October 9, 2014 – How Much Should You Risk Trying to Make a Doubled Contract?

The match from Saturday did not go our way, but almost all the IMPs swung on one rather unlucky hand. I found plenty of interesting hands, though, with some small room for pick-ups. The first board out gave us a chance –

 

The auction was quite simple: South opened 1NT in third seat, and got to four spades after Stayman. West leads the diamond nine, to the queen, eight, and your seven. Your opponents are using standard carding, and lead third-low, so the diamond nine is consistent with a short suit lead, or with K109 or K1092. In any event, the hand looks pretty straight-forward. Our declarer continued with a spade to the three, ace, and eight, and a trump to the queen, but West showed out, discarding the club nine. That complicates things, but, at least it appears the club ace will be onside. Declarer tried a heart finesse next, jack, four, five, king, and West returned the heart seven (six from East). Take over from here.

We have no chance unless the club ace is onside, so we’ll assume that. The diamond position is still unclear, but, particularly since West was short in trumps, it feels as though West led from diamond length. If West did start with K1092 in diamonds and the club ace, then we had some help – they could have scored two ruffs. What do we know about the heart suit? If we trust East’s count signal, then East started with three or five hearts. Throw in West’s return of the heart seven, and it appears that West started with the K73 in hearts.

If all this is accurate, then the full hand will look something like this:

 

We appear to have ten tricks, but can’t tackle diamonds without drawing all the trumps, and can’t tackle clubs early without setting up extra club winners to cash after trumps are drawn. Still, it is all simply a matter of playing our cards in the right order. Draw the other two trumps, ending in hand, and lead a low diamond. West will certainly win, but we can get back to hand with the diamond ace, throw a club on the good heart, and lead up to the club king.

All this will work provided West has the club ace, and no more than three hearts, and that seems quite likely.

In fact, the full hand was very close to that:

However, declarer won the heart return and played a club immediately, and couldn’t keep control of the hand. Down one was still a small gain. At the other table, South opened with a Precision 1C, and West showed the minors. North cue-bid 2C, doubled by East. This got West to lead a low club against four spades, and declarer naively did not rise with the king. When East won and shifted to a diamond, the hand fell apart, and declarer finished three light.

We won three IMPs, but had eleven in the bag.

The declarer play was again a bit off on board 4, but we were rescued by a friendly defense. I’ll let you try to improve on that defense:

With both sides vulnerable, you went for blood:

You lead your spade three, to partner’s ace, and South’s queen. Back comes a spade to declarer’s king. South leads a trump to the king (eight from partner), and runs the club jack (five, ten, seven), and continues with a club to the queen (three from partner). Your carding, by the way, is standard. Now South leads the diamond jack to your queen, while partner discards the heart two. Plan the defense.

The hand is pretty much an open book. South was certainly 2-3-5-3. We’ve seen A10972 ??2 8 K543 from partner, who almost certainly holds the heart ace, leaving South with KQ Kxx J10754 AQ10. We have three trump winners, and the spade ace in, and will obviously score two heart tricks, so the contract is set. Can we set it another trick? Can we keep South from scoring a heart trick? Maybe, but we will need some help. It has to right to play our other spade here, so we do, and South trumps. Now comes the club ace. Back to you.

Good. We were hoping declarer would do that. Trumping can’t be right. If we do, we’ll get our trumps, but have to break hearts. Our trump tricks aren’t going away, and discarding will leave South on play. What can South do? If South exits a trump, we draw trumps, and partner has the rest. What if South exits a low heart to us? No good, we are still endplayed, and will have to set up the heart for declarer.
But, if partner holds the big heart nine, and we unblock, then partner can win that heart and put the club king through declarer. We will set the contract 500 if the full hand is this:

We should discard a high heart on the club ace, to leave:

 

South has no answer. If South tries a low heart, East will win the nine, and lead the club king. Whether South trumps or discards, we have the rest.

This was, in fact, the actual hand. Back up the play one trick:

 

Declarer could have ensured seven tricks by leading a low heart from hand, rather than the club ace. Since the heart ace was now doubleton, declarer would set up a heart trick, and keep control of the hand. Should South have worked this out?

Yes! Most of the cards were marked. The key was East’s shape. It was right to play the club ace if clubs were three-three originally, if East was 5-4-1-3, but wrong here, when East was 5-3-1-4. So South had to guess the club distribution. There were two major indicators pointing in the right direction. First, the spot cards played, 5-3 by East, 7-9 by West, suggested this layout. Secondly, East would never cover the club jack with K543, but might cover holding K53, lest declarer steal a trick with AQx, but no ten. Covering would cost if South held A109, not covering would cost if South held, say, AQ9. That’s a tough choice on defense, and no defender could duck that club jack smoothly from K-third.

Our declarer should have gotten this one right, but West trumped the club ace (thanks!), and we escaped for -200.

Finally, we get to the big swing board, board 7. At one table, we declared four spades, doubled, on these cards:

 

The auction went, with both sides vulnerable:

West leads the trump jack against your doubled game. Plan the play.

Good lead. Without it, you could cross-ruff for ten tricks. As it is, the cross-ruff will yield only nine winners. Still, down one ain’t bad. Is there any way to make the contract? Well, suppose both major suits split, 4-3 hearts, 2-2 trumps. Could we set up hearts?

Let’s see – win trump in hand, ruff three hearts and three clubs, draw the last trumps, and … No good, we are out of trumps, and hearts aren’t established. What if we use two trump entries to hand? Win, heart ruff, trump to hand, heart ruff, club ruff, heart. We will still have two trumps in hand, and one more heart to knock out. Yes, that will work – we’ll lose only two hearts and one diamond, +790.

Of course, if trumps don’t split, we’re in big trouble, and may end up with only four trumps in hand, two ruffs, and the diamond ace, -800. Which was my title question:

               How much should you risk trying to make a doubled contract?

To answer such a question, we have to calculate the probabilities of success, versus failure, and the IMPs at stake. For instance, if we judged that our team-mates would be +650 at the other table, then down one wins ten IMPs, down three loses four. So we would be risking 14 IMPs trying to go +790, and a 16 IMP pick-up. Risking 14 to gain 6 seems like a bad bet, when we could settle for a nice 10 IMP gain.

Before calculating the probabilities, let’s look at the play a little more carefully: If we try to make the hand, and East shows out on the trump king, we’ll know trumps aren’t splitting, so we’ll let that hold, and cross-ruff. That’s down two, not three. If East follows, and we overtake, only to see West show out, then it looks like 800 away. Can we do better?

Maybe. I actually like this approach, if you decide to play to make: Since playing to make means losing a couple of heart tricks, how about conceding a heart immediately? What will happen?

If West wins the heart, and continues trumps, we can win in hand, continuing to set up hearts if trumps split. If they don’t, we can trump on heart on the table, play a trump to hand, and lead a heart. Now, if hearts behave, we’ll take nine tricks, losing three hearts and a diamond. Likewise, if East wins the heart to play a trump, win the ace, hoping trumps split. If they don’t, trump a heart, club, heart, club, diamond ace, club, and we will take eight tricks. Better!

The defense would do better not to play a second trump. On a club back, we will always win eight tricks, or ten. Only a diamond back puts us in danger of -800. This is definitely how to play the hand, if we judge to try to make.

So, big question: Do we settle for down one, or go all out?

What do we know? West would certainly have introduced a five card heart suit over our spade bid, so West will not have five hearts. Likewise, East might well have bid four hearts over three spades, but didn’t. Hearts certainly rate to split. As for trumps, who knows? The double certainly suggests that they will split, so we have to be at least even money to make our contract.

What will happen at the other table? Our opponents have 27 high-card-points, so our teammates are going to be in some game, but, with the foul splits, games are hopeless. If spades are 2-2, there are three top losers, so no minor suit game has a chance. Four hearts, in the four-three (or 5-2) looks like a great spot, but not with trumps splitting 6-0. If spades are 3-1, then five clubs looks like a claim, but not with these awful splits. It feels like your teammates will end up down a couple of tricks in some game, maybe even doubled. Let’s predict an optimistic -200 their way. Settling for down one costs 9 IMPs. If we turn that into 800, we increase the loss to 15, six IMPs gone. But, if we finish +790, we win 11, for a 20 IMP gain. 20-6 odds if we try to make! So, here, we should definitely go for broke. Win the trump in hand and concede a heart.

This was the full hand:

Our declarer went for the make: He won the trump in hand, trumped a heart, and played diamond ace, diamond (strange choice). East won to play a second trump, and South rose with the ace, trying to make. Good play! However, when West showed out, that meant three off. Here was the position:

 

Declarer trumped another heart, as West followed with the ten, ruffed a club, and exited a heart. Since West had to win, the defenders could never draw a third round of trumps, and South ended up scoring all five trumps, down two, not three. Had West unblocked on the second round, the result would have been -800. What went wrong?

That’s simple – East, on the first round of hearts, should drop the queen, telling partner about the jack. Then it would be easy for West to unblock.

What odd symmetry. In one doubled contract, the defender had to drop a high heart from QJ107, to unblock the suit, and let partner gain a second entry. In the other, the defender had to drop a high heart from QJ5 to help partner unblock the suit. Alas, the defense failed both tests.

At the other table, we bid up to the sound five club game. North doubled, and that contract was fated to go down two. Unfortunately, East ran back to diamonds, which was much worse, and watched partner go down -1100. 17 IMPs gone on this one wild hand. Too bad, but fun for a kibitzer and mentor.