Sunday, October 9, 2011

Event 3 - Match 2 - Board 2

Board 2
Our side vulnerable

♠ 10 6 4 2 A 7 5 2 ♣ A K 6 3 2

RHO opens four hearts, which ends the auction. Our convention cards says "ace from ace-king." But, since one is quite likely to lead an unsupported ace after four of a major--all pass, I lead the club king. This will make it easier for partner to place my high cards if I decide to shift at trick two. The downside is that it may make partner's trick one signal harder for me to read. But making things slightly harder for me and much easier for partner seems like a good trade-off.

♠ K 9 7 5
Q J 9 4
♣ J 10 9 8

♠ 10 6
4 2
A 7 5 2
♣ A K 6 3 2

West North East South
Phillip Kate Jack Stella
(All pass)

Partner plays the club seven; declarer, the four. The only time partner's club seven isn't forced is when he has queen-seven-five or seven-five. Playing with a human partner, I would rule out the former holding. I don't think partner would encourage with queen third looking at jack-ten fourth in the dummy. Playing with Jack, however, it is the latter holding I rule out. Jack tends to encourage with an honor and discourage without one whether that makes any sense in context or not. So I will assume that partner has either the club queen or a singleton.

There are three possible active strategies I might adopt at this point: (1) Cash out. (2) Go after slow tricks. (3) Go after ruffs. In addition, there is (4) Defend passively. Let's look at each strategy in turn and consider what conditions would make each strategy necessary.

(1) For a cash out to be necessary, declarer must have fast tricks on which she can pitch her losers given the chance. The only possible fast trick in dummy is the spade king. And the only way declarer can pitch something on it without giving up the lead is to have a singleton spade ace and a dummy entry. This gives declarer,

(A) ♠ A A K Q x x x x x x x ♣ x x.

While I would never open four hearts myself with this hand, I'm not so sure about Jack. The description Jack offers is "six to thirteen high-card points, six to nine playing tricks, and seven or more hearts." This hand fits that description, so I do believe it's a possible hand. Even on this layout, however, a cashout is not necessary. Playing a trump before declarer has a chance to unblock spades will work as well.

(2) For it to be necessary to go after slow tricks, declarer must have slow tricks herself and we must have the tempi to take our slow tricks before declarer can take hers. The only suit we can have slow tricks in is spades. So for (2) to be the right strategy, declarer must have something like,

(B) ♠ A x x A K Q x x x x x x ♣ x.

We have a slow spade trick, and declarer has slow diamond tricks. If we defend passively, declarer can drive the ace and king of diamonds and take a pitch. To prevent that, we must lead a spade now and lead a second spade on winning our first diamond trick. Again, this hand does not look like a four heart bid to me, but I suspect it's possible for Jack.

(3) For it to be necessary to go after a ruff, we must have exactly three winners aside from the ruff. Playing partner for the ace-queen of spades and going after a spade ruff, for example, implicitly assumes that neither of my minor-suit aces is cashing:

(C) ♠ J x x x A K x x x x x x -- ♣ x.

This the first hand I've constructed that actually looks like a four heart opening.

The ruff does not have to be immediate. Take this hand, for example:

(D) ♠ Q J x x K Q x x x x x x -- ♣ x.

Again, a spade shift is necessary to beat four hearts. (Although if we take away declarer's spade jack, it isn't.)

Can it be right to go after a diamond ruff? Declarer would need,

(E) ♠ x A K Q x x x x K x x x ♣ x.

While we must get a diamond ruff to beat four hearts, it is not necessary to switch to diamonds to get our ruff. A spade shift should work as well, since it can hardly be wrong for partner to switch to his singleton diamond at trick three. A spade shift would fail if declarer's small spade were a club. But, given partner's failure to balance with four spades, I'm not worried about finding declarer with a spade void.

If it's actually necessary to switch to diamond, I probably need to switch to a small one:

(F) ♠ A x A K Q x x x x x x x ♣ x.

Could it be right to go after a club ruff? For that to be necessary, we must have only one trick in the pointed suits:

(G) ♠ Q x A K x x x x x x -- ♣ Q x x.

Now I must continue clubs (either the ace or a low one will do). But if we simply take the spade queen away or make declarer one-one in the pointed suits, the club ruff is unnecessary. I don't mind losing the club ruff if it's not the setting trick.

All in all, a spade shift seems best if an active defense is called for. How about strategy (4)? Could a spade shift cost when a passive defense would succeed? The danger in playing spades is finding declarer with queen-eight third and a dummy entry:

(H) ♠ Q 8 x A K Q x x x x x x ♣ x.

Actually, while a passive defense makes things easier for partner, it isn't strictly necessary on this layout. If I shift to the spade ten and declarer plays the king from dummy, we still beat it if partner ducks.

A spade seems like the best choice. But there is no clear, demonstrable answer to this problem. When you have so few constraints to work with, it's impossible to consider all the possibilities. So you can never be sure you've found the best solution. But you can be sure you've found a reasonable solution. As long as you can construct at least one specific, plausible layout where the defense you have chosen is necessary, you know you have at least some chance of doing the right thing. Failure to do this is one of the prime causes of defensive errors. Often a defender faced with a difficult problem like this will base his decision only on general principles (I'm going to cut down ruffs; I'm going to try to set up diamond tricks; etc.). If you do that, you may discover later, to your embarrassment, that there is no plausible layout where your defense is necessary. In this particular case, I have found three plausible layouts--(B), (C), and (D)--where a spade shift is the only play that succeeds. So I can rest assured that I have done my due diligence.

I shift to the spade ten--five--eight--ace. Partner should not encourage with queen-jack sixth of spades. With six spades, he knows good and well he doesn't want me continuing spades if I get in. So declarer's spade ace should not be a singleton. Unfortunately, I can't count on Jack for such subtleties, so I must ignore that inference.

Declarer leads the diamond ten. Why isn't she drawing trumps? The two reasons I can think of are (1) declarer has solid trumps and wants to use the heart jack as a later entry, or (2) she wants to finesse partner out of a trump honor.

One usually ducks the ace in this position to avoid setting up a ruffing finesse against partner if the ten is a singleton. For example, if declarer has

(I) ♠ A x x A K Q x x x x 10 ♣ x x

hopping with the ace will give declarer the contract. If I duck, we beat it, provided partner takes care to cash the club queen before exiting. (If he doesn't, declarer can lead the diamond queen and pitch her club.)

Is there any reason ducking might be a bad idea? The diamond king is partner's only entry. What if declarer has:

(J) ♠ A x x A K Q x x x x 10 x ♣ x

Now I must hop and continue spades. If partner wins the first diamond, he's out of entries and there is no way to collect our spade trick.

How can I choose between these two layouts? Playing with Jack, I have nothing to go on. Playing with a partner I could trust, I would rule out (J) based on partner's trick one signal.

It might also be wrong to duck if ducking gives declarer a dummy entry:

(K) ♠ A K 10 x x x x x x K 10 ♣ x x

If I duck, declarer overtakes, pitches a loser on the spade king, then plays a heart through partner's ace-queen. If I hop and play a minor, declarer is down two. That brings up another problem with hopping. I don't know what to play if I do hop. If declarer has (I), I must play a spade. But if declarer has (K) or even

(L) ♠ A A Q x x x x x 10 x ♣ x x

hopping and playing a spade lets her make it. If I do hop, I must play something else.

If I could count on partner to signal intelligently, I could rule out (J) by partner's club signal, and I could rule out (K) and (L) by partner's spade signal. I could then duck with some confidence. Playing with Jack, I just have to make a percentage guess. Since hopping and playing a spade works on only one of the four layouts I've constructed and ducking works on two, I duck, playing the seven.

Declarer overtakes with the jack, giving me a moment of panic. But partner takes the king and shifts to the queen of hearts. Declarer takes eight heart tricks and the spade king. We have no discarding problems. I save two aces, partner saves two spades, and we get a trick at the end. Making four.

♠ K 9 7 5
Q J 9 4
♣ J 10 9 8

♠ 10 6
4 2
A 7 5 2
♣ A K 6 3 2

♠ Q J 8 2
Q 7
K 8 6 3
♣ Q 7 5

♠ A 4 3
A K 10 9 8 6 5 3
♣ 4

To test my trick two decision, I had Jack analyze the position. He agrees with me. After examining 1000 hands, he concluded that the spade ten was the best play, with an expectation of +21.4 points. Second best was a low club, with an expectation of +10.0 points. Since the prime factor in determining my best play is Jack's idea of what a four heart bid looks like, and since he knows that better than I do, I have to trust his judgment.

The other table plays the same contract with the same result. Why is it that the deals that require the most extensive analysis always seem to be pushes?

Table 1: -420
Table 2: +420

Result on Board 2: 0 imps
Total: +2 imps

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