What an exciting morning! With no fewer than 4 grand slams on offer this was a challenge for the bidders. But how many were realistically sensible bids?

Board 6, declarer has 7 diamonds missing the king and 8 clubs missing the queen. Statistically the correct play for both of these is to play for a finesse. On this hand they both work but statistically a finesse has a 50% chance of working so to get both finesses to work the probability of success falls to 25%. Much safer is to bid a small slam where the probability of getting just one of the finesse to work jumps to 75%.

Board 10, declarer has 9 spades and 9 diamonds each missing the queen. Now statistics tell us that the best play is to drop the queen. The odds for dropping a queen when four cards are missing is 52% so only slightly better than a finesse with five cards missing. So to drop both queens the odds are around 27% whilst the odds of dropping at least one queen is around 77%. Again the small slam is a much safer bid.

Board 12, If N-S go to Roman Key Card Blackwood they will find one key card missing and will not know if it is the diamond ace or not. But if south starts cue bidding with 4C and north responds with 4H south will be able to pin down the missing diamond ace and with a void in diamonds will bid 7S, a slam dunk contract. Although north must be disciplined not to bid 7NT.

Board 16, is the most interesting hand as this 7D does not rely on any finesses but instead requires very careful timing from declarer. It is worth noting that 7NT can succeed if declarer plays to finesse the spade queen but this is only a 50% chance. Playing 7D declarer must be careful to win the lead in hand, except for a heart lead which must be won in dummy. Now play a round of diamonds and fortune shines and the diamond queen falls marking east with the remaining two trumps. Next declarer plays clubs winning king then ace to end back in dummy. A third round of clubs is ruffed in hand and declarer returns to dummy with second round of trumps reduces east to one trump. Another club is led from dummy clearing the suit and ruffed back in hand. Declarer now pulls the final trump and returns to dummy with the spade ace. The final club is played allowing declarer to ditch the losing heart and collect 13 tricks.

We all know that you generally need 33 points to bid slam in no trumps but have also experienced hands where twelve or sometimes thirteen tricks are made in a suit contract with very much less than that. Often the key lies in having a two suited fit or for one partner to have a significant shortage. This may either be the potential to ruff partners string of losers or the ability to discard your own losers on partner's strong suit. In today's hand we will look at how to find these shortages. So on this hand your challenge is to see how you and your partner would bid your way to 6 hearts or better still 6 no trumps.

This week's hand is particularly difficult to bid  and yet relatively easy to play. Every pair only managed to reach 3NT and all made 12 tricks. How would you bid south's hand on this board to reach 6C, 6D or for bonus points 6NT? Actually this hand is less a lesson in bidding than an indication of a potential confusion that should be discussed and worked out with your partner.

An effective suit preference signal is one that is given upon your partner's lead when it is clear from the cards in dummy that the suit is a bust and is either not worth continuing or not possible to continue. The idea is to signal to your partner where your strength and interest lies so that if your partner should gain the lead they will know what to do next.

In this example a suit preference signal gives east the courage to make a most unlikely lead that is the only play to prevent north making 12 tricks. North is in 6 spades and east leads the singleton 3 of diamonds and declarer calls for a low diamond. Can you see what to do playing west?

This hand was played in spades by north at every table but not all norths managed to make 10 tricks. The answer is to end play east. during the early rounds of bidding east will surely have interjected a bid in diamonds, marking the hand with 5 diamonds and most, if not all, of the missing points. East starts the ball rolling with a diamod honour and continues with diamonds on round two which north trumps.

At this point north is probably thinking that with fair odds, the trumps can be cleared in 3 rounds, the hearts will yield 3 tricks and after giving up the club king there are 2 club tricks and the remaining trump for 10 sure tricks and if a defender can be led into discarding aclub or two maybe 11 tricks are available. But after a round of trumps at trick three, declarer gets the bad news that the trumps are splitting 4-1. There is now a real danger that west will trump one of the winning hearts unless all the trumps are removed. And this is where the squeeze and end play start to take shape. At tricks 4, 5 and 6 east must find discards. There is an old adage that says you must never discard from a four card suit if you can see four cards of that suit in dummy. That is very true in this case, if east discards a heart north will be able to continue the squeeze by playing 4 heart tricks after the trumps have been removed. East can easily discard a club on trick  4 but on tricks 5 & 6 must discard diamonds. 

Now declarer is ready to try their luck with the hearts, playing two honours from hand and then crossing o the heart king at trick 9 finding that this time the percentages do work with the suit splitting 4-2 and east now hold top heart, top diamond and Kx in clubs. Declarer throews est in with dummy's last heart, allows east to cash a winning diamond but now east has to lead clubs from Kx towards A&Q. This kind of endplay where the opponents cards are eliminated before throwing them in to lead away from a holding in caled a Fork Strip.

A number of pairs managed to land this board on 3NT but the results ranged from 8 tricks to eleven tricks. The par score would be 10 tricks. So is it possible to see whhere the declarers and defenders might have gone wrong. After two passes north will surely open 2H and E/W compete from there into 3NT. Now south is on lead and has very little hope of taking a trick in a black suit and cannot lead away from the DQ. So the only sensible lead is the H6 to partner's holding hoping that partner has enough entries to run some heart tricks. Declarer will see ten diamonds headed by A&K and think Christmas has come early. But sensibly will want to keep the HA as an entry to dummy just in case the diamonds break 3-0. So trick one is captured with the HK over the HJ. Now declarer leads DA and finds the bad news that not only is there a 3-0 diamond break but they are in south's hand. East can still play a second rond of diamonds at trick three east must stop and think. Yes, giving up the DQ will give declarer 9 top tricks but leaves it open for south to return a heart and then if north is able to stop the spades or clubs will cash heart tricks to prevent any over tricks. But at trick 4 declarer switches to SK and a second spade if north holds up. Now 10 tricks are assured when the DQ is given up.

For the defence, it all comes down to nort's discards on the diamond tricks. Logic would say hold on to club Qxx but that would require jetisoning heart winners or two spades giving up a second spade stop. Correct play is to jettison the CQ and rely on south to hold onto club Jxx.

Back on 23rd November I couldn't find any interesting hand to comment on. Instead I talked about three types of dummy and the two types of defensive strategies and when to play each strategy. In the hand above east bid to 3H on all but one table. West had not shown any shape during the course of the bidding so south can expect a roughly balanced hand. So with a balanced dummy defence should be looking for a passive play. Sure enough, when south makes a passive lead of a small club or a small diamond declarer can be held to 9 tricks. Even a passive lead of a small spade (not one to be recommended!) allows the defence to take 4 tricks. But the aggressive lead of the CK brings the CJ crashing down from north's hand and marks south with the CQ allowing east to find an all important entry to dummy with C10x.

Try the 'Play it again' button and lay out the hand and you will find that east has little difficulty making 10 tricks after the CK lead.

With this deal every pair made 12 tricks in hearts but nobody managed to bid the slam. I was asked how it could be achieved. Despite having a great spade fit, the unfavourable vulnerability will keep E-W silent throughout except possibly for a double of spades by west if south should bid spades during any slam investigation. North should open 1D (ACOL players will open 1NT) and to show length and strength south should jump to 2H. What north does next is crucial to any attempt to reach slam.

North knows that the pair are now committed to game and if that is all then north can just bid 4H but it is not for north to decide, the strong hand is with south. North must describe the hand in more detail. With only 2 spades, 2NT would be rash and the club suit is not worthy of a bid yet. 3H will help south to determine there is a fit but a better bid is 3D. This is a slight exageration as north does not have 5 diamonds but the strength of the suit makes up for this. This is the point where south must now recognise the potential for a slam for north has expressed an interest by continuing to describe the hand rather than bidding 3NT or 4H. This implies that either north has heart support or the diamonds are strong enough to make a slam. The pair are two suited, a very powerful combination, and first/second round controls of the black suits are key. If south asks for aces and finds two aces south can bid 7D and north will correct to 7H. But if only one ace shows up north will surely hold a king but which one? With CK small slam is on but with SK it is not. The solution when it is imperitive to know a specific card rather than how many is cue bidding.

Cue bidding is initiated by north introducing a new suit at the four level. in this case 4C. Now Fee and I cue bid 1st round control on the first mention of a suit and 2nd round control on a subsequent mention. So for us the bidding would go 4C-4D-? If south bids 4H this could be seen as a sign off, 5D would deny control in the spade suit and north would sign off in 5H. But the really hot shot players bid 1st or 2nd round control on the first bid. Now the bidding might go....

4C-4D-4S (2nd round control)-5C(second round control. South can now jump to 6D which north corrects to 6H. So with the correct partnership understandings, this slam is biddable by the best players in the world but for the rest of us 4H is the best we should aspire to. But I would still encourage you all to learn to cue bid.

The power of squeeze. When north led a small club, west was assured of the contract unless there is a very poor 4-1 or 5-0 split on the spades. There are two sure club tricks, 3 heart tricks and 7 spade tricks.

If west plays the hearts first there are three discards to make from the diamond and club suits but as soon as west enters dummy to cash the spades, the 13th card is exposed for all to see and one of the declarers will surely hold onto the winning card.

By contrast, if west plays the spades first there are 6 discards to find and when west returns to hand with the second club trick and cashes the three winning hearts will be left with one card which may be a heart, diamond or club. The defenders unless they are counting very carefully and have signaled their length in each suit (odd or even count) will have little idea which. But more importantly the defenders also have to find discards. For hapless south, there are 5 discards to find. Two small diamonds are safe and west will surely also discard from the useless diamond suit. South can also safely discard one heart whilst west discards the final diamond. Now the squeeze starts to bite with south holding 4 hearts, DA and 2 clubs whilst west holds 5 hearts and 2 clubs. On trick 7, the 6th spade south cannot discard DA and must choose between a club honour or another heart whilst west discards a small heart. On trick 8, the final spade the game is up, throwing hearts on on both tricks 7 & 8 west will know the hearts will run and discard a club, if south discards 2 clubs, west now has 2 top clubs and discards the second small heart. Finally if south discards a heart and a club it does not matter if west discards a small heart or the lower club 13 tricks are assured.

Sitting north your enthusiastic partner has put you into 6H. East leads the 10 of diamonds. It is unlikely that east has led away from DQ so you win trick one with DA. With 5 trumps missing, the odds of finding the HK as a singleton are about 5.7%, so it goes without saying that you will need to play to finesse the heart by leading the H5 from dummy and the HJ wins. Now how do you plan your play?

Your partner opens 3 spades, what do you bid next?

Choosing a defensive strategy requires the defence to either play an active defence or a passive defence. In an active defence the defending pair should grab their tricks as quickly as possible and in a passive defence the defending pair should take their time and try to develop extra tricks.

To determine which strategy to use consider the overall structure of dummies hand. There are three broad categories of structure and these are :-

• Balanced, a hand that is typically 3-3-3-4 or 2-3-4-4 in shape. It does not usually have a 5 card suit or two 2 card suits.
• Ruffing values, a hand with at least 3 trumps and at most 2 cards in an outside suit.
• Running suit, a hand with at least five cards headed by 2-3 honours which will give declarer an opportunity to discard some winners.

For balanced hands defence should be passive, don’t be afraid to hand the lead back to declarer by giving up certain losers. In no trump contracts it is better to establish a long suit whilst maintaining an honour to get the lead back than to play your honours early. You will usually make more tricks in your suit if declarer leads it. But do attack a suit that you like if your partner indicates an interest in that suit.

For ruffing value hands the defence should again be passive although you should consider drawing trumps to minimise the trumping potential. This is especially so if you have the same number of trumps as dummy.

For running suit hands, the defence needs to be active in taking their tricks before declarer is able to pull trumps and then discard their losers on dummies long cards.

On the board above, west ended up in 3C with north on lead. North only has two decent choices for a lead, a heart or a spade. At each table north picked the ace of spades followed by the jack hoping to get to south for a quick ruff. West will win trick 2 in hand with the spade king and lead a high trump to flush out the ace. South wins with the ace and must lead to trick 4. Now eight spades have been played and north's lead is almost certainly from a doubleton and south will realise that the thirteenth spade is in declarer's hand providing a route back to dummy once trumps are removed giving declarer three discards. South must cash ace of hearts and lead a diamond hoping to find the ace with north. 

"What should I have led?" A question I hear being asked all to frequently. The answer quite simply is 'the one that best conveys information about your holding to your partner, whilst avoiding silly leads'. Take for instance the hand below.

East had opened the bidding with 1NT and after a transfer to spades E-W ended up in 2S. Now with most of the points in the west hand south clearly does not want to lead away from the club holding. Although defending no trumps, the lead of CQ is as effective as any other card other than the CA. Indeed the analysis shows that a lead of any club is bad (yellow) and will only get 3 tricks for the defence whilst a lead of any other card is good (green) and will yield 4 tricks for the defence.

So having dismissed the silly lead of a club, which card should south select? Well in the absence of any other clues south might think 'west has an unbalanced hand with ruffing potential, I should lead a trump'. There is nothing wrong with this but which trump? If you use standard leads then a low card promises an honour so south must not lead the S2. Top of nothing or middle up down are valid choices and the S9 will certainly deny an honour as would the S7. Either card is a valid lead. 

South might decide to attack hearts. Now the H3 is a valid lead, it promises an honour and south has two (in the cotext of standard leads the ten counts as an honour) but this leaves room for doubt for north. North can see HQ in dummy and holds the HA but does not know where the king is. West will surely play low from dummy and unless north plays the H9 the defence will get one less trick. But if south leads with HJ standard leads would promise the honour below. Now there is no room for doubt in north's mind and north will either cover the HQ and return a heart or will duck when the H8 is played from dummy.

Or south might wish to attack diamonds hoping for an early ruff. The problem here is that south would wish to play Hi-Lo to show the doubleton but the Hi card is DT from which north would expect south to hold D9. Lucky for south the D9 is in dummy and north will realise what is going on but south cannot rely on the missing promise to be visible to partner. Leading the D3 would promise an honour and south has the DT but does not really convey the right message.

So which card would you lead? 

In the last review I alluded to the need to make modifications to the LoTT. It has been shown that the LoTT is accurate in only 40% of cases. Just like in counting points modifications are needed to account for shape and missing honours. There are three factors that should be considered when making adjustments. The most important is the existance of a second suit fit. The existance of a second 8 card or better suit fit is often worth an extra trick. Next in importance is posession of the trump honours, when the declaring side hold all the trump honours they generally do better than when the opponents hold 2 or more top honours. And finally, distribution of the other suits can have an impact. When both hands have equal length in each of the side suits ruffing is only possible if the defenders lead a suit that both declarer and dummy are void in. Or when declarer is very short in one suit and dummy is very short in another suit the potential for cross ruffing emerges.

In this hand, N-S have 20 points, 9 spades and an eight card second suit in diamonds. Things are looking very positive, except that they do not posess the top two honours in their trump suit. As a result they only can make eight tricks in spades not nine.

By contrast, E-W have 20 points 8 hearts and a nine card second suit in clubs. Again things are lookng positive but in this case they hold all of the top honours and can make nine tricks in hearts not eight. 

So if you wish to adopt the LoTT do so with caution and be sure to consider adjustment factors.

Last week I took a look at the LoTT and showed how the total tricks in a hand where the points are roughly evenly split between N-S and E-W is equal to the sum of the length of each team's trump suit. I left a bit of a cliff hanger asking how do you know how many trumps the opposition have as well as how many your side has. Now on your side one of you will have made a length limited bid. For example a major suit opening not repeated is 5 cards, repeated it is 6 cards. A weak 2 opening is 6 cards and a minor opening followed by a major is 4 cards. So partner armed with this information and seeing how many of the suit is in their hand knows exactly the total count. This is the hand that must take control and decide how far to bid. Assume you and your partner have 8 trumps between you, your opponents may have an 8, 9 or 10 card fit but the LoTT equates to 16, 17 or 18 tricks respectively. Your side can safely bid to the two level and you should expect to go -1 if you push on to the three level.

So take a look at today's example. E-W have an 8 card fit in hearts and should be willing to bid to 2H even though this will go down by one. N-S have an eight card fit in spades. Again they should be happy to bid to 2S. In fact they can make 1 extra trick for a 3S contract. NOTE that the LoTT holds true, E-W can only make 7 tricks and N-S can make 9 tricks so the total is still 16. Next week I will try and explain some of the modifying factors that experts using the LoTT use to add or subtract value from their trump holding.

One of the most interesting, and challenging, aspects of bridge is when the points are evenly divided and the two opposing sides both find a fit in one of the suits. This leads to a competitive battle in which the sides need to decide whether they can afford to bid one more time for a makable contract, bid one more time for a profitable sacrifice or simply pass. There are many tools to help with this but one that I have been researching and will share is called the 'Law of Total Tricks'. First developed in France, it was popularised in the English language by English players in bridge journals and later popularised by Marty Bergen and Larry Cohen. Simply stated the LoTT is:-

The total number of tricks available on a deal is equal to the total number of trump cards both sides hold in their respective best suits, where the total number of tricks is defined as the sum of the number of tricks available to each side if they could choose trumps.

The LoTT works best when the points are evenly divided and becomes less accurate as the distribution of points moves away from 20-20. In today's example I will look at how the LoTT works and show what contracts each pair should bid.

In the example above the makeable contracts were N-S 3H and E-W 4C. The number of trump cards is 6+4=10 clubs for E-W and 5+4=9 for N-S giving a LoTT total of 19. So when N-S bid to 3H E-W should calculate that if N-S can only make 9 tricks then they should be able to make 10 tricks and so E or W must bid 4C. Equally N-S should now calculate that if E-W can make 10 tricks then they should be able to make 9 tricks and therefor a bid of 4H-1 is a worthwhile sacrifice and north or south must bid 4H which is the optimum score for both sides. 

Of course the difficulty is knowing exactly how many trumpcards there are between the two teams and knowing when to stop playing the if-then game. In this example E-W could legitimately argue that if N-S can make 4H they can make nine tricks in clubs makeing 5 clubs a viable sacrifice. So although the law seems to work I fail to see how to apply it accurately.

On this board each N-S pair elected to play in 3NT. A very easy contract to reach, it is unlikely that many people will find the superior contract of 6 clubs. The hand holds two interesting points, one for defenders and one for the declarer. So the first question which goes to the defender sitting west is 'What should you lead'? and the second question and much easier to answer is as declarer 'how do you play this hand given a lead of the five of clubs'?

In this example east is in 6H. How would you plan to make this contract against any lead?

In this interesting hand west can make a seemingly impossible 6H contract. Can you see how?

In