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Well, If Trumps Break...
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A few months ago I was playing on BBO in preparation for the Collegiate Championships.  Sitting South, I'd been playing quickly, looking for interesting play, in order to prepare for a tournament in the evening.  I slowed to a halt when this problem appeared:

North
AK74
KQ765
QJ76
South
J3
AJ9
AK943
K32
W
N
E
S
1NT
P
2
P
2
P
3
P
4
P
4
P
4NT
P
5NT
P
6
P
6
P
P
P

The auction seems reasonable enough.  6 is perhaps optimistic, but, regardless, here we are in 6.

 

The lead is the 5.  E/W lead 3rd from even, lowest from odd against suits, although against slam creativity may be called for.

Win or duck?

This is not an obvious decision.  On one hand, if we duck and lose to the Q, we are down immediately.  On the other hand, if we fly ace, we are left with a position that will need a lot of skill and perhaps some luck to have play.

Would West lead away from the spade queen here?  It's possible, if unlikely.  A trump lead is more obviously attractive, and if W held the A, he might very well lead that.  On the other hand, with an unattractive trump holding and unattractive holdings in the minors, the underlead of the Q might be her only option. 

On the whole, ducking is likely to give up the contract, and even when it works, it may not be enough.  Flying A seems right.  E follows with the 6, UDCA.

North
K74
KQ765
QJ76
South
J
AJ9
AK943
K32
W
N
E
S
1NT
P
2
P
2
P
3
P
4
P
4
P
4NT
P
5NT
P
6
P
6
P
P
P

Now what?

Here the play becomes obscure.  Where are our tricks?  If we plan to play off the top and set up clubs, we likely have two , five , two , and two , for a total of 11 tricks.  Thus, we would need to ruff a spade or catch the stiff club A (which seems unlikely).  However, ruffing a spade breaks up our communication.  If we cash the K and ruff a spade high, we are forced to cross back to the board through a trump, as canny defenders will duck once or twice in clubs.  Thus we are unable to cater to hearts worse than 3-2, else we have two losers.

It is perhaps also possible to avoid a heart loser when hearts are 4-1 with West.  We start by playing a small club, playing E for the A.  If he rises, we have the extra winner we need, and so long as W does not hold a stiff club, and we successfully navigate trumps, we are home.  Hence, E should duck.  Supposing the K holds, we now cash the AK, pitching clubs, leaving this position:

North
K74
KQ765
Q
South
J
AJ9
943
32
W
N
E
S
1NT
P
2
P
2
P
3
P
4
P
4
P
4NT
P
5NT
P
6
P
6
P
P
P

On some layouts, we will be able to pull one round of trumps, then crossruff spades and diamonds.  This may execute a coup, leaving West to ruff his partners winning A on the final trick.

Which is better?  On the one hand, the second line gives us extra chances when trumps break poorly.  On the other hand, we're going to look very silly when W ruffs a spade or has a stiff club, or E ruffs a diamond, when trumps were breaking.  I am not certain what is correct, but it does not look to harm us too much to lead a small heart towards the A, checking to see if a honor (the T or 8) will drop.  This leaves us enough communication to execute both of the plays we suggested earlier.  A small club could be more beneficial, but loses to a singleton club in either hand, and may not gain.

To your extreme chagrin, East shows out to the , pitching the 5 (UDCA).

North
K74
KQ76
QJ76
South
J
J9
AK943
K32
W
N
E
S
1NT
P
2
P
2
P
3
P
4
P
4
P
4NT
P
5NT
P
6
P
6
P
P
P

Ouch.  You've gotten this far: what do you play for now (spoilers on the next page, make up your mind before moving on).  

 

I am not a strong enough player to decide what is right in such a spot, so I will instead present the full hand, and let better players sort out what to do with such a dilemma.  The deal was 

West
10852
108432
Q7
94
North
AK74
KQ765
QJ76
East
Q96
J108652
A1085
South
Jx
AJ9
AK943
K32
W
N
E
S
 
1N
P
2
P
2
P
3
P
4
P
4
P
4N
P
5N
P
6
P
6
P
P
P
D
6 South
NS: 0 EW: 0
I had to take a phone call in the middle of the board, so we will never know if I would have gotten it right (or how horrendously long it would have taken me), but there IS a way to make the contract after crossing to the heart ace.  It requires good timing and the spade-diamond crossruff.  As we ruff in dummy through diamonds, West will be forced to ruff in low once, then ruff in high once, and then be couped at trick 13. The details are tricky: I'll let you work it out yourselves.  It is a sort of repeated trump coup, which nets a winner and eliminates a loser.  Not a position I had seen before, and not one I expect to see again!

If anyone has opinions on the best lines at any stage, I'd love to hear them.

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