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Here is a problem given to me by Jeff Juster:

 

In first seat, at favorable vulnerability, you pick up an excellent 14-count, and start with one heart.  Partner responds 2, a game force, either balanced, or clubs, and you have to pick a rebid.

 

South
AJ63
AQJ1092
Q75
W
N
E
S
1
P
2
P
?

 

Your call?

You certainly want to show your 4-6 shape.  Normally, you can do this by bidding hearts, hearts, spades, or hearts, spades, hearts.  We could choose either if partner leaves us room.  What if partner doesn't oblige?

Say we bid two hearts, and partner rebids three clubs?  Now a spade call would sound like a stopper, not natural.  That shouldn't matter much, but we would have been slightly better off bidding spades first.

Likewise, suppose partner supports hearts next?  If we had rebid hearts, three spades would be a cue-bid, not natural.  We'll have shown our sixth heart, but not our four spades.  Again, we would have been better placed rebidding two spades. 

To put it another way, two spades describes nine of our cards quickly, while two hearts only describes six of our cards.  Two spades has to be better.

You choose two spades, and partner raises:

South
AJ63
AQJ1092
Q75
W
N
E
S
1
P
2
P
2
P
3
P
?

leaving you with another decision.  You are surely worth some sort of slam try, and have two choices.  3NT would show a non-serious slam try, while a cue-bid would show a stronger hand.

Your choice?

This one is easy.  In a Standard context, you could hold as much as a 19 or 20  count on this auction.  Serious slam try auctions have to show extra high card strength.  This is a great 14-count, but, still, only 14.   So, 3NT it is.

Partner cue-bids four diamonds.  You general agreement is to cue-bid aces first opposite any holding where partner might be short, so this shows the diamond ace and denies the club ace.  It seems pretty obvious to cue four hearts in return.  Is that your choice?  

South
AJ63
AQJ1092
Q75
W
N
E
S
1
P
2
P
2
P
3
P
3NT
P
4
P
?

OK, what do we know?

 

Partner would hardly make a slam try, after our mild try, holding only one ace and little help in the major suits.  So partner pretty much has to hold two cover cards in the majors.  Given that, we are going to a slam.  Facing all three, a hand like KQxx Kx Axx Qxxx, seven spades is excellent.  Can we find out if partner holds all three cards?

Yes, maybe.  It seems odd, but we could Blackwood.  If partner shows two key cards and the trump queen, we ask for kings, and voila!

Is this dangerous?

 

Yes, a little.  Partner, thinking we have all the key cards, might bid a poor grand slam with a hand like KQxx x Ax KQJxxx.  I suspect partner would have taken over and asked for aces holding that hand, so the danger is small, but it is not nil.

Anyway, you opt for 4NT. 

South
AJ63
AQJ1092
Q75
W
N
E
S
1
P
2
P
2
P
3
P
3NT
P
4
P
4NT
P
5
P
?

Partner shows two without.  Your call?

Seven is out, missing the trump queen.  But we aren't stopping in five.  So, six it is.  West leads the club ace, and everyone has a little chuckle when you trump the trick. 

West
North
K1042
K
A63
KQ1032
East
South
AJ63
AQJ1092
Q75
W
N
E
S
 
1
P
2
P
2
P
3
P
3N
P
4
P
4N
P
5
P
6
P
P
P
D
6 South
NS: 0 EW: 0
A
2
9
3
3
1
0
1

East plays the nine of clubs at trick one, upside down count and attitude, if that means anything.  Plan the play.

This is easy if trumps split, and we could pick up Qxxx either way, so long as we start trumps in the right order.  For instance, if we decide to play West for trump length, we would start with the trump ace, and a low trump, sticking in the ten.  If that loses to the queen, we can draw the last trump with our jack, and run hearts.  And, of course, if the ten wins, and East shows out, we simply play trump king, trump, and claim.

Likewise, if East has the trump length, we succeed by leading a low trump to the king, and a trump back to the jack.  No problems if trumps split, and, if East turns out to have started with four to the queen, we simply run hearts until he chooses to ruff.

So, which way to go?

 

That is another easy choice.  If we start trump ace, and West shows out on the second trump, we are pretty much dead.  If, however, we go the other way in trumps, we still have plenty of play, even if we guessed wrong.  

So, we lead the trump six to the king, and call for a low trump from the table.  Naturally, East shows out, discarding the heart four.  

West
North
K1042
K
A63
KQ1032
East
South
AJ63
AQJ1092
Q75
W
N
E
S
 
1
P
2
P
2
P
3
P
3N
P
4
P
4N
P
5
P
6
P
P
P
D
6 South
NS: 0 EW: 0
A
2
9
3
3
1
0
6
5
K
7
1
2
0
2
4
3

This wouldn't be much on an article if I let you guess right.  Do you play the ace or the jack.  What is your plan?

If we play the ace, we'll try to run hearts next.  If West follows for three rounds, we are home - we'll have made two discards from dummy before West can ruff.  We'll over-ruff the fourth round, trump a club, and throw the last loser away.  If West trumps the second heart, we are finished, and if West trumps the third heart, we will need to get lucky in clubs.  So, that line, spade ace, works when West started with three or more hearts, or when West started with two hearts and clubs are friendly.

If we try the jack, West will win.  If West tries a heart, we run some winners, over-ruffing, with the trump ace as a re-entry.  That looks easy.  More likely, West will shift to a diamond.  We win the ace, discard both diamonds on the clubs, then run hearts.  This line fails if West can trump one of those clubs.  So we need West to follow to two more clubs.

 

There are six hearts out, and, ignoring the club ace and the five clubs in dummy, seven small clubs missing.  Playing the trump ace needs West to have started with two, and maybe three, of those six hearts.  Playing the trump jack requires West to hold two of the missing seven clubs.  That is clearly better.

So, you stick in the trump jack.  West wins the queen and shifts to a heart.  You overtake, and run hearts, confidently waiting to claim when West trumps in.  West follows to the second heart, and then calmly discards on each remaining heart.  That's annoying.  Why didn't we see that coming?

West discards, in order, the eight of diamonds, the five of clubs, the ten of diamonds, and the six of clubs.  East, on the fourth heart, discards the diamond jack, and East throws the club jack on the fifth heart:

West
North
K1042
K
A63
KQ1032
East
South
AJ63
AQJ1092
Q75
W
N
E
S
 
1
P
2
P
2
P
3
P
3N
P
4
P
4N
P
5
P
6
P
P
P
D
6 South
NS: 0 EW: 0
A
2
9
3
3
1
0
6
5
K
7
1
2
0
2
4
J
Q
0
2
1
6
K
8
A
3
3
1
Q
3
3
5
3
4
1
J
8
6
7
3
5
1
10
5
3
J
3
6
1
9
10
10
J
3
7
1
2
6
9

 

This is the end position:

North
104
A
KQ
South
A
2
Q75

We can certainly make the slam from here.  West, after discarding on the heart two, has two trumps left, and two other cards.  If those cards include a diamond, we simply throw a club, cash the trump ace, cross in diamonds, and draw the last trump.  If those cards include a club, we make by discarding the diamond ace, trumping a diamond, cashing one club, and cross-ruffing.  If West trumps in with the eight or nine, over-ruff, and now both clubs must cash.

OK, is West out of clubs now, or out of diamonds?

We can't go wrong if West has kept one of each, but West has almost certainly kept two diamonds and no clubs, or two clubs and no diamonds.  So West was, originally, 4-2-2-5 or 4-2-4-3.  Which?  Any clues?

Well, East did play the club nine at trick one, perhaps to show an odd number of clubs.  That would mean West started with an odd number of clubs, and so ... That doesn't help at all! 

4-2-4-3 looks more likely than 4-2-2-5, right?  Let's see.  There were seven missing diamonds, and, discounting the club ace, seven missing clubs to distribute.  4-2-2-5 means West got four of the clubs and two of those diamonds.  4-2-4-3 means West was dealt four of those diamonds and two of those clubs.  Identical probabilities!  This is really annoying. 

Anything else? 

Actually, the diamonds are not all identical, thanks to our queen.  If West had discarded the diamond king, we would guarantee the contract by throwing the diamond ace, and leading the high diamond queen.  If West follows, we discard and cross-ruff, while if West could ruff, the clubs must live. 

Of course, West knows this (thanks to the excellent discard of the diamond jack, denying the queen, from East), so West will never throw the diamond king away from Kxxx.  But if West started with the 4-2-2-5 pattern, and the diamond king, West could not fool us. 

That all means that playing for West to have a club left works in half the patterns, while playing for West to have a diamond left also works in half the patterns, or when West started with the diamond king.  We should discard a club, and cash the trump ace.

All goes well, and we score up the slam, for this was the full hand:

 

West
Q985
63
K1082
A65
North
K1042
K
A63
KQ1032
East
7
8754
J94
J9874
South
AJ63
AQJ1092
Q75
D

 

but we can't help feeling like we butchered this hand, and just got lucky.  Clearly we didn't look closely enough at the hand.  Our choice at trick three, to play the trump jack, led to an ending where we had little more than a 50-50 guess.   In retrospect, we should have played the trump ace.  Our chances then, that West would hold at least three hearts, or two hearts with the club suit setting up, were definitely better than 50%.  The fact that the better line would have failed leaves us a bit queasy.  

Of course, had we really looked deeper into the hand, we would have cashed one high club, discarding a diamond, before leading the second trump from the table.  Then we could stick in the jack with no worries at all.  Why?

With one diamond gone, we would have arrived at this ending:

North
104
A
K
South
A
2
Q7

In this ending, it wouldn't help West to discard.  We simply discard the diamond ace, and lead a diamond.  Either we ruff low, and cross-ruff, or over-ruff, and the club must cash.

So, yeah, we butchered the hand.  Did you?

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