The probability of a 5-5-3-0 deal is just 0.9% (Google).

Now matching the ♠ suit with a ♥ , one at a time (and working to 3 decimal places):

1. Matching any ♠ with the same ♥ value is 5/13, or .385 probability (any one of 5 ♥’s out of 13 will match one of the 5-card ♠ suit)
2. Matching one of the 4 remaining ♠ with the same ♥ value is 4/12, or .333 probability (only 12 ♥ to choose from, and 4 ♠‘s to match)
3. Matching one of the 3 remaining ♠ with the same ♥ value is 3/11, or .273 probability (and so on…)
4. Matching one of the 2 remaining ♠ with the same ♥ value is 2/10, or .200 probability
5. Matching the one of the 3 remaining ♠ with the same ♥ value is 1/9, or .111 probability

Now the overall probability is the combined product: 0.9% x .385 x .333 x .273 x .200 x .111

And that comes to 0.0006993%.  Or about 7 chances in 2,500 years if you play 25 hands twice a week. I’d have to triple-check that, but whatever, not for a very long time!

Let’s have your answers in comments, please 😊

Ian W.

*      *      *      *      *      *      *

The first thing to note is that, with partner limited to a maximum of 13 HCP, we are not looking for game, so our goal is to find a safe low level contract. 

The second thing to note is that the hand appears likely to be a misfit. Partner hasn't raised our suit and we don't have good support for either of partner's suits. The most important rule when faced with a misfit with partner is to STOP BIDDING AS SOON AS IS PRACTICAL. I would say that in most sessions, I would see at least one hand where the opponents are bidding themselves up and up on misfitting hands and end up in some contract down two or three.

Now to the options:

2NT   We have a diamond stopper, and no fit, so should we bid 2NT? In this case, definitely not. Even if partner has a maximum, we have at most around 20 HCP, so 2NT is dangerously high. Note also your hand is very poor on entries, so it is unlikely you could ever set the spade suit up (and that is really the only main asset of the hand in NT). I would guess 2NT would be two off, or worse.

2S   We have a five card suit, should we rebid it to tell partner? Now, partner has already not raised spades. The other thing partner did not do is reopen with a double. This tells you they not short in diamonds (unless they have a two suited hand). If partner has a heart suit, a club suit, and a few diamonds, how many spades have they got? Probably a singleton. So you can now see rebidding your spades is another road to disaster. Anyone for playing a 5-1 fit?

Both of these bids violate the basic principle written above. (Look up, it is in ALL CAPS).

So the choice is between pass (playing in 2C) or bidding 2H. There is no real right or wrong about this choice, one will work better on some days, and the other on others. What is there to consider between the two?

2H   Since it is IMPS, not matchpoints, there is no compulsion to prefer a higher scoring major suit contract. So the only advantage for bidding 2H is if partner happens to have a six card suit. However, bear in mind also it is just possible partner has only four hearts. But in any case, our heart holding of two small is basically useless in the play.

Pass   There are some reasons why we may be better playing in 2C. Firstly, partner could be 5-5 shape, and clubs is our best fit. We do have more clubs than hearts. But if not, how will we go playing in a 4-3 fit?

Our trump quality of KTx is quite good. It certainly reduces the risk of being doubled if we get say a 5-1 trump break. Also, these trumps may be useful in a finesse, perhaps. We might ruff some hearts with them (the 10 also gives the option of ruffing high), and note we are ruffing in the short hand, leaving partners 4 card trump holding intact. Our spade holding is useful in protecting partner from being forced to ruff that suit and reduce their trump holding. So I would expect a 4-3 fit in clubs to generally play better then a 5-2 fit in hearts.

At the table (on Board 30), I did pass, and John played 2C. Making 8 trick, despite the 5-1 club break, which was very well done. At the other table 2H went two off (and was maybe lucky not to have been doubled), so it was a 5 imp pick up in our match. 

Regardless of the result, the main point to be made is, when you can tell your hand is not fitting with partner's, and you don't have values for game, STOP BIDDING ASAP.

Cheers, Dave F

On of the basic principles of slam bidding when holding the strong hand is asking the question: "What information do I need about partner's hand?", and following that, "How will I get that information?". In this case, the answer to the first question is simple. We need to find out if partner holds the A♥ , and whether they have longer clubs or spades.

The answer to the second question is not so straightforward playing a typical Standard system. You might think it is automatic to open with 2C. Is anything wrong with that? Well, yes, a few things.

1. The Strong 2C opening is notoriously poorly suited to bidding two suited hands. After your first bid has been made, partner still doesn't know either of your two suits.
2. The 2C opening chews up a lot of bidding room. (This is why people play Precision or Strong Club systems. The 1C opening gives maximum space.)
3. There is a fair chance the opponents could interfere with your auction. There are a lot of hearts and diamonds somewhere around the table.
4. Looking further ahead in the auction, RCK Blackwood is not useful here. If partner shows one ace, you still don't know whether you have a cold grand slam or not. You need space to use control showing (cue bids).

So there are quite a lot of uncontested auctions where it may be difficult to get the required information. How will you be placed after:   

1. 2C - P - 2NT - P - 3S....     
2. 2C - P - 3D - P - 3S....       
3. 2C - P - 2D - P - 2S - P - 3H - P....   for example.

The opponents may make it even more difficult:   

1. 2C - 3D - P - P.... 
2. 2C - 2H - P - 3H....     
3. 2C - 2D*- P - 4H....        * two suiter D&H 
4. 2C - 4D - P - P....   with their cool 0481 hand.

The 2C opening can sometimes cause real headaches.

It may be much better to open the bidding with 1S. If the auction is uncontested, after partner bids 1NT, 2D or 2H, you can bid 3C which is game forcing. Partner can now bid either of your known suits to support, and you can start cue bidding to find out about the A♥. Alternatively, if partner raises spades , you could cue bid 4C showing first round control. If partner now bids 4H, you can bid 7S. If partner bids 4D, you could use RKCB to see if they hold 2 aces, and bid the small or grand slam accordingly. 

Of course, if the opponents interfere, you are now much better placed than after 2C, and can show your clubs in whatever manner is appropriate and forcing. Or give up on the grand and bid 6C. This way partner can choose the better denomination.

Is anything wrong with opening 1S? Well, it could get passed out. That would be upsetting! This is why we have the 2C opening. What do you think the chances are of the hand being passed out?

Very low. At a guess, maybe 1%. Why? Well, with your 6610 hand, there is very likely to be shape around the rest of the table too. There are 13 diamonds and 12 hearts to be split between 3 hands. And 18 HCP in your hand is not too massive. That leaves 22 HCP to be spread around. If partner has 5 or less and passes, one of the opponents is almost certain to have enough points and shape to overcall, or balance in 4th seat.

So, to sum up, your bidding system is a selection of tools to be used to exchange information, and you can always be thinking about the best way to use it. It is not all set in concrete. Yes, it's a "2C opening", but maybe that isn't the best option.

Now go back to the top of the page, and have a look at the two questions. Keep these clearly in you mind when slam bidding!

Cheers, Dave

On this deal, we see all nine of our tricks ready for the taking, but unfortunately, there are two blocked suits that need to be untangled!!

As West leads the ♥K, it knocks out our one and only heart stopper so we need to be careful on this hand.

You can hold up one or two rounds of hearts, but that won't be of any use, since we already have our nine tricks, we just need to take them in the right order.

Let's say we win the ♥A and unblock the ♠AK. We would then go to dummy with a club and cash our spade winners along with the ♦A and ♣Q, however, we would have no way back to our hand to cash the ♣A after the ♣KQ are unblocked.

 Therefore, we need to tweak that plan. After winning the ♥A we should first unblock the ♣KQ. We now come back to our hand by unblocking the ♠AK, cash the ♣A and finally, cross over to dummy with the ♦A to enjoy the rest of dummy's spades!

 This deal demonstrates the importance of planning ahead. Playing out the whole hand in our head before touching a single card will often pay dividends. This will prevent you from making hasty plays which you might end up regretting, and that's what will happen if you played the spades first in the example hand above.

With thanks to Andy Hung.

As we are in a suit contract now, you have to count your losers. Here you have one in spades, one in hearts, and one in diamonds. That's only three in total, and with a finessing position available in hearts and diamonds, it appears that we are in good shape! Are there any potential dangers?

Let's analyse West's ♦5 lead for a second. What do you make of this lead? Well, it must be a singleton! Yes, it's true that West might have led from ♦Kxxx (away from an honour), but take a look at the auction.

We have bid and raised diamonds, would West really lead away from ♦Kxxx? No, therefore, the lead is clearly from a singleton, so reject the diamond finesse by rising with the ♦A. What next?

You will draw trumps, but again, you must be careful. Normally when you are missing the queen in an eight-card fit, you should always take the finesse ('Eight Ever, Nine Never'), but here, you should reject the finesse and just lay down ♥AK. Why?

Imagine if you cash the ♥A, and play a heart to your ♥J and this loses to West's ♥Q. What might happen next? West wins, switches to a spade to East's ♠A, and he will then cash the ♦K and give his partner a diamond ruff - one down!

When you can see that the opening lead is from a singleton, usually it's a good idea to draw as many rounds of trumps as possible without taking any finesses. Even if the trump suit was ♥A74 opposite ♥QJ1083. Don't try to cross to your hand to lead out the ♥Q - instead, play the ♥A and another heart so you draw as many rounds of trumps as possible. 

On this hand, you should double (a Support Double).

A support double is:

• A conventional double by the opener to show a 3-card support for responder’s suit, hoping to find partner with a 5-card suit for a 5-3 fit.
• Support doubles only apply to the opener’s re-bid after the fourth seat opponent intervenes. If this intervention is double, the opener can redouble.

Although your hand is very flat, you should still try and fight for the part-score with a support double.

Partner’s 1♠ response shows 4+♠s, so at worst in this example, partner will play in a 4-3 ♠  fit at the two level.

Thanks to Any Hung for this snippet.

Partner has six spades to the king (rule of 11) so we have a spade trick and a club trick. If we want to have any hopes of defeating this contract, we must assume that partner has a trump trick.

However, one trump trick is not enough. Since dummy's diamonds are good (with our ♦ J109 dropping) and the clubs are well placed for declarer (if he has the ♣ J or ♣ Q, the finesse of the ♣ 10 will be successful), we require two trump tricks.

Thus, our only chance is to switch to a small club at trick 2! Visualising partner with the ♥ A and a doubleton club, this switch is our most likely hope of defeating this contract (that is, we first give up a club trick, and when partner gets in with the ♥ A, he can return his last club to our ♣ A so we can give him a ruff).

Partner held: ♠ K98642 ♥ A9 ♦ 753 ♣ J9
Declarer held: ♠ 3 ♥ KQ8762 ♦ 642 ♣ Q85.

Thanks to Andy Hung for this successful defence to an otherwise likely contract.

There are some clues from the auction that may guide you. Firstly, we know for certain that East (our RHO) has a 6-4 (or maybe a 5-4) ♣-♥ shape. What about West, do we know much about her hand?

One thing's for sure - West (our LHO) must have a very good hand to have immediately jumped to 4NT over 2♥  to ask for key cards. What does this mean?

Well, because we are looking at their missing key card (♣ A), and due to our strength in the red suits, we can be fairly sure that the likely reason that North jumped to 4NT is because she has a long running spade suit!  And also that our partner cannot hold the ♠ A as the opponents surely won't bid a slam off two aces!

Thus, leading a diamond to try and set up a trick won't work - the declarer will just win the diamond lead, draw trumps, and utilise those spades. 

Therefore to have any hope of defeating this contract, we must only go for our one and only shot: Play partner for a singleton club. Lay down that ♣ A and hope!

Show all hands now.

Today is your lucky day, as your partner is there for you with a singleton club!

This hand was from the 2016 Australian National Championship (ANC) Final. Thanks to Andy Hung for this analysis.

1. Your trump holding is poor. You have no honour and only 3 card support. This makes a trump loser quite likely. Give partner AK to 5 trumps, say, you still have a certain loser. Maybe it will be 50% on a finesse with other holdings. In addition however, you may not be able to both finesse in trumps and ruff some number of clubs.

Your 3 card holding also increases the risk of a bad trump break. If your side has 8 trumps, a 4-1 or 5-0 break will still occur about one third of the time.

Holding a fourth trump would greatly increase the strength of this hand, especially if you are chasing a slam, by countering all the negative points given above. 

2. Using your bidding system to show a shortage is a powerful evaluation tool. This is why many people play splinter bids. In this case, partner showing singleton or void in diamonds is bad news. Holding a sequence of honours opposite a shortage is called duplication of values. Partner might count an extra 3 point for a singleton, while you are also counting 3 points for your king. You are in effect counting 6 points for one trick. So we can say that the king has lost value on this hand.

The other problem with partner having a diamond shortage is it may be difficult or impossible to set up the diamond suit, which may be necessary to make slam. One opponent is quite likely to have length in the suit, and you don't have many outside entries to dummy after drawing trumps.

3. The club Q is not a card we want to hold. It is virtually worthless. If partner has the A, then before ruffing a club or two, they will play it and the Q will fall under it. If the opponents have the A, the same thing will happen. It is wasted.

This is the wrong Q for us to hold. Consider the effect of swapping it for the Q♦  or the Q♥ . Wouldn't your hand go up in value significantly? If the opponents held the Q♣, would we care? So don't count anything for this card.

When you pick up your hand, and count your 14 HCPs, be prepared to reevaluate those points after a round or two of bidding. On this hand, although we have a nice hand, reevaluating tells us it has lost value, with several negative features, and that slam is unlikely unless partner has some extra values and trump length in his hand. In which case he can still bid on, you have game forced after all. So at this point bidding game is sufficient.

You should jump to 4♠. Bidding 3♠  is a bit too timid here - whilst we "only have eight points", remember, partner has made a takeout double so is showing an opening hand with support for all unbid suits! Additionally our length in clubs suggests partner will likely have a singleton ♣ rather than a doubleton ♣.

Try to visualise a minimum hand from partner: ♠A854 ♥AJ52 ♦QJ73 ♣4. Opposite that hand, game is a very good prospect!

If we only bid 3♠, partner will (rightly) expect us to hold a relatively weak hand, and would therefore pass with a minimum hand. Remember, when responding to a takeout double, it is our duty to show our strength. With weak hands, we bid our suit at the cheapest level, and if we have a stronger hand, we must make a jump (or sometimes even a cue bid)! 

With thanks to Andy Hung

It might be tempting to compete to 3♠ given that we are not vulnerable, but take a look at your hand.

All we know about partner's hand that we have an 8-card ♠ fit and we have the worst possible shape to be competing 3-over-3 (a very balanced 5332 shape).

Our Q♦ is known to be a wasted card (they bid ♦ twice), and looking at our hand, our honour cards are scattered everywhere!

Contrast this hand to one like this, even with one less HCP: ♠KQ1092 ♥65 ♦42 ♣AQJ3 where all of our points are concentrated - it makes a world of difference and by all means bid 3♠!

With all signs pointing to defence, passing 3♦ is best. If partner has an unbalanced hand and a fourth trump, then partner could compete to 3♠, but for all we know, hers may just be a defensive-oriented hand with only three ♠ trumps.

With thanks  to Andy Hung.

North has 4 or 5 hearts, which means that partner has at least 4 hearts, and declarer may have a problem in the trump suit.

The only useful values in dummy are the singleton diamond, allowing North to ruff losing diamonds, and the club suit, possibly allowing North to discard losers.

You can't do anything about the diamond situation, but you can attempt to kill the club suit. When declarer leads the ♣K, you must duck and observe partner's length signal. If your partnership has studied Kantar's "Introduction to Defender's Play", they will play the ♣7 on this trick.

With the 9, 8 and 6 missing, you need to decide whether partner has 9-8-7 and has played low to show an odd number, or 7-6 and has played high to show an even number. When declarer leads the ♣6, however, all becomes clear, and you take this trick, locking declarer out of dummy.

Declarer cannot eat the ♠2, and partner will take the setting trick in spades.

Defence is so easy!

You seem to have only one side-suit loser, the ♠A, since the small club can go on the ♦K.

You can therefore afford to lose two heart tricks, and any 2-2 or 3-1 heart break will be OK. Just play the Ace and another.

In the unlikely scenario where North has all four trumps, you will go down, as North will make three trump tricks. Since a 4-0 break in either hand is a 10% chance, the chance of North having all four trumps is 5%, and protecting against that seems worthwhile.

Therefore, the best play is a small trump towards the queen. If South has all four, playing the King or ducking won't help - you will always lose only two trumps. If South shows out, the Queen loses to North's King, and you can now lead twice through the remaining J-10-4 and lose only one more trick.

On the actual deal, the trumps are 3-1, so virtue was its own reward.

The ♠2 goes on the opening lead, taken by the ♦A, and all the side suits are "in the bank".

The contract depends on playing the trumps for one loser. The correct line with this holding is to take a double finesse, just as you would with A- Q-10-x opposite x-x-x-x.

Lead a small heart and finesse the 8 unless West plays an honour. On this deal, the 8 wins the trick!

Now that you know West has both honours, return to the South hand with a spade and lead the ♥Q. You will lose one trump trick and chalk up +1430.

If East had produced the King or Jack, you would finesse against the other honour on the next round.

You chances are a bit better than 75% - excellent odds for a small slam.

There are two possibilities, both of which need the King onside.

Line 1: Lead a small heart to the Queen, and cash the Ace. If the King is onside and doubleton, you can now drop the Ten with the Jack.

Line 2: Lead the Jack, intending to run it. If North covers, take the Ace, return to the West hand and finesse the Nine.

Line 2 is better, but has only a 22% chance of success. On this deal, your luck is in.

Without the Nine in the East hand, line 2 is not available and you must play line 1, which succeeds only about 13% of the time.

These suit combinations are tricky things!

If you happen to land in 6♣  instead, things are no better. You still need to play the hearts in the same way for no loser. You can discard one heart on the third spade, but you will still have that pesky ♥9 to deal with.

... and if North doesn't cover the ♥J? You must still assume that the King is there, and thank the gods that North didn't "cover an honour with an honour", because you can now finesse the Queen and get home without worrying about the Ten.

We have 12 top tricks: 6 spades, 2 hearts, 3 diamonds and 1 club, so we need to find a 13th trick.

After winning ♥ A, the plan is to make an extra diamond trick by bringing down the ♦ J. Thus we take ♠ A, ♠ K (preserving entries to hand) and the trumps behave themselves.

Next, ♦ A, ♠ Q, preserving the ♥ K as a later entry, and ♦ K, ♦ Q, discarding a heart and a small club. The bad news is that the ♦ J is not coming down, and the 13th trick needs to come from somewhere else.

There is one hope: North, who started with 2 spades and 1 diamond, presumably has the heart stopper (since South would have played the J from Q-J), and the club stopper (K-Q-x and more). If so, we can ruff a diamond to hand and run all of the trumps, leading to this end position:

North can keep only 2 cards: if they are hearts, the ♣ J is good. If North has kept the ♣ K, the hearts are good. Now you can see why the ♥ K had to be preserved.

Voila!

You have 2 diamond losers on this nasty lead as well as the ♠ A. That's all you can afford.

Counting winners, you have three spade tricks by force, one diamond, and three clubs, a total of seven tricks.

One possible source of extra tricks is a ruffing finesse in hearts, pitching diamonds and hoping West has the ♥ A. If this fails, it's instant death as you will lose the heart as well as the above three tricks.

A better line could best be described as an undignified scramble: win ♦ A, club to the ♣ K, heart ruff. club to the ♣ Q, heart ruff.

Now, ♣ A to pitch a diamond. If they ruff this, you have swapped a diamond loser for a trump loser (on the ♣ A). Wonder of wonders, they both follow and your clubs are good.

Next is to drive out the ♠ A. They have no defence now. You will just lose a diamond and a heart by drawing the last trump and driving out the ♥ A.

When you have a difficult deal like this, the "Play It Again" button is your friend.

South appears to have two choices: 3♠  (forcing), or a responsive double, which tends to deny support for partner and suggest the unbid suits.

If South bids 3♠ . North has a right to be excited. 4♠  is the safe option; 4♦  is the exciting option. Your partnership should decide what this means. It would be nice if it promises a good hand, a fit, and slam aspirations.

If North bids 4♦  with this meaning, South should go quietly now with 4♠ . The ♦ Q figures to be worthless, and the spades are a bit tatty. North will need very good cards to continue.

If South chooses the responsive double instead, North will show the clubs. South's minimum in context will dictate raising this to 5♣, which is the second-best spot.

This deal is a good illustration of the effect of "bidding the trumps". East assumes that West has 4 diamonds (3 is very unlikely) and raises the ante, taking the maximum bidding space at reasonable risk.

The hearts appear to be 6-1, and the club finesse will lose to West if the ♣ K is wrong, so no holdup is necessary, since West is already out of hearts after trick 1.

Counting our tricks, we see 2 hearts, 3 diamonds, and 3 or 4 clubs. If the club finesse is wrong, there are only eight tricks.

This is one of those times when a "just in case" play, routinely made by top players and difficult for us mere mortals, is worth a try: cash the ♦ A before doing anything alse and lo! East is void.

Now, a diamond to the 10 and we have four diamond tricks. Deblock the ♦ Q next and try the ♣ Q. If it loses and West returns a spade, we need to put up the ♠ K as the only chance, since if East has that card, we are dead.

Sadly, this is real life and down we go, but the diamond play is worth remembering.

You can see the full deal by clicking "Show All Hands".

Footnote: Which spade do you think West should return? A low one to the Jack will make East nervous about cashing the Ace, since it's not obvious that the King will drop. The Queen lead is the winner this time, since West is pretty sure it's necessry to run the spade suit to beat the contract.