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Finding the Forest by Steve Bloom (Page of 7) Jan. 21

This fictional story is based on a post by Scott Nason to Bobby Wolff.  Scott and his young nephew were playing in a sectional, and bid this hand (slightly modified) to 6 by North (the best slam is 6 by South).  Looking at the hand records, he discovered that 6 was cold, at least according to Deep Finesse, but the winning line didn't seem obvious.

A number of "expert" analysts, myself included, got involved in the discussion, proposing various double-dummy lines of play.  Finally Anthony Moon noticed the forest hidden among all this garbage, and pointed out a successful line of play that should, in fact, be found at the table.

So, I have written this up as a play problem.  Let's see if you can spot the forest.

West
North
K104
QJ6
KJ3
AK107
East
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
1

It is matchpoints, against a strong pair, and you get a trump lead against 6.  Assuming the clubs produce three winners, you have eleven tricks, and will make if the heart finesse is on.  So let's start by figuring out how to survive if the heart finesse is off.  What's your plan?

There are two extra chances when the heart finesse will lose.  First off, the clubs might produce four tricks.  The best play to bring in the club suit is by playing a club to the ten.  This will land the slam when West holds QJx in clubs, three cases, or QJ54, one more case.

The second possibility is to throw West in on the third round of clubs, to lead away from the K, or, hopefully, the Q.  This means drawing trumps, cashing the A, and playing clubs from the top.  We can also change our mind and pick up clubs if East has a singleton honor.  This works, then, in those two cases, or when East holds any doubleton club (except for QJ) without the diamond queen, half of nine other cases.  So this is the better option, by a fair amount.

Would this endplay option still be best if our clubs were a bit stronger, say:

West
North
K104
QJ6
KJ3
AK107
East
South
AQJ63
A83
A
9832
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
1

With the 8, we can pick up any QJxx onside, or even QJxxx onside.  So the club play works in six or seven cases (but we can probably ignore 5-0 clubs with no Lightner double).  Moreover, opting for the endplay line will cost us the contract when West had QJxx in clubs and the heart king is onside.  That is another three cases to add to the mix, and tips the scale away from the endplay line.

Back to the original hand.  We opt for the endplay line, and draw trumps in three rounds.  East shows out on the third round, discarding the 2.

West
North
K104
QJ6
KJ3
AK107
East
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
3

So now, we intend to cash the A and the top two clubs.  What is the proper order?

There are sound reasons for leading the second club from hand, but this is just normal good technique.  Seeing West's second club, or seeing West show out, will leave us with more options.  So we lead a club to the king, a diamond to the ace, and another club.  On this second club, West plays the Q:

West
North
K104
QJ6
KJ3
AK107
East
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
Q
6

We now have a new option.  If this is from QJx, we should win, but if the queen is doubleton, we should let this hold.  Your choice?

Restricted choice seems to argue for ducking the Q, but that is bogus.  Holding QJx, West would have to play the queen the second round to give you a losing option, so restricted choice doesn't apply.  There are, in fact, two strong reasons to play the ace.  (1) Holding Qx in clubs, and both the Q and K, West should have gotten rid of the Q on the first round.  (2)  Perhaps this is the full hand:

West
987
K543
Q87
Q84
North
K104
QJ6
KJ3
AK107
East
52
10972
1096542
J5
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
Q
6

If you let the queen win, and see East drop the jack, and then West produce a low club, you'll have to put up with gloating for a year.  This is matchpoints, and no amount of matchpoints are worth a year of gloating.

Anyway, I lied.  On the second club, West shows out, throwing the 5.

West
North
K104
QJ6
KJ3
AK107
East
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
5
6
With clubs foul, we'll need some other luck.  We certainly need the heart finesse.  If East also holds the Q, we can make the hand with a strip squeeze.  Win the A and lead the Q.  If East covers, win and run trumps, then back to the J:

West
987
10542
108754
5
North
K104
QJ6
KJ3
AK107
East
52
K97
Q962
QJ84
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
5
A
8
1
6
0
Q
K
A
2
3
7
0
Q
5
6
7
3
8
0
J
7
7
9
3
9
0
3
4
J
10

Likewise, if East does not cover the heart, we have a new strip-squeeze, in hearts and clubs.  Unfortunately, there will be some ambiguity in the ending.  Our panel of experts found a truly beautiful way to avoid all this ambiguity.  We can guarantee the contract if East has both the diamond queen and heart king.  How?

This is really elegant.  Play the 10 from the table, endplaying East.  East must return a heart, which we win on the table.  Now we cash the K and A, then lead one more round of trumps, discarding the club from the table:

West
987
10542
108754
5
North
K104
QJ6
KJ3
AK107
East
52
K97
Q962
QJ84
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
5
10
J
2
5
1
7
3
2
J
1
6
1
K
9
8
7
1
7
1
6
9
A
4
3
8
1
Q
7
7
10

That is a gorgeous ending, but totally silly.  Have you found the forest yet?  How should you play?

As Anthony Moon pointed out, once West shows out on the second round of clubs, the hand is cold so long as East holds the heart king.  Simply play the 10 from dummy, win the forced heart return on dummy, cash the K, throwing our heart, ruff a diamond, and lead the last trump, discarding dummy's 7.  East is dead.

West
987
10542
108754
5
North
K104
QJ6
KJ3
AK107
East
52
K97
Q962
QJ84
South
AQJ63
A83
A
9632
W
N
E
S

P
1
P
2
P
3
P
3
P
4
P
4
P
6
P
P
P
D
6 South
NS: 0 EW: 0
9
10
2
3
1
1
0
K
5
6
7
1
2
0
4
2
A
8
3
3
0
2
5
K
4
1
4
0
3
6
A
4
3
5
0
3
5
10
J
2
5
1
7
3
2
J
1
6
1
K
9
8
7
1
7
1
J
Q
J
8
3
8
1
Q
10
7
10

For some bizarre reason, I often overlook criss-cross squeeze positions.  And, since we could all see the Q in the East hand, we didn't bother to figure out how to make the hand when West held the Q.

Stupid criss-cross squeeze.  Stupid forest.

Steve Bloom
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Retired mathematician and general curmudgeon.