One throw of the dice

What are you bidding sitting South on this hand in response to partner's opening 1NT? I'm raising straight to 3NT. I've got enough points for game, together with a long suit I might be able to set up plus entries to get to it. Sure, we might make 5♣, but if we can then surely we can make 3NT as well - maybe with overtricks. In other words, it's the usual story: with a minor fit, go for NT, and only settle for the minor as a last resort or if you've got a slam on (which you won't have here with just 26 points between you).

More on the auction later. Meanwhile, you're now sitting North in 3NT and East leads the ♥J. Plan your play.
 

Just the one chance

Hmm. Looks as if the opps have found the right opening lead. Right. How many tricks have we got?

We have eight tricks: 6 clubs and the ♥A and ♠A. Where's the 9th coming from?

Well, once you come in with your ♥A (which you will very soon!), you can easily set up a trick in diamonds by leading the ♦K. The trouble is, you'll be off before you get the lead back again. The opps will win with the ♦A and cash all their heart winners. No good - you simply can't afford to lose the lead. 

Which only leaves spades: your only chance of bringing this contract home is if you lead a spade towards dummy's ♠AQ and if East holds the ♠K. 
 

Playing it out

So exactly how do you play it? 

OK. You've won with your ♥A, either at trick 1 or 2 - you can hold up if you like, but it won't help unless the hearts are split 7-2: unlikely, on the auction you've just had. What happens next?

You lead a little spade. Right away, at trick 2. It's very tempting to cash all those lovely clubs first, isn't it, just to get them under your belt and make you feel a bit more secure. The trouble is (again!) that it's a sure route to disaster: once the last club is played, you can't take the spade finesse because you have no entries left to your hand. You'll be leading away from your ♠AQ instead of towards them.

Which is why you have to cross your fingers and take the spade finesse as soon as you get the lead. Sure, if the ♠K is with West, you're down. But it's the only chance you've got - and as it happens it comes off, as you'll see if you take a look at the whole deal.

On the night

On the posh night, 5 pairs were in 3NT, all getting the ♥J lead, and just three making. (Guess who didn't lead a spade at trick 2, then?). Two others were in 3♣ and one in 5♣ - which somehow made although it should go 1 off.  

In AP, no one bid 3NT. Most were in 3♣ and one was in 5♣, again somehow making.
 

Back to the auction ...

As a raise to 3NT is a no-brainer, how come so few people were in it? Probably because East overcalls 2♥. This makes life rather more difficult for South. She has game-going points but nothing in hearts, so you can see why she might want to bid 3♣. 

A better bid would be 3♥. Huh? Well, actually, there's only one thing it can mean. You're obviously looking for a NT contract, so 3♥ must mean 'Hey partner, I want to be in 3NT but I'm worried about the hearts. Have you got a stop?' And with the ♥A, North will bid 3NT. Without a heart stop, she'd have to bid something else, and you'll probably end up in 4♣ or 5♣.

3♣, on the other hand, is weaker. It means something like 'I've got some points here and a nice club suit and I don't think they should be getting away with being in 2♥.' Which is why so many pairs ended up in 3♣.

The 3♥ cue-bid isn't 'basic bidding', sure, but as it can't be natural, it just has to be asking partner for a stop.

cj

A declarer's best friend

Here's a nice auction which exemplifies some of the basic bidding features we've been looking at recently:

West  1♥  A balanced hand with too many points to open 1NT. With 4-4 in hearts and spades, open 1♥, not 1♠. 
East  2♦  With 11 points, East is strong enough to show her suit at the 2 level.
West  2NT  Now's the time to rebid NT, showing a balanced 15+ points. Note that both players are now committed to bidding game: 15+ added to 10+ comes to 25+.
East  3♥  East is aware that partner might well have 5 hearts, in which case 4♥ will be the best contract. So instead of simply raising to 3NT, she tests the water: 'I've got 3 hearts, p, just in case you have 5.'  
West  3NT  Nah, I've only got 4. But thanks for asking.

North leads the ♣4 ...
 

Planning the play

... and before you play any cards, you need to plan your play. How many tricks do you have? How many more do you need? And where it is / are they coming from? 

• You have 8 tricks: 2 clubs, 4 hearts and 2 spades. So you need one more trick.
• You might be able to generate this if the opps' spades are split 3-3: then your 4th spade will be worth a trick. The problem with that is that the odds are only around 35%. Not great.
• Diamonds are a better bet. You'll have to give them tricks with the ♦A and ♦K, but if the ♦10 drops (or if you can finesse against it) you can generate your 9th trick. The chances are better than 50%. 
   

An unavoidable risk

OK. But even if the diamonds work out OK, there's a risk, isn't there? Can you see it?

Well, when you lose your first diamond trick, they're going to return another club. That's your club stops gone. Then when they win their 2nd diamond trick, they can take their club winners. OK. So you have to hope that the opps' clubs are split 4-4. That way you're only losing 2 diamonds and 2 clubs. But if the clubs are 5-3, you're losing three club tricks: one too many. But there's nothing to be done: you have to hope for the best and get on with it.

So let's start playing. You duck the first club, South winning with the ♣Q, and win the club continuation. Now for the diamonds.
 

Playing the diamonds

How do you play them? The best plan seems to be to start with a low diamond from dummy towards the ♦Qx. If South is daft enough to rise with the ♦K or ♦A that's your diamond trick set up. If not, you can try a finesse the next time you have the lead: a low diamond from your hand towards dummy's ♦J9, hoping for the best.

Let's try it: First you have to get out to dummy to lead the small diamond. How? Lead a heart. Sure, you have ♠AK in dummy, but if you take that route, they may change their plan in midstream and lead back a spade, causing you all sorts of problems. In hearts, however, you have four stops, not just two! So ...

• Lead a low heart to dummy's ♥K.
• Lead a low diamond to the ♦Q. North wins with the ♦K and leads a club. That's your last club gone.
• Now lead your ♦5 ... and as luck would have it, the ♦10 appears from North. Lovely. You cover with the ♦J, South's ♦A wins the trick ... and your ♦9 is now the top diamond. Phew.

Now the opps can cash their clubs ... but it turns out that the clubs were 4-4, so they get their 2nd club trick and you get the rest. 3NT bid and made. Take a look at the whole deal.
 

On the night

On the posh night, everyone was in 3NT. Just one went off, three made 9 tricks (as we just did) and the other 4 somehow (see below!) all made overtricks.

In AP, most declarers were in 3NT (though 2 managed to end up in hearts). Two made overtricks, but three declarers went one off.
 

Points to take from this hand

• The opening lead. Sure, North's got a nice sequence of 5 hearts, but EW have seven, probably including all the top honours, so leading a heart's a waste of time. What happens if they lead a heart is that you can set up your diamonds without running out of club stops, and end up with a very pleasant 11 tricks. 
• It's worth holding up on the first club trick in case the clubs are 5-3. You never know. If South holds ♦AK and has only 3 clubs, they'll never be able to make their club tricks. Even if the top diamonds are split, the opps may misplay it and get stuck in the wrong hand.
• In the auction, East does well to bid 3♥: if partner does have 5 hearts, then you want to be in the suit rather than 3NT.

cj

Responder in ?Wonder?land

9-card suits don't come up very often, but they've been getting a bit London-bus-like in recent weeks. On this hand you're obviously going to intervene (especially after your partner's opening pass) - but how high should you go? 2♣? 3♣? 4♣? 5♣? And how do you decide?

There are two things to guide you: the length of your suit and a peek at the vulnerability.

The level of a preempt is related to the suit length, 6 being suitable for a weak two, 7 a weak three ... and so the default opening bid (or jump overcall) for a 9-card suit is at the five level. The word 'default' would suggest equal vulnerability, so that at 'favourable vulnerability' (ie they're vulnerable and you aren't) you might risk going one higher, and at 'unfavourable vulnerability' (ie you're vulnerable and they aren't) you might decide to go one lower. the equal vulnerability would suggest that on this hand, you should go straight to 5♣. *

Note the straight to 5♣. This stops the opps from having further sensible conversation. South's now stuck in a 'Wonderland', where all she can do is wonder what to do next and take a guess - as you'll see if you take a look at the whole deal.
 

South's choices

Your 5♣ will have given South a bit of a jolt - as well as a difficult choice. Fortunately for NS, they at least know about their major fit, and South has to decide whether to punt 5♠ or X for penalties:

• The X is an easy option. South has 15 points (including ♣Kx, which must be worth a trick) opposite an opening hand. It's pretty certain that East isn't making 5♣.
• But can you make 5♠? This is less sure. You could easily be missing the ♥AK as well as the ♣A ... but on the other hand, partner might be void in clubs or have the heart honours herself. You simply don't know.

Add to this the fact that if you can get East three off in 5♣X that'll be worth 800 - more than making 5♠. Most Souths will surely prefer to double than to risk bidding on. 
 

What happens?

• 5♣ goes just 2 off, for a penalty of 500 points if doubled.
• 5♠ makes, thanks to some fancy footwork by declarer in setting up the hearts, and is worth 650.

Which means that East's 5♣ bid is great value for money: it gives EW a good chance of getting away with just -500 instead of the 650 that NS would otherwise score.
 

On the night

My prediction turns out to be wrong: on the posh night, all but one of the Souths faced with the choice plumped for 5♠, and with one exception made it. (Two were allowed by rather flaccid Easts to get away with bidding just 4♠.)

In AP, 3 were in spades (two making), 3 were in 5♣X-2 and one was in an extraordinary 3NTX+1, for a score of 950.

cj

* Here's an easily remembered guide to sacrifices and vulnerability:

• At unfavourable vulnerability, you can only afford to go ONE off doubled ...
• At equal vulnerability, you can afford to go TWO off doubled ...
• At favourable vulnerability you can afford to go THREE off doubled ...

... compared to what you'd lose if you let them make their game.

Child's play

This is another of those 'strong unbalanced' opening hands like last week's HOTW. On this one, sitting South, you decide to open just 1♠ (on the grounds that if partner's too weak to respond you probably haven't got game anyway). In the event, she responds 2♦, and it's child's play to find 4♠.

West leads the ♦7, down goes dummy and ...

... it's time to plan your play

It's looking pretty good, isn't it - so good, in fact, that you're regretting not making a slam try. Never mind, you are where you are. What to do?

The first question facing you is whether to go up with your ♦A or whether to take the 'free' finesse and play low. Each has its pros and cons - playing low is great if West holds the ♦K (unlikely!) and OK if the 7♦'s a doubleton, but if it's a singleton they'll be getting a diamond ruff. Going up with the ♦A stops their ruff, but uses up your only certain entry to dummy.  

But the crucial question is the one that all declarers in suit contracts must ask as soon as they see dummy:

Is there any reason why I shouldn't clear trumps at the first opportunity?

The answer here is a resounding 'no': you have plenty of tricks in all three side suits and no reason at all to leave trumps till later.

Why is this so important? Well, let's see what happens when you don't clear trumps ...

You decide to play low to trick one. East wins with the ♦K and leads back a low diamond, which West ruffs. Two tricks to the bad guys. East leads back a small heart, which you win with dummy's ♥10. This is the crunch time: you have the lead and your first chance to clear trumps. OK. Let's say you don't - say you decide to cash a second heart winner instead. 

To see what happens, take a look at the whole deal:

• East ruffs and leads a diamond
• West ruffs and leads another heart
• East ruffs and leads her last diamond
• West ruffs ... and you're three off. The opps have won a trick with each of their 5 little trumps.
   

Rewind 

Let's go back to trick 3 and try again - you've just won your first trick with ♥A. Cash your ♠AKQ and the opps have no trumps left - and you have nothing left but winners. The top two diamonds, the top three hearts and two more trumps.

When you're in a suit contract, you don't want the opps to be ruffing your tricks - you want to be ruffing theirs. So get rid of their trumps asap. It's child's play, really - and the alternative can be a nightmare!

On the night

Everyone on the posh night made 10, 11 or 12 (yes, you can make 12, but you have to be pretty devious to do it). In AP, most made 11 or 12 tricks but a couple of declarers went off, and the only way that can have happened is that they didn't clear trumps.

cj

* Your rebid is 3♥ - an unconditional game force. Partner now knows that you have at leas 5 spades, so has no problem signing off in 4♠.

The right shape?

What do you open with this hand? A lot of players will open 2NT: 6-3-3-1 isn't exactly a NT shape, they'll agree, but the long suit is a minor and you have the points - as well as a stop in your singleton suit.

Personally I don't like opening 2NT with a singleton, even if it's an Ace: the opps are likely to lead the suit (they've probably got more of it than any other suit) and there's your stop gone at trick one. There's another reason, which we'll come to, but for now, if you don't open 2NT, what to open instead?

The usual answer is just to open 1 of a suit - in this case 1♦. But what if partner passes? Well, if partner's really too weak to respond, you probably haven't got game on anyway, so no problem.

But this hand's so strong - only needing the ♦Q or a successful diamond finesse for 3NT to be on - that I think it's worth a 2♣ opening. * 

Say you open 2♣.

• Over partner's 2♦ response *, you bid 3♦, telling partner you have a strong unbalanced hand worth 9 tricks with diamonds as trumps. 
• Partner now bids 3♠, promising a few points (maybe 5+) and a 5+-card spade suit.
• At this point, you can stop worrying about your singleton spade and bid what you wanted to all along: 3NT.

OK. So if the spades are safe, then opening 2NT would have been OK after all, then? Well no, maybe not on this hand ...
 

Disaster!

Take a look at the whole deal. What's partner going to do if you open 2NT? Well, she's going to think you've got at least 2 spades for your bid, meaning that you have a spade fit. So she'll transfer you into 3♠ (via 3♥) and then raise you to 4♠! Which, as you can see, will usually go off.

3NT, on the other hand, makes 10 tricks. Note that your ♠A on its own isn't enough: that's knocked out at trick one, so you need a second spade stop to keep you safe when you lose the lead to the ♦Q. And it's partner's 3♠ bid over your 3♦ rebid that tells you it's now safe to bid 3NT.

So, how did the more experienced players do on the 'posh' night?

On the night

Just 3 pairs were in NT (including one who punted a very frisky 6NT!). All the rest - 6 pairs - were in 4♠, nearly all going off - which suggests that many (most, even!) experienced players are happy to open 2NT with a singleton. Well, it works some of the time ...

With a bit of help, the AP players did better: all but one pair were in 3NT, mostly making 9 or 10 tricks. The one pair in 4♠ went one off.

cj

* No, 2♣ does not 'promise 23+ points': it promises either a balanced hand with 23+ points or a strong unbalanced hand with 9 'playing tricks' in a suit. It's usual to respond 2♦ (a 'relay' response which has nothing to do with diamonds) to give opener a chance to clarify which kind of hand she has: 2NT to show a balanced 23+ or (here) 3♦ to show 9 playing tricks in diamonds.

Choose your rebid

With a pleasant 15-count, you open 1♣ and partner responds 1♥, the opponents both passing. What now?

There are three choices, all of which are misleading in one way or another:

• 2♣  Technically the 'correct' bid, but understates your strength a bit. It would be a shame if partner had 10 points and passed, having concluded that game was too unlikely to bother with. *
• 3♣  The 'jump rebid' describes your hand better (16-18 points and a good 6-card suit), but technically you're a point short.
• 1NT  Not quite a 'balanced hand', but gets your points spot on.

Any of these choices is kinda OK, but consider our 'holy grail': seek out a major fit; failing that look for no trumps; and only as a last resort settle for a minor suit. The major fit looks unlikely: this would require partner to be holding 6 hearts, so why not go straight for the 2nd best destination: no trumps. 1NT gets my vote. ** 

As it happens, it doesn't much matter which you choose on this deal. As you'll see if you look at the whole deal, partner has a chunky balanced 13 points, so if you rebid 1NT she's raising you to 3NT. And if you rebid clubs, she's bidding 3NT anyway.
 

Who rebid what?

On the posh night, everyone was in 3NT, and it's interesting to note that five of the eight declarers were West: meaning that most Wests preferred to rebid 1NT instead of rebidding clubs.

It was a similar story in AP: three of the four 3NT declarers were West.

As always, the trick tally wasn't as good in AP. The posh declarers made 9, 10 or 11 tricks, which in AP, two declarers went one off.
 

Where are the tricks?

If West's the declarer, North will probably lead the ♥10 (top of the 'sequency' bit of the broken sequence ♥Q109). So where are the tricks coming from? In the event, South wins the trick with the ♥A and returns another heart, which you take with your ♥K. So what's next?

You've got one heart trick (two if they carry on with hearts), three spades and at least one diamond, so you only need 4 more from clubs to make your contract. So attack clubs NOW, while you still have (a) stops in the other suits and (b) entries to your clubs. It's probably simplest to cross your fingers and bang out the ♣AK, and as long as they're 3-2 you've got 10 tricks. You lose a trick to the ♣Q and probably to the ♥Q, and the rest are all yours.

cj

* With 10 points, partner shouldn't pass, as you're by no means denying a 15-count if you rebid 2♣. I have a 'rule of 10', which says that if partner opens and I have 10+ points, I keep the auction going until 2NT. Sometimes you end up getting too high, but on the whole you find yourself missing games a whole lot less.

** If partner does have 6 hearts, you won't miss your fit - she's sure to bid them again.

Temptation

The shapelier you are, the less you have to worry about point-counts. So when her partner opens 1♠, North's bidding game - even without the 2♦ overcall from West. With a great trump fit, North's hand has just 7 losers - enough for game in itself - and it looks even better after the overcall, as there's a max of just one diamond loser. Add to that a void in hearts and long clubs (a good chance that partner's short in them, then) and 4♠ is a no-brainer. And if you go off, you're not vulnerable - so even if you're two off (-100) that's less expensive than EW making (say) 9 tricks in diamonds for 110. 

But you've no intention of going off ...
 

Making 4♠ 

West starts off with the ♣AK (everyone following suit) and switches to a low diamond. Sitting South as declarer, are you going to make your contract?

Well, if you play sensibly, the answer's yes. It's pretty well a lay-down. This is the situation:

You have just two possible losers: the ♠K and a diamond trick. Lose both and you're going off. Lose just one and you're home. Lose neither and you're making an overtrick.

OK. How do you get home with pretty much 100% chance of success?

Easy. Simply dump dummy's diamond loser. You win with the ♦A, cross to your hand with the ♠A and lead a heart, discarding dummy's ♦2. You will still lose a trick to the ♠K, of course - unless it was a singleton and dropped under your ♠A - but you can put up with that because you've just made your contract.
 

Trying for an overtrick

The temptation, of course, is to try for the overtrick. Instead of leading to your ♠A, you take the finesse: play your ♠Q in the hope that East holds the ♠K. If it works, that's lovely: you can dump your ♦2, as planned, catch the ♠K and make 11 tricks. 

The trouble is that if it doesn't work - if West holds the ♠K - you're off. She wins a spade trick, leads a diamond and you lose a diamond trick as well.

Which explains (as you'll see if you look at the whole deal) why so many people went off instead of making a comfortable 10 tricks ...
 

On the night

In AP, apart from one table in 2♦, everyone was in 4♠ by South. Good so far. The downside was that only one of the five declarers made the contract.

On the posh night, everyone was in 4♠ and six out of the eight made it. Two fell for the temptation and made just 9 tricks.
 

A final thought

There's no suggestion here that declarers went down because they were greedy. It's declarer's job to be greedy! In pairs, an overtrick can make all the difference between a top and a bottom.

So it would, of course, be correct to try the spade finesse if you could afford it. If dummy had, for instance, one club fewer and a singleton heart, you could come over to your hand with a heart, then discard dummy's ♦2, get back to dummy with a diamond ruff and then take the spade finesse. It still loses, but you'd be right to give it a try. Here, though, with no other sure entry to your hand other than the ♠A, it's better to play safe.

cj

Sacrifice?

9-card suits don't come up very often, so when they do it's as well to make the best you can of them. If the opps have a spade fit (which looks pretty likely from where you're sitting) you want to shove your oar in as high as you can - but how high is that?

Well, think about opening pre-empts. With a 7-card suit you'd open 3♦ and with an 8-card suit 4♦ ... so with a 9-card suit 5♦ looks about right. What's nice about 5♦ is that it forces the opps above their game slot of 4♠, so they're either going to have to stick their necks out and risk 5♠ or else (presumably) double you for penalties. So the next question is:

Can you afford it?

The difficulty is that you're vulnerable and they're not - the worst combination if you're making a sacrifice. They only have to get you two off for a penalty of 500, which is worse than the 420 they get for making 4♠.

On the plus side, though, you have a very nice hand. You have none of their spades - no losers there, then - and will lose a maximum of four tricks: the ♦A, ♣A and possibly two hearts. So partner will have to stump up just one of those tricks to make it all worthwhile.

So do you bid 5♦ or settle for something a bit more modest? Up to you! Let's say you go for it ...
 

What happens?

Take a look at the whole deal. Partner's hearts are good enough to save you one of those four tricks, anyway. East will probably lead the ♠5 * - her partner's suit. Plan your play.

Well, it's easier if you can see all the hands, but it turns out that you can make your contract. Can you see how?

It's all about the ♣K, isn't it? Once you've got rid of their trumps (which doesn't take long!) you cross your fingers and lead your singleton club towards the ♣K, and whether East takes her Ace or not, you're home. Let's say she does. All you have to do now if get over to dummy, dump a small heart on the ♣K, and, crossing your fingers again, take the heart finesse ... job done!

... Erm. Fine. But how am I supposed to get to dummy? Easy - lead a small trump to dummmy's 10! 

So there you are, thinking you're sacrificing in 5♦ to stop them making 4♠ ... and it turns out that you're the one making the contract, while they can't make 4♠ anyway. They're the ones that should be sacrificing in 5♠ to stop you making game. 
 

On the night

On the posh night, three Norths were in 5♦ (two of them doubled) and two of them made 11 tricks. All the others were in 4♠ or 5♠, all going off. 

In AP, three Norths were in 5♦ and one was in 6♦ (!): two made 11 but two made just 10. The other two EWs were in spades, both going off.

cj

* NOT the ♠2 or the ♠7. The ♠2 (see last week's HOTW) would be promising an honour (lead low for like), while the ♠7, followed by a lower card on the next spade trick, would be promising a doubleton. The ♠5 is MUD (middle-up-down), which, followed by the ♠7, promises what you've got: three rubbish spades! 

Two chances - either will do

Here's a nice hand. I already sent notes about the auction to Wednesday AP players (summarised below) so here we're focusing on the play. It's simple enough: You're sitting North and East leads the ♠6 against your 6NT contract. What are your thoughts?

The first thing to do is to count your tricks, and here you have 11 tricks 'off the top': 3 spades, 4 diamonds and 2 each in hearts and clubs. Where's your 12th trick coming from? 

Well, if East has led from the ♠J, you can make an extra spade trick right now, so let's try that before anything else: you play the ♠10 from dummy, but West goes up with the ♠J and you win the trick in hand.

So you're still looking for your 12th trick, which will clearly have to come from hearts or clubs. You hold AKJ in each suit, so the 12th trick will have to come from either the ♣J or the ♥J, How to proceed, then? There are two lines you can try:
 

No contest

Option 1  Bang out your spades and diamonds and then cash the ♥AK and ♣AK, hoping that one of the Queens will drop, This is pretty unlikely to happen. The chance of a player holding just Qx in either hearts or clubs is less than 10%. So assuming that the defenders aren't daft, this option has around 17% chance of succeeding.

Option 2  Finesse, hoping that the Queen is in the right place. That is, lead a low heart (say) towards the ♥AKJ and play the Jack, crossing your fingers. If it works, you've made your contract. And if it doesn't, try it again in clubs: lead a low club towards the ♣AKJ and play the Jack, again crossing your fingers. The chances of a finesse working are 50% (the Queen might be in either hand), but here you only need one of the two finesses to work to make your contract. That's a 75% chance.

No contest, then. Finessing is almost 5 times as likely to succeed as playing for the drop. Let's try that, then ... 
 

What happens?

You've just won trick one in hand. Lead your small heart and play the Jack. It works - East has the ♥Q. No harm, then, in trying for an overtrick with the club finesse. Lead a low club from dummy and play the Jack: again, it works: West has the ♣Q. You've just made all 13 tricks.

And Option 1? Well, as neither player started out with ♥Qx or ♣Qx (as expected) you end up going one off with just 11 tricks.

So in this case, 'finesse for success'. If that seems a bit obvious, read on ...
 

On the night

In AP, nearly everyone was in 6NT, but only three made 12 or 13 tricks. The other four - presumably following Option 1 - went one off.

On the posh night, two declarers made 12 tricks and the other 5 all made 13.
 

When leading: low is for like, high is for hate

We all know about leading the '4th highest of our longest and strongest suit' against NT contracts. But that only applies if the suit has something to offer. The lead of the ♠3 here, then, would promise at least one honour. From a rubbish suit (and the ♠7643 is just that!) you should lead the 2nd highest: the ♠6. Please take note if you were one of the Easts that led the ♠3. Leading low from an honour and high from rubbish is a great way of telling partner what you have and haven't got.
 

A note on the auction

• 1♦: Sure, you've got 20 points, but I don't like opening 2NT with a singleton (especially a small one!) so I make a standard opening bid and hope partner doesn't pass.
• 1♥: sure, you're strong, but first things first: show your longest suit and see what partner says next: it's opener's 2nd bid that really puts you in the picture.
• 3NT: you're pretty sure that NT is where you want to be, but you're too strong to rebid 1NT (15-16) or 2NT (17-18), either of which can be passed. To be sure, go straight to game.
• 6NT: you now know that partner has at least 19 points. Add that to your 15 and that's enough for the small slam: go straight there!

cj