I held the East hand in an inter-county match this season. My 3♦ opening bid was passed out, and South led ♥K, switching to a club at trick two. I took the ace and led a diamond to my king, South playing the ten. How should I continue? 

I have two choices. I can continue with ♦Q, hoping South started with J10 doubleton, or with a small card, hoping the ace is now bare. If I guess right I can make nine tricks by way of six diamonds, two aces and play up to ♥Q. If I guess wrong I'll lose two trump tricks and go one down. (There's no point in fretting about other diamond splits as I can never play them for one loser - the trumps have to be 3-2.) 

I think I went with the odds by leading a small card next, playing North to have started with Ax. My teammates had little sympathy when I went down, and thought it was obvious to try to drop the jack at trick four. The a priori odds that North started with Ax (one of two possible combinations) rather than Axx (only a single card combination) are 2:1. Of course, this supposes that South will always play an honour on the first round from a holding of J10x. Will they? Would you? You should. It cannot possibly gain to play the small card from that holding, as this will leave declarer with no alternative but to play for the ace to be bare on the next round. Dropping an honour (picked at random is best) gives declarer a losing option, but one they shouldn't fall for, as the odds that the cards lie as you are being tempted to believe are so small. 

Of course, a beginner will not think to play this false card, and you have to judge your opponent. Playing in the first county team (no guarantee of quality, I know) I thought I was on safe ground. As this time South genuinely had no choice but to play an honour, I won't know what they would have done, I'll have to wait until it comes up again, but the reaction of my teammates have given me reason for doubt. I think I'm right in saying that so long as my opponent will false-card an honour on average at least one time in two, I will show a profit in the long-run by trying to drop the ace. That must be good odds for first-team players, surely? 

This hand was from a teams-of-four competition held at Wolverhampton Bridge Club in November. At IMP scoring the goal is to defeat the opponents' contract wherever possible, so when partner led ♥7 to my ace and declarer's five, I had to picture the most likely layout of the cards to allow the contract to be beaten. What would you have done? 

This is a hand from the County Teams-of-Four League. Keith opened 1♠, while at the other table East passed. I can see arguments for both choices - it is a little aggressive, and doesn't quite meet Ron Klinger's criterion for an opening bid (hcp + cards in the two longest suits + quick tricks should be 21½ NV or 22 vul). My choice of response was between a diamond splinter and a Jacoby 2NT. While I'm strong enough to splinter and continue over the inevitable sign-off from partner, it's hard to see how I'm going to be able to find out what I need to know. I suppose if I cue-bid 5♣ and get a 5♦ response I could bid 5NT, asking him to bid seven with two of the top trump honours, but it's taking a risk on there being no loser in hearts or clubs. Anyway, I decided to bid 2NT, and Keith bid 4♠ to show a minimum. (Our agreement is that 3♣ shows every minimum hand to allow more room to explore a slam if West is very strong, but I understood the space-consuming sign-off.) I bid 4NT (RKCB) and got a 5♠ response to show two keycards and the queen of trumps. What should I do now? 

I could bid 5NT to ask for kings (the modern responses are to cue-bid a side-suit king, or the lower of two, and to bid a grand-slam with three, sign off in six of the trump suit with none), but I don't really need the king of diamonds. What I need to know is whether partner has a third-round control in clubs. That is what my next bid of 6♣ was intended to achieve. We didn't have any agreement, and I didn't expect it to be understood, but logically it cannot be anything else. We've accounted for first-round controls, if I wanted to know about second-round controls I'd ask with 5NT. It must be a grand-slam try as we're committed to the six level, and it can hardly be suggesting an alternative trump suit. In response, holding Jxx(x) or worse (no third-round control) partner should sign off in six spades, and bid a grand slam (or cue-bid a feature at the seven level) with the queen or a doubleton or better. 

If partner has ♣Q we will have thirteen tricks, barring an unlikely trump loser or an opening club ruff. If partner has ♣xx we have a good chance of ruffing out the queen, and with a singleton the contract may rest on a ruffing finesse, but that's a worst-case scenario. It's surely a grand-slam you'd want to be in. 

At the other table the auction continued with 1♣ from West, 1♠ from East, 4♠ from West, passed out. I could easily see that happening at our table if Keith had passed, although alternative rebids for West are 4♣, which should show a very strong six-card club suit and four-card spade support, or 4♦ as a splinter in support of spades. Opposite either of those East should cue-bid ♦A and the small slam should be reached. 

It's not often one gets the chance to ask for a third-round control in a suit, but it's the key to bidding this hand. 

Playing a weak no trump, I opened the West hand one heart. Judy’s 2NT was a limit raise or better in hearts, and my 3NT showed a balanced hand with enough for game. When Judy cue-bid four clubs I decided we had enough for slam provided we were not missing two keycards.

We were the only ones in the slam with two balanced hands and a combined 27 points. I’m not proud of the bidding. I was minimum for my game bid, but I liked my controls in diamonds and spades too much to sign off. North led a trump, which at least gave me a chance (a minor-suit lead and probably a spade would have defeated the slam), but it still looks beyond hope. How could I avoid a loser in each minor suit?

I won the lead in dummy and led a diamond to the king. It looks far from obvious to South to play the ace (I wouldn’t have done), but ducking let the contract through. I drew trumps and ran the spade jack, picking up the queen. I discarded my losing diamonds on the spades, and South had to find a discard in this position: 

South was squeezed without the count on the last spade. Baring ♦A would mean I could ruff a small diamond to set up the queen for my twelfth trick, so they discarded a club. I ducked a club, won the return with the ace, ruffed a club, ruffed a diamond back to dummy and led the established club to make the contract.

I found the end position interesting because the technique is a strip squeeze - the squeeze card (9♠) inflicts the damage on South before the count has been rectified, and a trick is conceded afterwards. It's also a ruffing squeeze - a winner is ruffed good after the squeeze has taken effect. A ruffing squeeze requires two entries to the long menace (dummy's clubs) when the squeeze card is played - one so that the suit can be led for a ruff, and the second to reach the established winner. Dummy has those entries in the ♣A and the trump to ruff a diamond, but South can break the squeeze by playing a diamond before the club has been ruffed to remove the entry before it's needed. Unfortunately, they can only do this at the expense of setting up ♦Q for declarer, so it's all for nought. 

Another interesting point occurred to me: I think South's best play at the end is to discard ♦J rather than a club. A general principle of defending against squeezes is to unguard the threat you can't see, rather than the one you can see. South can see dummy's clubs, and knows from the bidding that West has at least two, but do they know West, rather than North, has the ♦Q? What if West had started with ♦K106 rather than ♦KQ6? Might they have played the hand the same way? Now when declarer ruffs ♦6, bringing down your ace, partner still has ♦Q preventing the establishment of the diamond, and you are still guarding the clubs.

This is the most complex squeeze I've ever played. I've pulled off some strip squeezes in my time, and some ruffing squeezes, but never a ruffing strip squeeze. I'll be on the lookout for more interesting play opportunities like this, but in the meantime, more importantly, I think I need to work on my bidding. 

Tony reports on board 18 from day 1 of the EBU Year End Swiss Pairs:  I picked up the North hand Red v Green - and hear the 2♠  opener on my left. The first toy I received from the Grizzled Old Man, was leaping (and non-leaping) Michaels.

This was the perfect hand for it, and so I could bid 4♦, a big hand showing Diamonds and a Major. When Lis now bids 4♥, I can wheel out the 2nd of Santa’s toys…. 5♣ , Exclusion Blackwood, RKCB excluding the suit bid.

Lis with her hand in South Bids 5♦ (1 K♥, we don’t count A♣ , remember) and I can comfortable raise to 6♥. 7♥  is of course comfortable as is 7NT but 6♥  still got 71% of the mps, and we got there confidently.

This hand came up in the weekly county duplicate pairs on Wednesday 7th April. This was our auction, and while it didn't get us to the top spot, at least it got us a plus score. Everybody else played in a slam, four making twelve tricks in 6♥ or 6♠, one making an overtrick in 6NT. Four pairs bid to a grand slam in spades or no trumps and went one or two off. 

The first difficulty with this hand is whether or not to open the South hand. It has eleven HCP and some shape, and good controls, but it would mean rebidding that awful spade suit if partner responds in hearts. It meets Bergen's rule of 20, and Klinger's extended rule of 22 (add HCP to cards in the two longest suits and controls, open if the result is at least 22). Judy and I play weak jump shifts at the two level, but don't really have an agreement about the three level, so Judy just bid 2♥. I had to rebid my spades, and she now jumped to 4NT to agree spades and ask for keycards. I showed one or four, and she asked for the queen of trumps (even though she had it herself), and I denied possession with 5♠, which is where we finished. Deep Finesse says that's as much as we can make in spades, probably because of the difficulty of getting to the South hand to lead spades towards dummy. Those who made twelve tricks probably met a compliant West who failed to see this difficulty and went in early with the trump ace, although they can arrange the entries on a non-heart lead. Six hearts can be made by North, but not South, as West can lead ace and a spade for a ruff. 

Of the ten times the board was played, nine Norths asked for aces or keycards (the tenth time it was South, more understandably, who used Blackwood). On hearing of one keycard opposite, four North players assumed it was the trump ace and jumped to a grand slam. This shows the danger of using RKCB (or ordinary Blackwood) when holding a void. Is there a better way? 

Exclusion Keycard Blackwood allows a player to ask for keycards outside a particular suit, normally one in which they hold a void. The asking bid is a jump to a suit above the level of game in the agreed trump suit, or the suit that is agreed by implication. So in our auction after the first three bids North could jump to 5♣ to ask South how many keycards they hold outside clubs. The responses are as follows: 

• step 1: 0
• step 2: 1
• step 3: 2 without the queen
• step 4: 2 with the queen
• step 5: 3 (this never happens)

So South would respond 5♦ to deny any keycards outside clubs, North would know the spade ace was missing and could sign off in 6♠, hoping there wasn't a second trick to lose (as here, unluckily). 

If the asker wants to know more they can use the next step (excluding the trump suit) after a one- or two-step response to ask for the queen of trumps (a sign-off in the trump suit denies, anything else shows the queen and a feature), or 5NT to ask partner to cue-bid side-suit kings upwards, or a new suit to ask for third-round control in the suit (don't try this last move without thorough research and discussion with partner). 

This hand came up in an inter-county teams-of-eight match against Derbyshire on 14.03.21. It was played 36 times (other county matches were playing the same boards) and no one managed to bid the laydown grand slam. This was what happened at our table, and many other tables had similar auctions. Not everyone opened the East hand 1♦. Some passed, and some opened a weak two, despite the four-card major. It looks clear to open 1♦ to me. You can raise either major if partner responds, or rebid 2♦ over a 2♣ response. I decided to show a good hand in support of diamonds, and when partner showed a minimum opener, I didn't know what to do. We could have thirteen tricks on ice, or be off two immediate club tricks. I decided to trust partner to have either the ace or queen of clubs, and bid RKCB. 

Partner responded 5♥ to show two keycards without the diamond queen, which you might think is what he's got. It's what everyone responded when West asked for keycards. I think they're all wrong. First of all, just by asking for keycards, West is showing four-card diamond support. As East has six, he knows we have a ten-card fit, so the queen is unlikely to matter. Three cards will split 3-0 only 22% of the time, and a fair proportion of that the queen will be finessable after a top card has been cashed, so East can bid 5♠ to show two with the queen. He can go one better if you have the agreement in place and raise 4NT to 5NT to show two keycards and a useful void. This is all West needs to hear, and they can now jump to 7♦. 

When I suggested this to my partner, he protested that he only a ten-count. But look at the assets: a solid trump suit, first-round control in a side suit, a second-round control in another, opposite a partner who's looking for slam. And since 5♥ committed the side to at least 6♦, he might as well show everything. 

Responding to RKCB with a void: 

Like most partnerships, we didn't have a firm agreement on how to show voids in response to RCKB, so I'm in no way blaming my partner for missing the grand slam, but for interest, this is a standard system of responses: 

• With no keycards, ignore the void and make your normal response. 
• With 1 or 3 keycards, jump in the void suit if it's below six of the trump suit, or jump to six of the trump suit if it isn't. 
• With 2 keycards, raise the asking bid a level (i.e. bid 5NT over 4NT). 

Note that partner is supposed to be able to tell if you hold 1 or 3 keycards, and only useful voids are shown, i.e. not in suits where partner has shown length. 

Minorwood: 

Some pairs have an agreement to play minorwood, so that a jump to four of a bid minor agrees the suit, shows interest in slam and asks for keycards. I play this in one partnership, and I saw looking through the results that a number of other pairs do too. One problem we've been having is deciding when it is asking for keycards, and when just raising the suit. Our rather vague agreement is that it asks for keycards unless we are obviously just pre-empting or competing, but we still seem very unsure of ourselves in these auctions. These are some thoughts I had about minorwood after this start: 

First of all, whatever your agreements, 1♦ - (X) - 4♦ cannot be minorwood. This bid must be a pre-emptive raise. Since 2NT is available to show a good diamond raise, the way to ask for keycards is to bid 2NT first, then 4♦ on the next round. In the same vein, no expert plays 1♠ - (P) - 4NT as RCKB for spades. To ask for keycards, they can agree spades with a game-forcing Jacoby 2NT first, and then ask for keycards on the next round, so 4NT in that auction may be Blackwood, but it doesn't agree spades. 

I hadn't really thought about responding to minorwood with voids, but I suppose a similar scheme could apply. Over 4♦, responses are: 4♥ (0 or 3), 4♠ (1 or 4), 4NT (2 without the trump queen), 5♣ (2 with the trump queen), 5♦ (two with a useful void), 5♥/♠ /6♣ (1 or 3 and a void in the bid suit). I notice that this system of void-showing responses would cause headaches if you use 4NT as RKCB with a minor agreed, as I do in most partnerships. If my partner bid 4NT with diamonds agreed, I would be very nervous of responding 5♦ with the higher number of keycards. What if partner thought I had one and passed? To prevent this I'd like to make a higher bid to guarantee we'd get to slam (if partner's asking, we must belong in slam if I have four keycards), but all the higher bids have other specific meanings. 

I think in this situation I'd just make my normal 5♦ response and trust partner to be able to work out from the auction so far that I can't have the lower number of keycards, but there must be some situations where it isn't clear. 

One final important point on the hand, I hope you drew trumps by leading the four to the three. You won't have the chance to do that again for a long time. 

This was board 43 in the first day of the EBU national inter-county pairs competition (the Corwen). I've been reading about this trump position since I was at school, and it's finally come up. 

The auction at our table was strange and is not relevant to the problem. 1♦ was either 13-15 balanced or showed a hand that would open a minor, with 10-15 points. 1♥ was natural, 2♥ showed at least three-card support, 2♠ was an asking bid, 4♣ showed two keycards, no shortage and denied ♥Q. 

My partner led ♣J. Declarer won with the ace in hand and led ♥A, on which I carefully dropped the nine. Had I failed to do so, declarer would have to play ♥K on the second round to be able to take a finesse against my jack. With the nine out of the way, declarer has the losing option of playing me to have started with a bare nine and cashing the queen next, to finesse against my partner's jack. The ruse worked, and declarer played the queen next, eventually losing a trump, two diamonds and a spade for one down. 

There is more to playing the hand than getting the trumps right, and declarer may decide to play the king next to retain entries to the East hand, or delay drawing trumps until the diamonds are set up, but I still think it’s correct to play the nine. It can never hurt your chances.

Since the board was played over fifty times, I was curious to know how many other Norths had faced the same decision I had, and how many had found the correct play. The board was played in hearts 45 times (once in 3♥, the rest in game). Declarers had made eight tricks (x3), nine tricks (x19), ten tricks (x21) and eleven tricks (x1). Since the North defender cannot afford the nine if partner’s known singleton could be the 10, I looked at only those Norths who played to the first trick after their partner, or who could see the 10 in dummy.

There were 33 North players in that situation, and only five of them played the nine (at two of those tables 4♥ made, at the other three it was defeated). So it seems the position is not so well known, among English county players at least. I posted the hand on the Bridgewinners discussion forum to see if there was anything I was missing.

I was gratified to see that Kit Woolsey agreed with me. He said that the nine was a false card that can never cost, but should also never gain. It is the only card to give declarer a losing option, but it shouldn’t gain because declarer, if they believe the defender is aware of the need to play the nine from J9xx, should always assume it has been played from this holding, rather than that it was a singleton. The reason is that in this case when South has J762 and North 9, South will play each small card roughly a third of the time, making that distribution only a third as likely.

Some people cast doubt on whether a defender really would play small cards randomly from this holding, and they have a point. It shows that it’s another situation the defender needs to be aware of to protect their partner.

I was directed to an interesting article on the subject by Jonathan Mestel, chess and bridge expert and professor of applied mathematics at Imperial College, London. He applied game theory to this situation and worked out that all the textbooks are wrong and that the best strategy for both sides is for the defender to false-card one third of the time and for the declarer to believe it’s a false card (rather than a singleton) half the time. If either side deviates from this line the other side can gain an advantage by changing their own strategy.

I also discovered that a frequent player can expect to meet this position about once every twenty years, so how anyone is supposed to build up a pattern of playing the nine a certain proportion of the time is beyond me.

In the online County Teams League our opponents bid to 7NT using an Acol system. 1♥ promised 4+, 2NT was 17-19, 3♣ checkback Stayman, 4NT RKCB, 5♠ showed two keycards and ♠Q. My partner led ♦10.