣).  They ended up in 4♠ and mainly went down when the breaks were foul.

2 Norths (Shirley Stewart and Geoffrey Schroder) made a negative double of the club bid. When partner said hearts, they landed in 4♥ making quite easily, despite those bad breaks.

Which choice is superior in theory? It won't surprise you that I think Shirley and Geoffrey did the right thing.  The negative double kept the auction lower (for example, suppose South had merely bid 3♦ over it: you now have the option of trying 3♠ or maybe 3NT). And it brought hearts into the picture.  Look at it this way: the negative double depicted 8 of your cards (4 spades and 4 hearts); 3♠ showed only 5 of them (5 spades).  The negative double was the more descriptive bid.

This is a theme that is quite common. When deciding between two bids, it's often a good idea to make the one that shows more of your hand. For example, suppose you have 6 hearts and 4 clubs, and open 1♥ .  Partner responds 1NT.  Now, should you bid 2♥ or 2♣? Whilst the quality of the two suits might affect your answer, in principle I prefer 2♣ (showing 9 of your cards) to 2♥ (showing 6 of your cards). The 2♣ bid both keeps the auction lower and widens the field of inquiry.

1) In third seat, South might take the option of opening light, 1♥. With 10 HCP after two passes, South suspects that West has a strong hand, and she can get in the way, as well as suggest a potential opening lead to partner. South plans to pass ASAP after this and hope for the best. An interesting alternative is a 2♥ weak-two opening, which has a lot more going for it than you might think. Cath Whiddon was one South who opened 1♥ and this paid off in spectacular fashion. 

West, with 20 HCP had little choice but to double 1♥ and Cath's partner, Patrick Starck, cleverly boosted the auction to 4♥ (obeying the Law of Total Trumps, competing to a 10-trick contract with a 10-card fit).  It's hard to blame East for bidding 4♠ over this, either as a make or a sacrifice. This made West regret getting out of bed this morning, as she didn't have spades for this particular double ... she showed the strength of her hand by bidding 5♣. Patrick pounced on this with a double (looking much more at his ♦AK than the singleton club), and soon after was writing down 500 in the plus column.  Poor East-West had done little wrong to deserve their bottom.

2) If South does pass, I strongly approve of the decision of Rosemary Polya and Jim Stewart, who opened 2NT on the West cards. Technically the hand was a bit too unbalanced for this (two doubletons), but the doubletons were strong and the length was in the minors (suggesting notrumps as a possible superior destination).  They ended up with middle-of-the-road scores, going down in 4♠ (partner transferred them to spades, then gave 4♠ a punt), but at least their blood pressure remained under control.  This is the good thing about 1NT and 2NT openings: they usually put you into a well-understood auction, and that has a lot going for it.

Partner has shown approximately 8+ HCP and a 6-card heart suit. 

There may well be a slam here, but if you're not going to go for one (and no-one did) it's essential to bid 3NT at this juncture. No question a spade will be led to 3NT, you'll win and play clubs. You'll then regain the lead and have AT LEAT 9 tricks: 7 clubs and 2 spades.  And that's without depending on anything from partner, who has 8+ points.  Almost invariably partner will provide some tricks and you will take at least one overtrick in 3NT ... and that will be a better score than anything you can get in 5♣.

The bottom line is this: 5-of-a-minor is matchpoint death when 3NT is a viable alternative. 

John Adams was the one East to bid 3NT in this auction. 12 tricks were his when North, perhaps unwisely, didn't take the ♥AK when given the opportunity.  But even 10 tricks (630) would have outscored all the Easts in 5♣ (making an overtrick for 620).

One other East, Sue Hammon, got to 3NT. She opened a slightly risky 1♣, and when partner responded in hearts and North overcalled in spades, she made no mistake, blasting to 3NT, again making 12 tricks. Same principle: no matchpoint death in 5 of a minor.

Postscript: South (remember South?) had a chance to score a near top on this deal. She has to notice the favourable vulnerability and make a brave supporting bid in spades. If N/S buy a spade contract, even up to the level of 6♠, they will do better than allowing their opponents to bid and make a game.

1) Double looks correct to me. The alternative is a value bid of 5♣, but you are honour-bound to look for the higher scoring major suit fit (spades in this case).

2) This is an ugly decision. I stared at it for a while (looking at all four hands) and still didn't know what to do. If you can survive the hearts, then 3NT might make overtricks (on the basis of your long strong clubs) and score well. On the other hand, there could easily be a slam: partner could have as many as 13 or 14 HCP after all. 

If you do move on from 3NT, you should bid 4♣.  Just like after a lower suit opening, doubling then naming a suit shows a strong hand. Partner would then raise to 5♣ and now ...?  Who knows. More and more I respect the decision of the Easts who gambled by passing partner's 3NT bid: Sheena Kay, Penny Robertson, Shirley Stewart and Derek Stringfellow. Personally, if I can bat at 51% after an opponent's preempt, I'm happy.

One South, Lesley Johnstone, responded 4♥.  I would characterize this as a "winner's misbid". It's a misbid, because it understates the power of the hand ... typically a direct response of a game contract to partner's opening bid shows a weak hand with a very long suit. Partner won't expect a solid 7-card suit, and a slam could easily be missed. But, it's the sort of bid that's typically made by winning players: not quite correct, but an attempt to put off the opponents. South fears successful spade interference by the opponents, and wants to minimize the chance of that: West may well be intimidated and not introduce the spades at such a high level.

Lesley's LHO, Jim Stewart, was not intimidated. He bravely came in with 4♠: he was not vulnerable, and had the makings of 8 tricks (5 spades and 3 clubs). A man's gotta do what a man's gotta do.

Now the spotlight was on North, Sandra Mansell.  She made the correct bid of doubling 4♠ - the last thing she wanted was to hear partner bid 5♥.  (At another table, where 4♠ was bid by West in a slower auction, North passed, and was mortified when South went on to 5♥, down 1.)  4♠ duly went down two, 300 to N/S, a good sacrifice against the making 4♥.

Finally, the play in 4♥. At one table, the defence took a couple of club tricks then switched to hearts. With a third club loser inevitable, Fiona Ferwerda made the correct play of taking the spade finesse for the contract, even though she had a singleton spade opposite the ace. Given that West had bid spades, that was a moral certainty to work. 

What does North's 2♥ show?  Well, it's a new suit at the two-level, so at least 10 HCP.  And it also promises a 5-card heart suit (at least), because with only 4 hearts, partner would make a negative double of 1♠.  Armed with this information, you can start counting points, including distribution points.  You have 19 HCP plus 3 distribution points, total: 22.  Partner has at least 10 HCP, and at least 1 distribution point (there must be a shortage somewhere, as partner partner has 5+ hearts), total 11.  22+11=33, which is the magic number for slam.

You don't see this sort of slam arithmetic much in textbooks, because it's crude. Very crude. But nonetheless, I think it means the 5 of 6 Souths who simply bid 4♥ were seriously underbidding their hand. The sixth South was Margaret Hughes who bullied her way to the 6♥ contract via Blackwood.  The other slam bidder was Jenny Sin, who had a somewhat different scenario, her West deciding to not bid 1♠.  Margaret and Jenny shared the well deserved top.

"Hold your horses!" I hear you cry.  "They'll lead a spade, and possibly take the first two tricks ... bidding slam is ridiculously dangerous"  A fair point. There's certainly room for 10 HCP in partner's hand, but missing the ♠A and ♠K.  Well, you can solve that problem using a slightly sophisticated technique. Over 2♥ bid 5♥. When the opponents have intervened with a suit bid, 5-of-your-major sends a specific message to partner: "bid slam unless you have two immediate losers in their suit".  This resolves the issue where Blackwood can't. Slam here will make if partner has a singleton spade, or perhaps ♠Kx - you're still missing the ace, but there aren't two losers. I'll admit this is an advanced technique, but you have to agree it's cute.

At this vulnerability, South's 4♥ opening should show around 8 tricks. On that basis, North could count three more for his three aces, and then the ♦K was a maybe, as were the spades (maybe declarer will be able to set that suit up by ruffing). There should be somewhere between 11 and 12 tricks available, and so it's a borderline decision whether to progress to slam. Well done to Derek for doing so. The other four Norths that faced this opening bid all passed.

Still, given that there were 13 stone cold tricks on the hand, perhaps we should look at South's 4♥ bid.  The hand's not really worth 8 tricks: it's closer to 10.  South can estimate 7 heart winners (assuming the ace is missing), and two tricks for the ♦AQ.  That's 9, and the fourth diamond has a fair chance of being established as a winner.  By my lights, that South hand is too strong for a 4♥ opening.

So I'm with the three Souths who opened 1♥ (Stan Angelidis, Jan Downing and Fiona Ferwerda).  Their plan was to open 1♥ and rebid 4♥, which should logically show a hand with long hearts that was too strong for an opening preemptive bid.  Alas, none of their partners were on the same wavelength, so they all languished in game. C'est la vie.

You'd like to compete, but how?  There's no real diamond support, and bidding either the long moth-eaten clubs or the short chunky hearts is unpalatable. 

The solution is to double. This is called a responsive double, and applies after the opponents open, your partner intervenes (with either a takeout double or a suit overcall) and the next hand raises their partner's opening bid.  It is basically takeout for the remaining unbid suits. Only one South, Rosemary Polya, made the responsive double, and it ended rather happily.  Partner bid hearts, and they arrived in 4♥. E/W were not up to the necessary trump plays to defeat this contract, and declarer took the ♦AK and all eight of the hearts via a cross-ruff. Impressive!  Good bidding was rewarded with an almost top score.

One more thing. Look at East's hand ... is the 2♠ bid wise?  No it is not! Technically the hand meets the requirements for a single raise: 6-9 HCP and 3-card support. But there are three strikes against it:

1. Minimum points, dead flat
2. A likely useless QJx in overcaller's suit
3. Vulnerable, heading for down in 100s if partner competes in spades

East was asking for trouble by bidding that hand, and in a few cases, trouble duly arrived.

There are only two clubs remaining, the ace and jack.  If you think about it, partner can't have either of them.  If partner started with either ♣Ax or ♣Jx, she would (should) have played her honour at trick 1 to clarify the position for you. And partner can't have started with ♣AJx, as that would mean that declarer has a club singleton, inconsistent with the 2NT opening bid.

No, declarer started with ♣AJx, and has executed a Bath Coup on you. The name comes from the English city of Bath and the olden days of Whist.  Playing small on the first round of the suit, when the king has been led, means that a second round will run up to the ace-jack, giving you two tricks in the suit. The four Easts who faced this situation all continued with another club, gifting declarer a trick.  On best play, declarer will then take the rest, as poor old West is mercilessly squeezed on the play of the black suits. The skilled declarers who gave their opponents a bath were: Yuko Yoshida, Sandra Mansell, John Robertson and Viv Braham.

East needs to switch to another suit, any suit.  My choice would be diamonds, as I would be a little nervous about giving away a trick with either the spade or heart combinations.

Finally, I mentioned that South had a key part to play on this deal. That was in the auction.  Some Souths insisted on a spade contract, to their regret.  The concept of transferring to your major (showing 5 cards there) and then bidding notrumps to give partner the choice between notrumps and your suit is a vital part of the game!

Let's see now. Ace and king of spades, and your hearts are winners after losing to the ace.  The diamonds are likely good for six tricks, and you can trump your second club in dummy. That will make 2 spades + 2 hearts + 6 diamonds + ♣A + club ruff to make 12 tricks.

Before you start trick 2, could anything go wrong? Only one possibility stands out ... South with all four diamonds, which is not impossible given North's big pre-empt.  You can deal with that scenario, as long as you find out about it in time.

The correct play is ♦K at trick 2. If all follow, a second trump to hand, ruff your club, then cross  to your ♠A to deal with any remaining trumps.  But if North should discard on the first diamond, your second trump to hand will include a foolproof finesse against South's ♦J.

Of the six diamond declarers, three got it right: Margaret Hughes, Jo Quinlivan and Valerie Remedios.  The other three diamond declarers all played a low diamond to the ace at trick 2, and discovered that they could no longer ruff a club and finesse South's ♦J.  A small error, but a crucial one. Bridge can be tricky!

A word about North's opening bid as dealer, not-vulnerable versus vulnerable. A variety of choices were made: pass, 1♣ (!), 3♣ and 4♣.  The passer and 1♣er seriously misdescribed their hand.  Two players who bid 3♣ subsequently volunteered 4♣ later: one of the worst crimes of preempters (bidding again, uninvited).  Of course they were ashamed of the pusillaminity (or whatever the word is) of their 3♣ opening and tried to compensate later.  But this has the downside of giving the opponents room they don't deserve. 

Those who opened 4♣ did some justice to the hand and one was allowed to play there for a fine score.  Personally, I'd open 5♣, assessing the hand as worth 8 tricks, but that's just me.

You can surely destroy their 4♣ contract, but before you gleefully double, consider the risk. It may clue the opponents in to the fact that 4♣ is not their best spot.  Perhaps West (or even East) will run to 4♥, a spot where E/W are likely to have a fit. Your defensive prospects against hearts are far less certain.

So I'm with Shyamala Abey and Lesley Johnstone who calmly passed 4♣, which duly became the final unpleasant (for E/W) contract.  Down a variety of tricks for good N/S scores.

One South did greedily double 4♣. She survived the opponents, but not her partner who got cold feet and retreated to 4♠.  This was duly doubled and defeated several tricks for a N/S bottom. Still, N/S were a class act in that when I checked the chat record, there was not a word spoken.

Now let's look at all four hands and as they say, 'discuss'.

I was pleased to see that all Norths ignored the moth-eaten four card suit in the other major and preempted in spades.  Seven opened 3♠ and one wimped it with 2♠.  The 2♠ choice got a 3♣ overcall, so at least E/W were able to play the horrible hand a level lower.

Over 3♠, we've noted that three Easts overcalled 4♣ ... a fairly normal bid.  Two instead doubled, which I don't particularly like, because when partner inevitably bids 4 of a red suit, you won't know what to do.  And two Easts passed 3♠!  I'm not going to name them, because I don't agree with their choice, but it worked superbly for them, allowing N/S to go down in a contract, rather than E/W.  

One "thinking-outside-the-box" option for East would have been to try 3NT. Sometimes, a stopper can be as strong as it sounds.  For example, if you boldly bid 3NT, maybe South will lead a low club!  I know it may seem ridiculous, but if you put this problem to an expert panel, I expect 3NT would gather the most votes. Experienced players love to bid 3NT.

8 of the 10 Easts opened 1♣, and you'll get no complaint about that choice from me. The hand has the points and the shape to justify this, and also an easy rebidding plan: more clubs, and yet more clubs.

On the downside, there's very little defence, and the low opening gives the opponents all the room in the world to intervene, if they have the hand for it.  As it turns out, many North-Souths did successfully get into the auction.

So I prefer the choice made by Shyamala Abey and Viv Braham, which was to open 3♣, preempting.  A vulnerable 3-level opening should have the makings of about 7 tricks, which is precisely what East has.  And it's much harder for N/S to successfully compete against.

The 3♣ openings met with mixed success. At one table, N/S got to 3♥ down 1; at the other, N/S brilliantly wriggled to 3♦, which could not be beaten.

Now let's consider a dramatic alternative opening bid for East: the Gambling 3NT.  Some (many) partnerships play a 3NT opening bid to show a solid (AKQ) 7-card minor, and nothing much outside.  It's a very descriptive preempt, and being at a higher level, more preemptive than a 3-minor opening.  The Gambling 3NT has significant downsides, one being that the correct contract might be 3NT played from the other side, but remains a popular gadget.  And after all, one doesn't particularly need 3NT as having an alternative meaning ... if you are really strong, you can always open 2♣.

Look what would have happened on this deal. East opens 3NT: that's too rich for South, who passes.  West also passes: there's 7 tricks in partner's minor and 2 aces to make 9 ... so E/W just need to survive the other minor to make 3NT. North passes, and South leads the obvious ♠K.  Voila: 3NT making +600 for a top.

If you make a heart bid here, you will often land in the soup. Partner will expect more high-card strength and likely take you too high.  That's what usually happens when you show more values than you have.

If (and it's a big if) partner recognizes a jump in hearts as showing this sort of hand, then perhaps it might work out. My experience is that this tends to put the partnership into unknown territory with mostly bad outcomes.  Today, two Wests tried the jump: one East read it correctly and passed, the other bid too much. 

The best approach in my experience is to try a two-step process.  Pass initially, then if the auction should continue, maybe later you can show the hearts. Partner will know you are weak, because of your initial pass. This worked a treat for Pam Richardson and Ray Carbuhn.  They coolly passed 2♣, then after either North or East had bid, they ventured 3♥. Their partners twigged to what was going on and passed, leaving their side in a safe and profitable heart contract.

Of course, this strategy is not infallible. Gordon Travers also passed, after South had stayed silent, as would I. Sadly 1♠ was the final contract (you can look at North's hand to see why), and even though Deena Pathy played the contract well to make it, their +80 was not a great score. Sometimes even the best laid plans of mice and men ...

Ever seen a hand fall apart before your eyes? This is one such hand.

What started as a delightful 16-count has gotten a whole lot worse. Partner's 1NT shows 6-9 HCP, without heart support, nor a spade suit.  Your hopes of a major suit fit have gone.  And there doesn't seem to be a minor suit fit either. So we are stuck with notrumps.

It's time to check the points: we have 16, partner has 6-9, so 22-25.  Only if partner has a tip-top maximum might we have enough points for game, and even then, without a clear suit to establish and cash, 3NT may be no bargain.

In short, game chances have shrunk to near zero, and we should be happy to let partner play 1NT.  Only two Souths had the discipline to pass 1NT: Pam Richardson and Margaret Skeen ... very well done to them.

Now take a look at all four hands, and in particular examine West's hand.  Four of the seven Wests doubled 1♥ for takeout: how would you rate that call?

I would rate it as seriously unwise: indeed I can think of four different reasons why it's a bad idea:
1. With 11 HCP, it can hardly be described as opening strength.  11 HCP might be sufficient for a takeout double, but consider first reasons 2, 3 and 4.
2. It's lacking 4 spades, the one suit that can beat the hearts.  Whilst 3 cards is all you're technically required in a side-suit, the absence of a fourth spade here is a serious minus.
3. Partner passed as dealer: she lacks opening points. In fact you'll be darned lucky to have a majority of the points on your side, and if you do, partner might bid too much anyway. This is particularly serious, because:
4. Your side is vulnerable. -100, -200 or -300 may well be heading your way.

Indeed if you do double, and North correctly passes, East will be in a nasty hotseat, where the only winning option may well be to make a hair-raising penalty pass of 1♥ doubled.  So a shoutout to Janice Meldrum, Rosemary Polya and Sandra McCaughey, all of whom coolly passed 1♠.

Maybe it says something about my character, but I like this deal, because it points out situations where your hand is bad, despite its points, and the correct choice is to shut up.

I have an idea.  North should open the bidding with 1♠.  Why? Let me count the ways:

Rule of 20.  This is a pretty reliable guide for deciding whether to open a marginal hand with 1 of a suit.  You add the length of your two longest suits to your HCP and if it comes to at least 20, open.  Here you have 5 spades and 5 diamonds and 10 HCP, equals 20. 

Length points. You're not allowed to include shortage points until your side has found a fit, but length points can be counted up front. They allow you to increase the estimate of the hand's value based on having long suits.  You count 1 length point for each card you have in excess of 4 in a suit. Here you have 2 length points, one in spades, one in diamonds, so add that to 10 to get 12 adjusted points and an opening bid.  You can see that the Rule of 20 and length points are very similar beasts.

Losing trick count.  This is a favourite of Ron Klinger's, and who am I to disagree with him, particularly when it reaches the same conclusion as mine. To open a hand, you're meant to have at most 7 losers. Here there is 1 loser in spades (the king), 1 loser in hearts (the ace), 3 losers in diamonds (with this estimation, you assume that after three rounds of a suit, the remaining cards are good, so you never have more than 3 losers in a suit) and 1 loser in clubs.  That's 6 losers only - why, not only is it an opening bid, but it has extra values! Who'd have thought?

Whichever way you slice it, this is an opening bid.  Yuko Yoshida, Margaret Sheen and Jolanta Terlecka were the three Norths (out of 10) to agree with me. And surprise surprise, they all got to the making 4♠ without much difficulty.

Confucius say that if both sides bid notrumps, one of them is wrong. But here, your partner's 2NT should be treated as "unusual", 5-5 in the minors.  On that basis, I think you should bid 5♣, competing in your 10+ card club fit. 

This might seem very scary when you're vulnerable and they are not. But consider this: partner also saw the vulnerability, and still chose to force your side in at the 3-level. He must have a pretty strong distributional hand.

Take a look at all four hands. 5♣ will go down 1 if the opponents take their two spade tricks immediately - otherwise it will make.  Meanwhile 4♥ is easy for them. Sometimes all it takes is a bit of courage.

No one wheeled out the unusual 2NT, but a few Souths overcalled 1NT with a natural 2♣ bid. Then if West bids 4♥, I think North should take the same inference that partner will be sound, and compete to 5♣ - but no-one did. 

Normally you would expect partner to accept the transfer with 3♠: after all, that might be the final contract you want to play. Her unnecessary jump to 4♠ is called a super-accept. It says: "I love your spades, partner". Essentially, partner is not going to let you play the hand in 3♠.

Failing to accept a transfer bid always shows strong support for the transferrer's suit.  After a 1NT opening, such a move should be reserved for the very best of supporting hands.   After all, who wants to be in 3♠ two down, when 2♠ would have been only one down?  After a 15-17 HCP 1NT, there is plenty of scope for such a scenario!

But after a 2NT opening, a super-accept is a far more likely and useful proposition. If you have a maximum in the 20-22 HCP, and a fit, you hardly need anything at all from partner to make game in the major a good proposition, and it may well be worth telling partner about your enthusiasm in case she has thoughts of slam.

Jolanta Terlecka super-accepted with 4♠ as North. Her partner, Rosemary Polya unleashed Roman Key-Card Blackwood, and was delighted with the 1 or 4 key-card response. She bid 6♠, which made in a breeze, despite the trumps misbehaving.

Maria Christensen also made the super-accepting bid. Her partner Jenny Sin damned the torpedoes and bid 6♠ then and there - that's what I call class. (They had met at the BBO Partnership Desk, so maybe had not discussed what sort of ace-asking they were playing.)

Two excellent auctions.

I would figure partner, who lacks a major and might not have too many diamonds given my long suit, to be packed full of clubs. So I'd bid 3NT here.

Look at all four hands to discover how much I know about bridge. 3NT is off the first 6 club tricks, whilst the computer says you can make a grand slam in diamonds. On reflection, perhaps 5♦  is the wiser choice.

Consider North's lead to 5♦. I detest leading from broken suits (such as clubs) ... so often they run up to declarer's honours. So I would choose a nice safe and constructive ♥J. Dummy comes down and declarer sees that this heart lead is nasty, threatening to take two heart tricks. West's hearts can be discarded on East's spades, but first something has to be done about trumps.

West doesn't want to lose the lead, for example taking a losing diamond finesse. Then you would go down in 5♦. Better is to bang down the ♦ A. The king will now most likely be outstanding, but then four rounds of spades will be played, and that ♦ K would be the only loser. In real life, the king drops under the ace, and voila, there's your 13 tricks. My ♥ J lead forces declarer into the winning play ... did I mention how little I know about bridge?

On a club lead, however, declarer has all the time in the world to take the losing diamond finesse.

Finally, what about 3NT? North should lead ♣J (top of an internal sequence) and South wins ♣ A. It is essential for South to return the ♣9, not the ♣5. Get into the habit of playing the higher of two cards, when you are left with a doubleton and returning partner's suit. Here the 9 traps declarer's club holding, and the first 6 tricks are safely negotiated for the defence. But if you return the 5, declarer covers with the 6, North wins the trick but now declarer has a stopper in the clubs.

This is the sort of problem when one should look a bit deeper than "fourth highest of your longest and strongest". Declarer, East, will have a strong balanced hand. In fact around 18-19 HCP seems likely, as they didn't open 1NT.

I don't know whether the hearts or clubs are the "strongest", but it strikes me that they are risky leads. Partner will have practically nothing ... for example, give 18 to East, 6 to West, and that leaves only 2 for partner. Either a heart or a club stands a good chance of donating a trick to declarer. 

A diamond lead, on the other hand, is pretty safe.  It gives nothing away at all. Of course, nor does it do anything for you, but sometimes there are hands where a "do nothing" approach is best, forcing declarer to make all the decisions about finesses. Dianna Middleton led a diamond, and I like her thinking.

That leaves the ♠K as an option. It's not a completely safe choice, but it's fairly safe, and of course it does do something towards beating the contract. Two players led it, but they were helped by their partner, who had bid spades. Well done indeed to Yuko Yoshida who risked a 3♠ bid over 3♦: this was certainly the time for it. That got Ray Carbuhn off to the winning spade lead, and they became the only N/S to defeat 3NT.

This hand is a fine example of the power of distribution.  Yes, your LHO has 15-17 HCP, which is a lot, but your diamond void may well negate much of that.  Picture West with, oh I don't know, maybe ♦AKQ94, and her 15-17 HCP becomes much less scary.

So I think the best choice here is to make a penalty double of 1NT. Pam Richardson was the only one to agree with me, so perhaps there's a partnership in our future.

If 1NT doubled is the final contract, then even if partner leads a diamond, I like our chances. Sure, declarer may be able to run some diamond tricks, but the sight of dummy will likely give me a clue on what to discard, and which suit (hearts or clubs) I'm likely to be able to establish. 

If someone (partner or RHO) runs from 1NT doubled - a likely scenario, as both of those hands will be weak - then I can bid my hearts.  I will have painted a picture of a strong hand with hearts, which is what I've got. 

On the actual deal, this is what will likely play out. Partner may run to 2♦, but even if she decides to tough it out in 1NT doubled (I think she should), then East will surely escape to 2♣.  Now when I bid 2♥, partner with support and distribution should give me a lift to 3♥, which I will raise to 4♥.  Maybe I'm a dreamer, but I think this is the sensitive auction.

With 12 HCP, it would seem you're worth about a game invitation. In fact partner also had 12 HCP, a minimum opener, and there was insufficient combined strength for a game in, say, 3NT.

But one moment, please. Is this hand really 12 HCP? Consider your hearts, ♥KQ8. Assuming South has the ♥A for his vulnerable overcall, then your heart holding represents two stoppers. Two tricks. Just like ♥AK8.  If you had in fact been dealt ♥AK8 with the rest of your hand the same, that would have been 14 HCP, which is easily enough for game. Here, ♥KQ8 has about the same trick-taking potential as ♥AK8. As the auction progresses, and you see bids from the other players, the strength of your hand ebbs and flows as you consider the location of your honours. The ability to notice and act upon this (it's called 'plastic valuation') is one of the great skills of the game.

Well done to Marg Ferguson, Ismail Gulec and Ray Carbuhn who correctly upgraded their hand and jumped to 3NT.

Technically, 3NT can be defeated, but when the play went low heart by North to South's ace and a heart returned, 9 tricks had easily appeared. The ♥KQ8 of hearts had done its job.

1) When we first learn bidding, we are told to open a weak two with 6-10 HCP and a good 6-card suit. This hand would appear to qualify. However, I would respectfully suggest that the hand is too strong for a weak two. I point you to two factors that indicate this:

- a great rule-of-thumb for deciding whether to open with one of a suit is to add your HCP to the length of your two longest suits, and if it comes to at least 20, then open at the 1-level. On this deal, you have 10 HCP, a 6-card suit and a 4-card suit, so 10+6+4 = 20, suggesting a one level opening.

- the location of the points is powerful. The queen and jack combine. The ace and king combine.  Honour cards working together are more potent than those on their own. Take the ♣AK: that's two tricks, right? But now make it ♣A and ♦K: that's not 2 solid tricks. It's one for the ♣A, and maybe one for the ♦K, but maybe not.  In the very old days, those separated honours would have been evaluated as 1.5 quick tricks.

4 of the 5 Easts agreed with my evaluation and opened 1♠: great minds think alike.

2) Now to the play in 3♠. When we first learn bidding, we are told to "get the kids off the street" - the kids being the enemy trumps. And often that is right: we want to remove their trumps so they are unable to ruff our side-suit winners.

But there are plenty of exceptions, and this is one of them. The most common scenario is that you need to retain some or all of dummy's trumps to ruff a side suit. When you draw trumps, you are drawing your own trumps as well. In this instance, you may want to keep one or two of dummy's trumps to ruff club losers. 

The correct play, not found by anyone (in this case great minds did not think alike) is to play a diamond at trick 2. If South has ♦A, he might duck, and lose his ace altogether. Or if he takes it, that gives you two winners in dummy. Either way, that's good news for you.  And if North has ♦A, at least you've set up one diamond trick, and there's no damage North can do to you.

1) North is bang-smack in the middle of the 15-17 HCP range. In such situations, one needs to look more deeply into the hand. The negative is that there's only one 4-card suit. The more long suits you have, the better the chances of establishing them.

But there are two significant positives: the two 10s. They're worth like half-a-point each: that definitely improves the quality of the hand, particularly as they are in conjunction with higher honours. Indeed if you look at all four hands, the ♠10 and ♦10 are each worth a trick, as it turns out.  I think the positives outweigh the negatives and so agree with Julie More, Maggie Kelly, Yuko Yoshida and John Robertson who continued to 3NT.  The other four Norths passed 2NT, and no discredit to them: it was a close decision.

2) Normally you would lead a heart to this contract, but did you notice that South (maybe) implied hearts with her Stayman bid?  (Actually, depending on the opponents' system agreements, that may not be the case ... you have every right to ask the opponents about this before making your opening lead). 

If I found out that South was showing four hearts, I would stay off the suit.  I don't want to lead a spade (that's North's suit), which leaves the minors.  A club is possible, and some Easts chose a club, but it's a suit that is not particularly attractive to break. (In fact it gives away the contract, allowing declarer to win a trick with ♣K).

That leaves the totally passive diamond lead, which would have been my choice. Well, it's food for thought.

3) On a heart (or spade or diamond) lead, West can defeat 3NT by switching to the queen of clubs when in with ♦A. The low club play, found by Shirley Stewart, was a good attempt, but not good enough, because declarer just ducked it. East had to win, and now the the ♣ K was protected. Only the queen lets you run the suit. More food for thought!

This hand is a classic example of assessing the situation before you make a move. This usually involves counting your tricks: winners, or losers, or both.

Winners: you have 7 spades in all likelihood, and a pair of side aces = 9.

Losers:  none in spades, 2 in hearts, 1 in diamonds,  1 in clubs = 4.

No question about it: unless you do something clever or meet a particularly kind lie of the cards, you're taking only 9 tricks for down 1. The way to reduce your losers is via the heart suit. As long as North has at least one of the king or queen, you can take two finesses in hearts, and reduce your losers in that suit to one. But to finesse twice you need to properly use dummy's two entries.

The correct play is to cross to the ♠K and take a heart finesse, even though there are still trumps outstanding. Then when you get back in, you can pull remaining trumps and use the ♣A to take a second heart finesse. Several declarers made the mistake of drawing all the trumps first and taking only 9 tricks. Gordon and Viv were not amongst them, and completed the deal by bidding and making the 4♠ that their partner had encouraged them to bid.

(Actually, some winning declarers missed an even better play. After the first heart finesse loses to South's ♥K, a trump was returned. After drawing trumps, declarer can ignore the second heart finesse and simply play the ace and another heart, setting up the hearts in dummy, allowing declarer's second club to be discarded.)

Open at the one-level or preempt? If the deal belongs to you, then opening at the one-level is the way to go. A pre-empt will probably just make partner miserable.

But if the deal belongs to your opponents, then pre-empting will make them miserable. A one-level opening will cause them little stress.

You can't know, so either choice is acceptable. (Position is important: if you had been in second seat, with RHO passing, the odds would tip towards opening one, as one of your opponents is weak; in third seat, the odds would favour preempting, as LHO may have a strong hand).

If you do choose to preempt, 3♦ is not enough. Whilst it is impossible to know what the singleton ♣K is worth, the ♦AKJxxxxx represents 8 probable tricks, far too strong for a pre-empt at the 3-level, even vulnerable. You should open 4♦. Google "Rule of 2 and 3" for more information!

Finally, if you open 1♦, hoping for a construction auction with your partner, your rebid needs to communicate the significant playing strength that you have. If partner responds 1♥, you should do as Elaine Watson did, jump to 3♦. This is where the raw HCP total of your hand misrepresents its strength.  In fact you have 4 length points for the 8-card suit, and this hand should be re-evaulated to 15, justifying the aggressive rebid. Well done to Elaine. Take a look at the South hand. Only 8 points (but 8 excellent points with the two aces) and 3NT is a moral certainty, with a combined 19 HCP. As someone once wrote, Points - Schmoints!

First, did you notice that you're vulnerable? That's bad news, because it's likely that LHO has you down in his hand. For example, she could have ♥AK, ♦A, ♣AK, 18 of her 20-22 HCP, and that's 5 tricks. Not to mention any problem you might have in spades.

But even if you were not vulnerable, I would be cautious. 7222 shapes are not frequent, but they do pop up, and when you get one, beware. They usually play very badly for you. They're like the distributional equivalent of the 4333 shape ... too flat!  7321 shapes, for example, are far stronger.

So well done to Susan Shand who calmly passed out 2NT. As you can see, no one can make anything much. 3♠ certainly will not make, and nor will 2NT. 

And well done also to Jenny Matheson, who sitting East, doubled an impertinent North for penalties in 3♠. +500 for 2 down was the E/W top.

The takeaway: with 7222 shape, proceed with caution.

You don't have to get to the doomed 3NT. All the Easts bid 1♥ over North's double, essentially ignoring it. But you shouldn't ignore it, because your opponents have wandered into the auction, a place that they don't belong. They are in fact in deep doo-doo.

East should redouble North's double, the so-called "Omnibus Redouble", which simply shows 10+ HCP.  It says: "partner, we have the balance of strength - let's see what happens next".

What happens next, I would imagine, is that South bids 1♥ with a sense of foreboding. West, with nothing particular to say, passes - in this auction, East is not allowed to pass out 1♥ - North passes, and East says DOUBLE.  

In Omnibus Redouble auctions, either party can double the opponents' bid for penalties: that is the whole point of the gadget. East's double is for penalties, and West with a relatively balanced hand and a couple of nice hearts, should be delighted to cooperate with this. On the ♥Q lead, the defence can easily take 3 hearts, 5 diamonds and the ♣A for a score of +500, more than the value of the 3NT contract that they can't make anyway.

Of course N/S could maybe wriggle to 2♣, although I wouldn't bet on it. That contract is only two down. The point is that in such auctions, it's worthwhile at least giving yourself a chance of extracting a penalty. 

1. After West opens 1NT, should North double for penalties?

I don't know for sure, but would be inclined to pass. There are a few factors at play here. First, I'm a little nervous about partner removing it to 2♥ ... that would put me proverbially up the creek. And I'm not sure what to lead (see question 3). Finally, doubling 'squeals' on the hand, telling the one-notrumper where all the cards are. He may be able to use this information to his advantage.

2. If North doubles for penalties, and East passes, what should South do?

South should pass. The rule for what to do when partner doubles 1NT for penalties is to pass with any balanced hand, no matter how weak. Sure it might make, but if it does, running is not too likely to work either. Meanwhile, partner might have the contract down in his own hand. So only run away with a weak unbalanced hand: one with at least a 5-card suit to escape to. Well done to Maggie Kelly who passed her partner's double. The contract went one down for a good score.

3. What should North lead?

I feel strongly that you should lead the ace or king of diamonds. As the saying goes, "a peek is worth two finesses".  The normal looking low club lead may give away an unnecessary trick, and meanwhile it will still be available once you have led a top diamond, gotten a look at dummy, and received a signal from partner. The ploy of "having a look at dummy" is underutilized.  In this case, dummy will tell you not to go after clubs, and that you are better off, after partner's encouraging diamond signal, to continue that suit.

4. If North leads a low club against 1NT passed out, declarer winning, how should the hearts be played? (Ignore that you've peeked!)

Now we turn to West, the declarer. When a club is led, and South plays a low card, it is obvious that North has long clubs and South short clubs. In the heart suit, we are missing 5 cards. If they divide 3-2, there are 4 easy tricks, but if they are 4-1, then we will want to be in a position to finesse against the jack. Given the club information, it is far more likely that South, if anyone, will have the long hearts.  So the heart suit should be played as follows: ♥A, then a low heart to ♥Q. Then if South does have the long hearts, their jack can be finessed.  Cashing the ♥AK first is a big mistake.  Fiona Ferwerda was one declarer who handled the heart suit correctly.

5. Having won the club lead in the East hand, what should be played at trick 2?

OK, we've won the cub opening lead in dummy, as South could only contribute the 3. Leave the heart suit alone for the moment: now is the time to take the spade finesse. If that works, and we can gather 4 heart tricks, then our 1NT is made. Terry Passlow was one declarer who did so. Alas the spade finesse lost, and he ended up in the soup anyway, but it was a well thought-out play. This was one table where 1NT had not been doubled, so he had every reason to hope the spade finesse might work. 

Did you gleefully overruff the ♣Q with ♣K? Wrong!

In situations where declarer ruffs high, and you have the option of overruffing with an honour that you are going to be taking anyway,  it is almost invariably correct to not overruff.

Look at all four hands now, and follow the play if you coolly discard on the third heart. Declarer, who has only trumps to lose, crosses to ♠A and leads a club. Partner wins ♣A, perforce, and persists with a fourth heart, which declarer ruffs with the ♣J. Again you decline to take your king, and discard. And now look: you are left with ♣K9 sitting over declarer's ♣10, his last remaining honour. Your ♣9 has been promoted to a trick, and it is the setting trick.

This position is particularly pretty, as it was necessary to refuse to overruff twice, in order to bring power to that ♣9. If at any point you do overruff declarer's honour, you will find that declarer makes the contract.

The first thing is to work out what partner is showing with 3NT. A balanced hand, one would think, and with what points? Not in the range for a 1NT opening (let's assume 15-17) because partner didn't open 1NT. Therefore because it's a jump, it must be stronger. Opener is showing about 18-19 HCP, balanced.

West has 12 HCP, bringing the HCP total to 30-31. But it's stronger than that, because of the 6-card club suit. That long suit translates directly into extra tricks. You can quantify this by adding length points, a valuable tool for estimating how high to go in notrumps. Add a point for each card over and above 4 cards in a suit. The 6-card clubs contains 2 length points, bringing the adjusted point total to 32-33. You are in range of 6NT.

Personally I would just bid 6NT at this point, but you can consider yourself to have passed the bidding test if you make any move towards slam after partner's 3NT. A quantitative 4NT, for example, would be a possibility.  Looking at partner's perfectly normal 19-point hand, you can count 2 spades, 2 hearts, 2 diamonds (after the ace has been knocked out) and 6 clubs, for a total of 12 tricks. It's the power of the long suit.

It's an irritating problem, because you'd like to bid a slam,  but there's no guarantee it will make. 

This is where being armed with Roman KeyCard Blackwood can help. What you really want to know about is four cards: ♠A, ♠K, ♠Q and ♥A. That's what RKCB is for!

Bid 4NT, which is a form of Blackwood in which there's a trump suit set ... in this case it's spades. (If you haven't formally agreed trumps, the implied trumps is the last bid suit, spades here.)  You can google the formula for the responses, but partner will make a bid that shows exactly one of the 5 key-cards (the four aces and the ♠K).  One is not enough: you are either missing the ace and king of spades, or the ace of hearts and one of the ♠AK.  You sign off in 5♠ ... just in time.

Two pairs bid and went down in slam, and I am going to give them the elephant stamp this week, despite their shared bottom, because they were the only two pairs that started, eminently correctly IMHO, with 2♣: Deena Pathy (S) - Gordon Travers (N) and Patricia Stewart-Uden (S) - Don Stewart-Uden (N). They didn't unravel the hand but at least they tried!

The first thing you should always do as declarer is make an assessment. That means counting your tricks. In this case, there are 7 heart tricks and 2 clubs. The ♠K and ♠Q will combine for another trick. So that makes 10. If you are in 4♥, you're happy. If in a lower heart contract, you're sad.

But no matter whether you are happy or sad, the next  thing to do is think about whether you can wangle another trick or two. Indeed, if you are in a heart partscore, you can still earn an above-average score by making 11 tricks here.  Good play can make up for bad bidding!

So where can you get another trick?  Hearts and diamonds  ... impossible. Clubs ... unlikely (unless there's a miracle: clubs 3-3 and hearts 2-2 - do you see how?).  But in spades, there's a straightforward route to an 11th trick: by ruffing a spade loser in dummy. Win the club lead and attack spades by leading the ♠Q. The defenders can belatedly win and play a trump, but it will be too late.  You play ♠K and spade ruff, and eventually get back to your hand to draw the rest of the trumps. You end up with 11 tricks, losing just a spade and a diamond.

There are a few things that might go wrong with this plan, but none of them are likely.  

The takeaway: as declarer, start with an assessment: counting your tricks. Then look for ways to take more of them!

Maybe I'm looking at the hand through rose-coloured glasses, or maybe I'm influenced by knowing what North actually held, but it seems to me that there might well be a slam here.

I would need partner to have one of the ♥A or ♣K.  That side suit of diamonds is very powerful, and is a fair chance of being  played for no losers whatever partner holds in it. If she has the queen, great. Alternatively, if she has 3 or 4 of them, the queen might drop. And if she has shortage, the suit can probably be ruffed good.

So I think 4♥ is not enough. I suggest a 5♥ bid, offering for partner to go to slam. 5 of a major, inviting 6 of the major, is an often overlooked bidding tool. 

As it turns out, partner had the ♥A and ♣K, with 4 diamonds to boot. There were 13 top tricks to be had in either red-suit. Like I say, maybe the full layout has biased me. But surely at least a small slam could be bid. So well done to Jenny Matheson and Mariette Read, the only N/S to reach a slam (after a takeout double of 1♠). A well deserved top.

What's partner got? Who knows!  Here's what I do know ... partner could have bid 2NT, showing 23-24 balanced, and you are allowed to pass that, if you have zilch.

So partner must have decided he didn't want to stay short of game under any circumstances. So in my opinion, he must have a stronger hand that 23-24 balanced. 25-26 balanced perhaps?

That would total you up to 32-33 and put you in the 'maybe slam' zone. And whilst you're flat, you do have three 10s as bolster. Let's just just say that I've seen worse 7-counts. 

Or to put  it another way, you are maximum for your 2♦ bid. It all adds up to making a slam try.  I would suggest a quantitative 4NT bid (how could that bid possibly be Blackwood?)  Offering partner the possibility of slam, without committing to it.

Well, North had 27 HCP, a real monster ... any offer would have been accepted.

Just two pairs reached the excellent 6NT contract: Alan Casanalia -  Terry Passlow and John Robertson - Lanny Chan.  They both achieved this via South showing some strength with their initial response to 2♣, a bid showing 6-9 HCP in one case, and a bid showing 7+ HCP in the other. Either of those was enough for North to take over.

This deal confirms one of my long-held beliefs: that the responder to a 2♣ opener should attempt to describe his hand at all costs, and not to decide the final contract (as the pass of 3NT does here). 

This was an excellent auction overall. The one bid that I would have a tiny quibble with is North's 4♣.  At the time it seemed (and was) reasonable enough, but as the auction panned out, you can see a flaw. North might have recognized that when her RHO bid 2♥, she would probably need to be dealing with an opposing 4♥ bid in the near future, given her singleton heart and West's bid. When that did occur she made the correct decision to sacrifice against it, by bidding 5♣.

The problem is: if you're planning to bid 4♣ and if necessary 5♣ later, you are a whole lot better off bidding 5♣ in the first place. This maximizes the pressure placed on the opponents. Can you see how awkward an immediate bid of 5♣ is for East? Will she bravely bid 5♥ with an 11-count and 3 little hearts? Maybe, or maybe not.  And what about West? If East does pass an immediate 5♣, then it's not clear for West to keep going in hearts.  The hearts are excellent, but the three low doubletons are awful, and West doesn't know what level of heart support partner has.

North's actual 4♣ bid could pay off big time if it ended the auction ... but how likely is that?  My advice is: with weak supporting hands in a competitive auction, give it your one best shot immediately, and then leave the rest to partner.

I think there were two outstanding bids made in this auction. Dell Macneil's pass as East over 5♣ by North was perfect. She didn't want to bid 5♥ herself, having supported with minimal hearts. But she wasn't ready to double the sacrificing opponents, given her singleton club. This was the time to pass the final decision back to partner, who understandably chose to go on with his one-track hand.

The other bid I loved was Fiona Ferwerda's bid of 6♣.  Normally, having pushed the opponents up to the 5-level you would leave them there, hoping to take them down. But Fiona didn't think this was likely. Her ♥Q10 doubleton was useless, and given her partner's bidding and the opponents' progression to 5♥, she knew there would be at most 1 trick in clubs. It seemed 5♥ was likely to make, and the favourable vulnerability made a further sacrifice attractive. Well bid!

Let's see. You have 13 HCP and partner has opened the bidding. You would like to think there is a game here, but where? 3NT is a possibility, as long as partner can stop the diamonds.  Or maybe 5♣ as we might have a decent club fit. The third option is 4♥, should partner have a bit of support there.

It's hard to know. You need more information. You need to get partner to help you. And the only way to do that is to bid 2♦, the opponent's suit. You know partner won't pass that, and whatever she does bid, it will surely help.

In fact, if West had not bid 1♦, then 2♦ would still be the correct bid, but now you would see it as 4th-suit-forcing. I think in this auction, people just didn't see it as a possibility, but it's the only call that will keep the ball rolling and not commit your side to anything.

Choices actually found were 2♥, a distinct underbid, 3♣, which in the main was passed, and 2NT which led to a notrump contract off the first 5 tricks.

Look at the South hand. Over the 2♦ bid all this hand can bid is a grudging 2♥.  There's no diamond stopper for a notrump bid, nor extra length in either of the black suits. Heart support of Jx will simply have to do. And indeed it's just what the doctor ordered: as long as North plays carefully: ruffing the third round of diamonds, and going over to dummy to finesse in hearts, 4♥ will roll home.

The bottom line: if you have a good hand and don't know what to do, try bidding the opponents' suit. 

Playing Standard American, the jumping 2NT rebid shows 18-19 HCP in a balanced hand.

A quick piece of arithmetic will tell East that the combined partnership total is 33-34 HCP.  33 is a magic number, the number of high-card-points you should have in order to bid 6NT. So the correct bid here is 6NT. There is no value in investigating 6♠ instead, because it is highly unlikely that spades will be worth one more trick in the play than notrumps. In a matchpoint duplicate, you are far better off getting 1440 in 6NT than a measly 1430 in 6♠.

Toni Bucknell (West) and Maggie Kelly (East) were the only pair to bid and make 6NT.  After Toni's 2NT rebid, Maggie stopped off to check on aces via a Gerber 4♣.  This wasn't strictly necessary, as having 33 points means you cannot be missing two aces. Still, better safe than sorry.

Why did so many pairs miss the excellent slam? Well, many Wests opened 1NT, which I assume showed 16-18 HCP (or maybe 15-18).  Now it was much more difficult (although it shouldn't have been impossible) to reach slam. 

Be that as it may, I want to make a strong pitch for using a 15-17 HCP range for your 1NT opening. Why?  Because it spreads the point ranges for notrump bidding more evenly.  Using 15-17 HCP, you have the following ranges of balanced opening hands:

  12-14: Open 1 of a suit, then make a minimum notrump rebid
  15-17: Open 1NT
  18-19: Open 1 of a suit, then make a jump notrump rebid
  20-22: Open 2NT
  23+:    Open 2♣ 

Notice how even it is: the entire range of points is broken in to 2 to 3 point blocks.  If you use 16-18 instead, you have a wide range (12-15) at the bottom, which is very very hard to work with. 15-18 1NT gives you an unworkable range in that opening. 15-17 is the sweet spot.

This is not a hand for science, nor having a dialogue with your partner.  Not in a million years can you communicate your hand to partner.  This is a hand for a blunt instrument: namely Blackwood.

That's what Jane Keyte did. She bid 4NT, partner answered 5♥ showing two aces, and she bid 6♦. That's the way I would bid it too.

Take a look at North's hand. It was perfect. 6♦ seems cold and indeed if the opponents don't take the ♠A at trick 1, they won't get it at all.

Alas, it only seemed cold. Sitting East, Trish Stewart-Uden led a club, without I imagine a lot of hope. When West ruffed it and cashed the ♠A, the Keyte's had their totally undeserved bottom. What can I say?

You might think this is just a flukey hand, not worthy of writing up. But it has hidden depths. Put yourself in the West chair. They bid to 6♦ via Blackwood, with your partner on lead. How good is your telepathy? You are willing your partner to lead a club, because you will ruff it and cash ♠A.  Several West's psychic powers were not up to it ... their partners led a heart or a spade, and 6♦ duly made.

But it's not all about telepathy: suppose West doubles 6♦. That's what's called a Lightner Double (named after Theodore Lightner who first came up with the idea). It tells partner to make an 'unusual' lead, typically from their longest suit, because that's the suit where doubler will be void. A Lightner double might just get you a top board, as partner will certainly lead a club, and now you have them down 1, doubled.

But wait just a moment! Now put yourself North. You open your 18-count with 1♦, partner goes crazy asking for aces, and puts you in 6♦.  West doubles it.  You can rescue the situation by running off to 6NT.  There's no ruff to be had against 6NT.

A pretty hand indeed.

The most reliable way to work out suit combinations is to list all possible layouts, and then take the play that works the most times. You might want pencil and paper, and since you are playing on BBO, then go ahead. (Technically, this is illegal, as one is not allowed to use external aids like a pencil, but hey, it wouldn't be the crime of the century.)

Of course in some layouts, it won't matter what you do. Here is an exhaustive list of the ones that do matter.

West   East
KQ     85
Q      K85
K      Q85
8      KQ5
5      KQ8
-      KQ85

Can you work out which play succeeds in all but one of the relevant combinations? 

Lead a low one from North, and if East plays a low card, play the jack.  If that loses, get back to dummy, lead another low card, and if East plays low again, finesse with the 10. That will bring home the bacon on any of the layouts listed, except the first one, where West has KQ doubleton.  All other strategies lose to at least two combinations.

On the actual layout, as long as you finessed on the first round, you were fine.  Joan Courtemanche, Penny Robertson, Jane Keyte, Ray Carbuhn and Lesley Johnstone were the declarers who got this right. I'm going to assume that if they'd lost the first round to an honour, they would have finessed again.

Examination of suit combinations like this runs into a lot of difficulties because players make illogical deductions based on cards that were played. Welcome to the weird and wonderful world of Restricted Choice. But the bottom line is: With 9 cards missing the king and the queen, finesse twice.

Let's begin with South, who passed originally, with 10 HCP. Now that a spade fit has been discovered, South can count distribution points ... 3 of them in this case, for the singleton heart. That boosts South's total points to 13, and this should be enough for game, even opposite a light 3rd seat opener.  Penny Robertson was the only South to bid a simple 4♠ here, and I think she was on the right track.  (An alternative, if you play splinter bids, would be 4♥, a jump in the opponents suit to depict spade support, a singleton or void heart, and enough strength to go for game.)  

Some Souths bid 3♥, a cue-bid raise: not an unreasonable choice, but perhaps not quite doing justice to the hand.

Penny's partner was Fiona Ferwerda. After hearing 4♠, she bid 6♠. That's how to do it!  South says: "I think we can make 4♠."  North says: "In that case, I think we can make 6♠."  This is good bidding.  North didn't wheel out Blackwood, because with a diamond void, knowing how many aces partner has is of little help.

We play bridge in a world of lots of conventions and lots of bidding theory. I love bidding conventions. But there are times, more frequent than one might think, when it's best to just blast away.  This was one such time.

West's problem is an ugly one indeed. Mostly, double was chosen, but this has a very significant drawback, one I need hardly point out. Let's just say that at several tables, East's takeout to 4♥ was not a welcome development. And since you can see North's hand, it will become clear that 4♥  was unsuccessful. Down 2, 3 or 4 where it was bid.

No, you can't double, you simply can't. When you double, you basically promise hearts, the other major, and you ain't got them. Some lies are white, some are grey, but this takeout double is a big black one. 

One West couldn't see a satisfactory bid, so passed. I don't like that either ... it's like you accept being stolen from. But I will concede this: it's better than a double!

The solution is to overcall 2NT. The points are right (16-18). The spades are right (a stopper or two). The hearts are almost  right: you're meant to have two of them, but singleton ace will have to do. 2NT is a white lie.

As for North, whether West doubles, passes or bids 2NT, North should apply the  Law of Total Trumps and bid 3♠.  North knows of a 9-card spade fit, and in this competitive (or soon to be competitive) auction, should bid ASAP to the 9-trick contract, i.e. 3♠.  Well done to Dianna Middleton, Peter Ferguson and Gordon Travers, all of whom found the blocking 3♠ bid. 

One final point: suppose West had bid the recommended 2NT, and North had bid the recommended 3♠ ... what would you do as East?  No one could blame East for giving  4♥ a whirl, and there you are, back in the worst of all possible contracts. That's how powerful the Law of Total Trumps is.

No one could complain about your passing ... after all it's not much of a hand.

But if you choose to do something, it should be double. When the opponents bid two suits, as here, then your low-level double is for takeout, showing a minimum of four cards in the other two suits.  One point to note about this particular takeout double is that you don't have to be short in the suit you are doubling ... all that is required is 4+ cards in both of the unbid suits.

There are two other factors that make the takeout double quite a good idea here. Did you note either of them when given the problem?

First, your side is non-vulnerable. If you win the contract and go down, it will be in 50s. That could be a good score if your opponents can make 110 or 140.  Vulnerability is crucial.

Second, you were dealer and passed. Partner knows you don't have opening strength, and shouldn't 'hang you high' for taking a bid.

Another way to look at this problem is to predict your unhappiness should you pass, and, for example, LHO raises to 2♠, passed back to you. It would be brave to come in now, committing to the 3-level, and yet, you don't much relish the idea of defending 2♠.  This is a common theme in competitive auctions: it is often a good idea to get in early, whilst the auction is low, and then bow out - as distinct from listening, and then having to make a decision at a higher level.

Looking at all four hands, the raise to 2♠ was not what was going to happen. However, the hand record says your side can make 3♦, with the opponents making 2♥.  If you come in with a double, then your side is quite likely to steal the contract at 2♦.  Well done to Rosemary Polya and Marg Ferguson, the two Souths that made the takeout double.  

Here's what one should 'see'. Partner has 6 diamonds to the ace.  For a vulnerable weak two, that makes sense, right?

So, in a spade contract, perhaps the opponents can take 3 tricks in hearts and clubs. But then you get in, and with a bit of racing luck, have 6 spade tricks. And 4 diamond tricks, because your 4-card diamond suit means you have a 10 card fit. If partner does have the ♦A, then assuming the outstanding diamonds divide 2-1, you have all the diamonds.  6 spades plus 4 diamonds = 10 tricks.

A visualizer, such as Michael McTiernan who faced this problem, will bid 4♠ over 2♦.  He won't worry about points, or rules, or system, or any of that stuff. He will see that there is a decent chance of making 4♠, which will be a higher scoring game than 5♦ (and of course, 5♦ risks losing the first three tricks in clubs and hearts).

Of course, it could become unstuck. There might be a spade to lose. Partner might lack the ♦A (although in that case, perhaps there's compensation elsewhere).  But on balance, it seems 4♠ will likely make.

Today, it comes home with an overtrick. 

Other Souths faced a slightly different problem. Their partners passed, RHO opened 1♣, they overcalled 1♠ and partner bid 2♦.  Whilst not as clear as opposite the weak two opening, you can make the same visualization. Your ♦Kxxx makes it likely that diamonds are running, and again 4♠ is a worthwhile proposition.

Two Souths rebid 2♦, a definite error. A simple minimum rebid shows about 12-14 HCP, and this hand was considerably stronger. If, on your second bid, you are about to bid a suit that has already been bid by your partnership, you need to come out of the woods with your strength. A minimum rebid (2♦ or 2♠ here) shows a minimum strength hand. With extra strength, one has to jump.

Accordingly 9 Souths jumped to 3♦, showing about 15-17 HCP and a good 6-card diamond suit, which is precisely what they had. Hard for me to complain about that.  But I intend to.

One creative South was concerned about not showing the nice 3-card spade support. She jumped to 4♠!  Whilst I admire the general attitude, 4♠ was a mistake on two counts. First, partner has promised only 4 spades, so this was potentially bidding to a 4-3 spade fit. And second, South's hand is just not strong enough to commit to game at this point.  A jump to 3♠ would have avoided the second mistake, and would not be the world's worst choice.

The 3-card spade support is an issue ... it would nice to be able to locate a 5-3 spade fit, and a simple 3♦ rebid might lose that possibility. There is a solution, and it was found by Simon Tissera. He rebid 2♥, a phony reverse. The phony bit was that he only had 3 hearts ... he bid a non-suit. But it was actually quite a safe choice, because if partner supports hearts (with four cards), then it implies that she has 5 spades (allowing a safe return to spades). Why?  Because with 4-4 in the majors, partner would have responded 1♥ not 1♠, bidding 4-card suits up the  line.

The phony reverse here was really very neat, and it worked a treat. Partner rebid 2NT, clearly showing a stopper in the fourth suit, clubs, and Simon gave 3NT a whirl.  There were 9 easy tricks in 3NT.

The only other pair to reach the top spot were guided by North, Alison Simon. She tried 3NT over partner's 3♦ rebid ... an aggressive but plausible option which got the big payout.

It looks instinctive to lead the ♠K, top of a sequence. But what is the spade layout?  You can expect North, who opened 1♠ to have 5.  That leaves 3 cards for South and East. OK, so far?

If South had 3 spades, you might expect she would have supported the spades at some stage. So South probably has 0, 1 or 2 spades. If South has 0 spades, then your spade lead won't help and could do damage, if South could take a useful discard on the North's ace.

The interesting stuff is what happens when South has 1 or 2 spades.  If 1, then your lead is safe enough, but won't do much good. If South has 2 spades, partner has the singleton. Your ♠K drives out the ace and you now have a cashing spade winner, but how will you get in to take it? It's very unlikely that you have an entry. And if partner gets the lead, she won't have a spade to play back to you!

In short, a spade lead can't actually achieve anything, in all likelihood, and you know it. That leaves the simple lead of the unbid suit, diamonds. And as it turns out, the ♦Q lead will get your side a trick ... and if you don't lead diamonds, declarer will take all 13.

Well done to Jane Keyte, Jo Quinlivan, Ray Carbuhn and Joan Craig, all of whom found the ♦Q to obtain a trick for their side.

Frankly, nothing fits. You have the points and shape for a 1NT overcall, but alas, no diamond stopper.

What about double?  What will you do when partner responds 1♥? Self-destruct, I would say.  Bidding 1♠ over 1♥ shows more strength and more spades. Any other bid is out of the question. And passing could leave you in a ridiculous 4-2 fit.

Speaking of passing, passing 1♦ is like conceding the match before the kickoff. In reality, you'll find yourself trying to defeat 1♦, which turns out to be impossible.

So now the naughty bit. Your best option, in my humble opinion, is to overcall 1♠ on a four-card suit. Sacrilege, I know, but the suit is very strong, and most importantly, it makes your subsequent bidding easier.  You might not get to the right contract, but at least your stress levels will be low.

Overcalling 4-card suits at the one-level is a slightly controversial subject in the world of bridge, but when all the other options are unpalatable, it should be considered.  Just make sure your suit is a strong one: the AKJ9 fits the bill nicely.  Here, it works a treat, getting you to a making spade partscore.

To get the play right, you have to count, keep counting, and then count some more. You have to count as you go. If you can build up the distribution of the unseen hands, you will almost surely know what to do.

Let's try it here. At trick 2, we discover that declarer has no diamonds. He discards three spades which means, unless declarer is playing a very strange game, he started with four spades in total (having played one at trick 1).

Then he plays three top hearts, and you discover that partner had two. A bit of subtraction will tell you that declarer started with 6 hearts.

You've isolated declarer's shape, using the simplest of arithmetic. He is 4-6-0-3 distribution.  Now, in clubs, declarer has either Jxx or xxx. If he has the jack, then there's nothing more to this hand: declarer will lose just one club trick.

But if declarer has three little clubs (as he did), you're in with a chance. When declarer leads a low club from hand, play low. The ♣K will win. Declarer returns to hand by trumping a spade and plays another club. Here's your moment: you duck again, without a care in the world. (And you truly don't have a care: you have worked out that your ♣A is always going to take a trick.)

Declarer is faced with a complete guess: whether to play you for the ♣A, or the ♣J.  In the latter case, your partner would have made a straightforward play of not taking his ♣A on the first round of the suit. Declarer is in fact quite likely to try the ♣10 on the second round of the suit, and miraculously a second trick has come to the defence.

What's the moral of this (rather boring) little story? It is that if you keep counting as you go, you will find yourself not quite in the usual defensive fog of "not knowing what's going on". Give it a try!

South's response:  The correct response to 1♠ is an anti-intuitive 1NT. This is one of bridge's problem bids. Normally 1NT is bid on a balanced sort of hand, but the 1NT response to partner's suit opening is different. It's a coded response, showing 6 to 9 HCP and nothing that can be bid at the 1-level. 

Bidding a new suit at the 2-level promises 10 or more HCP, thereby making the 1NT range 6-9. Indeed South's hand is by no means the most unbalanced one could have for this bid.

North's rebid: The correct rebid is 3♠, showing around 16-18 HCP and a strong 6-card suit. When you rebid a suit that has already been bid by the partnership, it is essential that you show your strength at the same time. That's because bidding suits that have already been bid (by one partner or the other) tend to be non-forcing.

Several Norths bid just 2♠.  South had no reason to bid over that: she would have thought North had as few as 11 or 12 HCP to go along with her spades.  2♠ is too little.

One North rebid 4♠.  That was too much. Put her 17 HCP opposite partner's possible 6, and there's insufficient overall strength for game.

South's rebid: South has no help (literally) in spades, but does have 8 HCP. That's in the top-half of her 6-9 range. So she should try 3NT. She has no idea whether 3NT will make, or how it might make, but better that than simply passing partner in 3♠.  The saying is: 'tis nobler to go down in game.

As it turned out, 3NT was a perfectly reasonable contract that made without much trouble.

Well done to these 5 pairs who had the officially approved auction:
  Carolyn & Bob Hart
  Shirley Stewart - Joan Courtemanche
  Deena Pathy - Gordon Travers
  Gordon Shinewell - Geoffrey Schroder
  Pam Richardson - Mary Day

1) If I just had one bid, it would be 6♠. Most of the time, both spades and diamonds run, and there's your 12 tricks. Or if one of the suits doesn't, then perhaps partner has the ♣A. Or even lacking the ♣A, perhaps they lead a heart and your partner has the ace there.

Nevertheless, 7 of the 11 Norths chose to end up in 4♠. If they weren't customers and therefore always right, I might accuse them of being just a little bit wimpish.

2) How might one bid the hand? One option is to open 2♣, planning to bid the spades and then the diamonds. If partner prefers diamonds, then go for the safer 6♦ ... for example, partner might have a singleton spade and 3 diamonds, in which case 6♦ is better: you might be able to ruff the spades good. That was the approach taken by Pamela Mathie, Joan Courtemanche, Fiona Ferwerda and Dianna Middleton. No wimps they! When partner was happy to play in spades, they bid 6♠ and there was not the slightest problem in the play.

FYI, a very old-fashioned but useful once-in-a-decade convention is an opening bid of 4NT. This should be played as a specific ace ask.  Partner responds:
  5♣ = no aces
  5♦ / 5♥ / 5♠ / 6♣ = ace of that suit
  5NT = two aces

Opener then names the contract.

That way you could give 7♠ a try if partner shows the club ace.  This came up for my partnership in a national event in 2004, and it worked a treat. I reckon it's due to happen again soon.

Finally, one further player needs congratulation. Mary Day sat East. Her RHO opened 2♣, then bid spades and diamonds before jumping  straight to 6♠.  She led a club, cashing her partner's ace, and salvaging a 30% score against one of the slam bidders. Obviously she didn't want to lead one of declarer's suits, and in choosing between hearts and clubs, she had a bit to go on. When players jump to slam without ace-asking, they often have a void (which renders the ace-ask less than useful). With 6 hearts and only 2 clubs, she suspected declarer was void in hearts, and therefore led the shorter suit. An excellent inference that paid off. All the other declarers made 13 tricks.

South's invitational-to-game 2NT looks spot on to me. With 9 HCP opposite 15-17, there's a combined range of 24 to 26 HCP.  With South's flat shape, 24 HCP might not be enough, but one can hope that 26 HCP is enough for 3NT.

What should North do with 16, the middle of the range? This is a not uncommon situation, and one has to look a little deeper into the hand to decide whether to accept or reject the invitation.

The two four-card suits provide a little bit of extra hope for developing an extra trick, but the real swinger is the ♦109.  That doesn't contribute a point, but in many situations will contribute a trick. For example, put it opposite South's actual ♦QJx. You will get 3 or 4 tricks, depending on the location of the ♦K.  But make North's diamonds ♦A432, again opposite ♦QJx.  Now 4 diamond tricks is out of the question, and you need a little bit of racing luck to even make 3 tricks. Similar calculations will apply opposite different South holdings.

So 3NT, accepting, looks good to me. Naomi Peters and Karen Jorin were one pair who conducted this simple but finely-judged auction.

Now to the play in 3NT. You win the ♥J at trick 1: have you decided what to do at trick 2?

There are four top tricks in the black suits, and 3 or 4 in diamonds, depending on the location of the king. It looks  for all the world as if East has ♥A: she has led this suit to a blind auction, so it's likely her best one. So there's another heart trick to be won by leading towards the ♥K.

The only possible extra trick is in clubs, should the suit divide 3-3, but even if it does, you still have much work to do to generate your extra red suit tricks. The club suit is a furphy.

The correct, and almost completely safe play is to play back a heart at trick 2. This will generate your extra heart trick, and provide you with a safe entry to dummy to take the diamond finesse.  If East wins the heart, and continues the suit, you take the ♥K and the diamond finesse. If it works, there's your overtrick. If not, you still have a 100% safe 9 tricks (as East can do no better than to win the diamond  and take two more heart winners).

The continuation of hearts at trick 2 looks strange, but it is the correct play. Did you find it?

Don't tell me you got fooled by that bit about being vulnerable!  This hand has pluses (the nice shape) and minuses (the singleton king), but the bottom line is that you have 8 HCP and a decent 5-card heart suit. You should bid it. Who knows what might happen next, but disrupting the opponents is usually a good idea.

I fully admit that I might not have the world with me on this, but this is my column, so sue me.

Agreeing with me were Sandra Mansell, Margot McCluskey, Jenny Matheson, Cathy Wilson and Anna Kearon, all of whom bid 1♥.

Other non-pass alternatives were 1♦ (selected by a couple of players) and 2NT (the Unusual Notrump, showing the two lowest unbid suits).  1♦ emphasises the wrong suit (you want partner to lead a heart, not a diamond, to a possible spade contract declared by East). 2NT takes you to the 3-level, which even for me, is a bit too high. Still, better a madman than a wimp.

All right then, take a look at all four hands, in particular East's monster.

Whatever North does, I think East should bid 6♠.  Partner has an opening hand ... surely 6♠ should be there. At the very worst, you may need a finesse. And I doubt even the world's most elite players would have methods that could find a grand slam here.  

No one bid 6♠ directly, but Dianna Middleton, Yuko Yoshida, Dorothy Stewart, Geoffrey Schroder and Moya Crowle all bid to the slam eventually, some with the 'help' of Blackwood, which is actually of no use at all, given your heart void.

One might think that would be the end of it, but perhaps not. Cast your eyes over the South cards, with partner overcalling  1♥.  Do you think 6♠ will make? I certainly would, even with my ace and a bidding partner. If East has used Blackwood, then they know they're not missing two aces. And if they haven't used Blackwood, then that's because East has a heart void, which is hardly a surprise given our 6-card support.

I think there's a strong argument for sacrificing in 7♥. It certainly would have worked, salvaging an averagish sort of score rather than a near bottom. 7♥ loses only three tricks, -800, compared to the -1430 you were headed for. Perhaps unsurprisingly, no one found it, but it was a real possibility.  North could have proudly said in the post-mortem, "I bid 1♥ so that we could go down 800 in 7♥ doubled".

One West passed in 2nd seat: that was too little.

Another West opened 4♠: that was too much. It's a recipe for going two down, vulnerable, against opponents who can only make a partscore. But as it happened, it worked: 4♠ being allowed to play for 10 easy tricks.

Seven Wests opened 1♠: better, but not just right. Mostly they were able to get to game, but of course it did leave the field wide open for their opponents to find a 5♣ or 5♦ sacrifice.  1♠ is not the world's worst bid, but it does lack a pre-emptive effect. Note that it does not satisfy the  Rule of 20.

Only one West, Anne Heyes, made the correct opening bid of 3♠.  She applied the Rule of 2 and 3, bidding two tricks more than she had in hand, vulnerable. Her hand had 6 spade winners (assuming you have to lose to ♠A) plus the ♣A, making 7 tricks. Add two to that, and you come up with a 3♠ opening.  This bid is designed to pre-empt the opponents whilst accurately describing your playing strength to your partner.

After 3♠ is doubled for takeout, East knows partner has about 7 tricks. Her two aces take it to 9, and the ♣K is  very likely a trick, particularly given that if the ♣A is with the opponents it's likely to be North. East should raise 3♠ to 4♠. Notice how this shuts out N/S. South could hardly bid over 4♠ and North has said her all as well. The minor suit sacrifice is lost.

The Rule of 2 and 3: don't leave home without it.

1) RHO opens 1♣.

This situation is not uncommon: RHO opens in your suit. Very often it is clubs, where the opening doesn't really promise many clubs, but it can happen in any suit.

My general advice is to pass (for the moment) in these circumstances. Perhaps you can bid the suit yourself later, and partner should understand what's going on. Meanwhile, if the opponents end up declaring in this suit, who are you to complain?

But there's an alternative, one that was found only by John Robertson, and that is to overcall 1NT, showing a balanced hand of about 16-18 HCP, with a stopper. That is a pretty good approximation of the hand: the strength is right, the stopper is certainly right (!), and it's almost balanced. The 1NT overcall gets the hand off your chest, and puts you into a comfortable bidding situation, where you can respond honestly whatever partner bids.

And that's what happened: partner Lanny Chan showed spades with a transfer, and they eased into the successful 4♠, no sweat.

Other Easts doubled 1♣, pitching themselves into a most uncomfortable position, without any happy ending.  (And  it could have been worse: partner might have bid hearts, your doubleton, and then you would really be in a mess.)

2) RHO opens 1♦.

Here the decision is closer.  Some doubled, others overcalled 2♣. With 17 HCP, it's a line-ball decision whether the hand is too strong for a simple overcall. The successful East was Gabrielle Costello. who doubled 1♦.  Her partner, Mary Buchanan, judged very well with her response to the takeout double. She jumped to 2♠, counting something for her 5-card suit and nice distribution. This emboldened Gabrielle to go to 4♠. Well bid!

On the surface, no one did anything wrong. West had a minimum 2♣ opener, and couldn't do much more than she did.  East's 2♦ shows 0-7 HCP, which is what she had, and her 4♥ showed a maximum in her range, with heart support.

But in most text books, there is some fine print on the strength range of the 2♦ response. It says that with a 7 HCP consisting specifically of an ace (4) and king  (3), the hand should be upgraded to a positive response. The reason is that aces and kings are generally undervalued by the 4-3-2-1 scheme, so such a 7 HCP hand is usually worth more than 7.

Just one East, Anne Heyes, recognized this, and she gave a positive response  of 3♣, showing a 5-card suit.  She gets this week's elephant stamp for accurately judging her hand. It didn't lead to a slam, but it probably should have, when she supported her partner's hearts.

The takeaway: A 7-point hand consisting of an ace and a king should give a positive response to 2♣.

You are missing two clubs: the king and the jack. The a-priori odds are that they split 1-1, but only by a narrow margin of 51% to 49%.   In fact the margin is greater than that, almost 60%, because of the bidding. It appears North has 6 or 7 spades, South 3 or 4. That leaves much more room in the South hand to have the last remaining club.

BUT, the bidding reveals another aspect. North has opened the bidding ... E/W have 25 HCP to N/S's 15. Most of these points will be with the opener, so that strongly suggests than North has the ♣K.  So the distributional odds are outweighed by the HCP odds, and the correct (and winning play) is to finesse the club.  Gordon Travers did so, successfully, as did Anna Kearon and Gordon Shinewell on slightly different plays.

I thought it was a nice try from John Robertson, sitting North, to lead that sneaky ♣J from ♣KJ doubleton.

Now, to my quibbles with the bidding. West's 3♣ doesn't seem enough to me. The ♠Q is certainly not worth 2  HCP, but the singleton should be worth 3. That gives West 12 total-points: was 3♣ enough?  I think West should have bid 4♣, but no-one did. 

And finally, what about South?  2♠ was almost a universal choice, but I much prefer the 4♠ bid made by Julie More, preempting.  Great bid!  That weak and distributional South hand needs to apply pressure to the opponents. And it worked by silencing West.  East came back bravely with 5♣, but now Janice Meldrum, sitting North, was convinced to go on to 5♠.  When that was passed out and defeated only two tricks, Julie and Janice had a most deserved near top.

Few would have the super-sophisticated methods to bid this hand accurately. And those that do might find it a pyrrhic victory. Suppose you scientifically find out that there are two top clubs to lose, so you stop accurately in 4♠ or 5♠.  The problem is that your opponents might listen in on your auction, as is their right, and know to lead a club.

It's often best to blast hands like these, so that no-one, including yourself, knows who can make what.  I would wheel out Old Trusty, Blackwood, and bid a small slam if partner shows one or two aces. Yes, we might be off two cashing aces, but the opponents haven't taken them yet. 

And wouldn't it be a buzz if partner showed 3 aces! Now you can bid 7NT, counting 5 spades, 6 hearts and the two minor suit aces.

Agreeing with me strategically were Marie Shenker and Terry Passlow.  They asked for aces, got two, and bid 6♠.

There was a funny old accident at another table where Penny Robertson held the South hand. She went the scientific route, responding 2♥. Partner rebid 2NT. Despairing of finding out what she needed to know, Penny now bid 4NT, ace-asking.  But partner Fiona Ferwerda interpreted 4NT as a quantitative try for slam (as would I).  With her tip-top hand, she accepted by bidding 6NT. Penny was aghast, but what could she do?  With North as declarer, protected from a minor suit lead, 6NT made easily, for a stone-cold top. 

1. Assuming you play a 1NT opening as showing 15-17 HCP, this hand technically qualifies, as it has the right points and balanced shape.

However, I strongly agree with the 1♦ bid chosen. Not only are you top of the range for 15-17, you have a strong 5-card diampond suit (think of it as a length point). Moreover, all your points are in aces and kings, which tend to be undervalued by the 4-3-2-1 point count. The hand deserves an upgrade.

In fact, even on a 16-18 HCP 1NT range, this hand is probably too strong. Indeed, on the famous Kaplan-Rubens hand evaluator (see http://rpbridge.net/cgi-bin/xhe1.pl), it comes to 19 points.

2. Did you realise that partner has shown at least 5 spades?  With 4 spades, she would have made a negative double of 1♥, showing exactly that number of spades.

In that case, you should give a vigorous support bid in spades.  Either 4♠ , recognizing that you have an effective 19-count, or 3♠ , recognizing that your heart king is a little devalued, due to the 1♥  overcall on your left.

(If you do bid just 3♠ , then partner should proceed to 4♠, based on the distributional points.)

With 10 HCP opposite partner's  (for example) 15-17, you want to reach the game level. In fact, your hand is better than 10 HCP, because you should count a length point for the 5-card diamond suit.

Which game?  Forget the diamonds: you can't sensibly get to diamonds in preference to notrumps. However, if partner has 4 spades, you'd like to reach 4♠ in the 4-4 fit.

So apply Stayman, and when partner bids 2♥, go to 3NT. If partner has 4 spades as well as 4 hearts, she should deduce that you must have spades yourself, otherwise why did you bid Stayman in the first place?

The auction 1NT - 2♣ - 2♥ - 3NT - 4♠ looks a little weird, but it is the correct way to bid this combination.  Well done to Shyamala Abey (N) - Susan Shand (S), and Valerie Remedios (N) - Lilian Young (S), who were the two N/S pairs to conduct the officially approved auction.

One thing I'm sure of: you should not go past 3NT yet. It's far too likely to be the right contract.

But simply bidding 3NT is dangerous. Sure, partner is likely to cover diamonds, but by being declarer, you are exposing his stopper to the opening lead.

There are two alternatives, both of which include their own point of theory.

3♥ here promises only a 5-card suit. Whilst normally you want to have 6 cards to rebid a suit, in this auction (1minor - 1major - 3minor) only 5 is promised. This is because the strong auction has somewhat preempted the bidding. 3♥ , looking for a 5-3 heart fit, is a sensible choice here.

3♠ is the other option. This shows a stopper, not length. Spades as a final contract is, for the moment, off the agenda. Partner doesn't have them (otherwise she would have rebid 1♠), and you usually have no more than 4 of them.

New suits in this auction are primarily stopper-showing, angling for 3NT. 3♠  would be my choice on this deal.

Looking at all four hands, it is clear that today you must steer clear of 3NT. The safest spot is 5♣, making easily. 4♥ will get you extra points, but the 5-2 fit is a little hair-raising. It works though.  

Who did best in real life? No one really. But Louise Leatham, in the problem position,  bid 3♦. Whilst not doing what 3♠ would do, it at least kept the auction ticking along below 3NT, and left room for partner to give some heart support if she had it. Partner innocently bid 3NT with spades stopped, and on this auction, one could hardly blame North for leading a spade. 13 tricks later, Louise had her shared top. 

East could have the following holding in diamonds:

1) ♦KJ6
2) ♦K6
3) ♦J6
4) ♦6

and each is about as likely as any other.

If East has ♦KJ6, you should let the ♦10 ride.

If East has ♦K6, you should play the ♦Q.

If East has ♦J6, you should play the ♦ A and drop the singleton king.

And if East has singleton ♦6?  Then you have an inescapable diamond loser, but here it's essential to play the ace.  Why?  Because then you will play on hearts, and assuming that suit divides 3-2, you can chuck your club loser on the third round.  The defence will be welcome to their diamond trick.

That aspect points the way to the correct play of the ace.  It works, and is necessary, in two of the four cases.  Furthermore, in case 2), if East has Kx, then you still will make the slam, as long as East can follow to two rounds of hearts.

And in real life, it's bingo! The singleton king comes down offside.

Counting through the effects of multiple plays one by one, whilst laborious, can be an effective way to work out what to do.

Very very well done to Trish Stewart-Uden who not only bid the slam (via a different, competitive auction), but played it exactly right to chalk up a top board.

West. If 1♣ is passed out, you could be ending up in a 2-2 fit ... how ridiculous is that? On that basis, it's tempting to jump from the possible frying pan into the possible fire by responding.

I don't think there's a definitive answer, but experience tells me to let sleeping dogs lie. Yes, the contract could be ridiculous, but it could also be your last making spot: partner doesn't have to have short clubs.  On this deal, if you do respond, you will next hear 2NT from partner: how are you feeling now?

If you do choose to respond, I strongly suggest you bid 1♦, making every effort to keep the level low. Then if partner should happen to rebid 1♥, you can pass with a sigh of relief, knowing that at least now you are in a 4-3 fit.

North.  It goes 1♣ - pass - pass to you. The guideline in the balancing seat (where 1-suit has been passed around to you) is to mentally add 3 HCP to your hand and bid accordingly. Well, here you have 11 HCP, add 3 to get to 14 "virtual" points.  Now if I heard 1♣ on my right, and I had a 14-point 2-4-4-3 hand, I would pass. I'm not strong enough for 1NT, don't have a 5-card suit to bid, and a double tells a ghastly lie about your spades: promising at least 3 of them when you only have 2.  So I'm with Jenny Matheson who calmly passed out 1♣.  

Now it was up to Jenny's partner Mariette Read, sitting South, to lead to 1♣.

South. South is on lead to 1♣ and knows quite a lot. She has 7 HCP, West has fewer than 6 HCP, and partner who has passed it out, even after mentally adding 3 HCP, can't have that much either. Clearly declarer has a very strong hand. When leading around to a strong hand, you want to avoid leading away from unprotected honours, because they often have the effect of giving declarer a trick for free. That rules out a spade and a heart ... I would decide between the minors.  Mariette settled on a diamond lead (leading away from a jack is not particularly dangerous at all), and duly defeated 1♣ by a trick for an excellent score.  A strong partnership result, that.

You might use the same reasoning as you did for the hearts, figuring that East was more likely to have the spade ace, due to the opening bid.

But you'd be wrong, and a piece of visualization will prove it.

What do you know about East's hand? She has Qxx in hearts, that's 2 HCP, and the ♦A, that's 6. And from West's ♣10 lead, East also has ♣AJ ... brings it to 11 HCP.  All the evidence so far points to East having a balanced hand.

Only two honour cards are unplaced, the ace and queen of spades.  And if East has the ♠A, that takes her count to 15, and would she not have opened 1NT with 15 HCP, balanced?  (Before you make your decision, you might want to ask the opponents about the range for their 1NT opening ... that is your legal right.)

So East probably doesn't have the ♠A, and probably does have the ♠Q (otherwise she might not have opened a balanced 11-count).  You should play the ♠J to this trick, which will ensure you 9 tricks.

The calculation given above is not hard to do, however you have to think of it. The issue of visualization is one of the most challenging of the game ... peering into an opponent's hand and making deductions from it, some of which are negative inferences (if she had this, she wouldn't have done that).

I have to admit I was completely befuddled when I gathered this data.

3♠? What if you're left to play there?

Double? This could perhaps work out, but there must be some chance of partner, with a fair number of diamonds, leaving your double in.

I'm not saying I know what to bid. I don't. But making a choice that could result on my side not even getting to game seems wrong. Still, maybe a few Easts know more than me ... Lorraine Pitman and Sandra Mansell were two who managed to reach slam after their first dangerous bid. But 7 of the 11 E/Ws languished in game. When you look at West's hand, you will know this was not optimal.

Actually, I would have got to slam myself, bidding 6♣ directly over 3♦. And if South had sacrificed 6♦, I'll try 6♠ next. It won't always work, but at least it will do justice to a hand that has 11 tricks in it, with plenty of chances for a 12th. 

This deal isn't particularly educational ... bidding freak hands is something of a guessing game.  But I write it up because it illustrates a malaise that I am increasingly seeing in bridge: the desire to bid scientifically when you should not.  There is a philosophy rooted in the Acol system: bid what you think you can make.  It has a lot going for it. Here I think I can make 6♣ so I bid it. But many players seem to feel they are not bidding 'properly' when they just make a simple bid suggesting a contract. Sometimes, that's exactly what you should do.

I was fairly sure no-one would choose what I believe to be the correct bid, myself included. And I was not disappointed.

The Law of Total Trumps tells you to, in a competitive auction, immediately bid to the level equal to your combined trump length.  Well, partner has shown 5 spades, you have 6 of them, for a total of 11. The Law suggests a bid of 5♠ (!), and this idea is supported by your favourable vulnerability (they are, you aren't). 

5♠ just happens to be the correct "par" contract: down one against their making 5♥.  As it turns out, the law is not an ass.  And of course the huge advantage of bidding 5♠ now is that your LHO, East, may be sucked in and bid 6♥, missing two aces. 

Several players in this position crept up on things, bidding just 2♠ ("walking the dog") and in a couple of cases this worked spectacularly, when they got to play 4♠.  Nevertheless, in the long run, this is a losing tactic.  I much prefer the immediate 4♠ bid made by Sandra Mansell and Geoffrey Schroder, which stimulated their partner to progress to 5♠ over the opponents' 5♥.  And Geoffrey landed the big fish, when his opponents overreached to 6♥. 

Here's my analysis:

Pass ... no guts.  Sometimes it's true that if you can't think of a good bid, don't bid at all. That's presumably was the passers' reasoning here. But this hand is simply too strong to let the opponents play 2♠. Even though 2♠ went down, +50 was no compensation for what your side could make, as it turned out.

Double ... no hearts.  A takeout double is not the answer. The odds are strong that partner will bid 3♥ ... what will you do over that?  Pass, and maybe land in a 4-2 fit. Or bid one of your suits in a 'hail Mary' attempt to get to a winning contract. If I was setting this hand up for teaching purposes, I would have partner bid hearts, and then you would regret it. Learning point made! Alas, today the double did no harm with partner responding in clubs. Lucky.

2NT ... no agreement.  A number of players bid an "unusual" 2NT, thinking to show both minors. But the unusual notrump really only works as a jump bid.  Here I would ask you: suppose you had 16 HCP balanced, with a spade stopper.  If 2NT is for the minors, what are you meant to bid with a normal notrump overcall?

2NT should be natural. It's hard to work out whether the various players who bid 2NT were on a wavelength here with their partners. I know that the pair who got the top E/W score achieved it by accident. West self-alerted 2NT as showing the minors and East bid 3NT, clearly thinking (as I would have) that partner's 2NT was natural.  10 tricks later, they had their top. Lucky, lucky!

That leaves 3♦ which I'm fairly sure is the best choice. It's not perfect, but it doesn't have any of the obvious flaws of the other calls. 3♦ is a perfectly valid bid, and if you get the chance, you can follow it up with a club bid later.  So I'm with Dell MacNeil and Ray Carbuhn who were the only Wests to make the simplistic overcall.  

Every single declarer took the heart finesse at trick 2.  This lost, and those Souths that were canny enough to continue with a black suit, found themselves taking 3 tricks: a spade, a heart and a diamond. The problem for declarer was that they were now stuck on the table. It was not a nice position to be in.

If the heart finesse had won, declarer would be in a far better position. They could take the ♥A and lead a diamond up. If South has ♦A, there's a discard for their losing spade.

My contention is this: the heart finesse was unlikely to gain ... it helps only when North started with ♥K-doubleton. Now try playing a heart to the ace at trick 2, then playing your diamond up. If South has ♦A, then there's your overtrick. If North has ♦A, well you haven't really lost anything.

Maybe I'm tilting at windmills ... it would have been nice to have just one declarer agreeing with me.  But it was not to be.