November 12, 2014 – Two Trick One Decisions

Sunday’s match went heavily in one direction, with East-West finishing up forty three IMPs. That is quite a lot, but the bridge at our table was quite strong. Thirty of those IMPs swung on trick one decisions at the other table. I’ll focus on those two swing boards.

First off, let’s try some simple suit combination problems, and probability calculations. Imagine that you are in a 3NT contract, and need two extra tricks, from either spades or diamonds:

 

You will have to decide immediately, winning the opening lead in hand, if you decide to go after spades, or on the table, if you opt for diamonds. Which is best?

That is pretty easy. Diamonds will split around 68% of the time, but a 3-3 or 4-2 split in spades will suffice there, and that is an 84% shot, so much better.

Now, let’s add some spot cards to the two suits:
For spades:

 

What is the best play to win four spade tricks in notrump. How often will that work?

We can handle one five-one split – a singleton nine on our right, and that adds a couple of percentage points. The proper play is to lead the spade six to the ten. SuitPlay lists this as succeeding 86.4% of the time.

How about this diamond suit:

 

If we have plenty of entries, our best play is to lead the three and, if West follows small, insert the nine from the table. This will pick up both 5-0 splits, and every four-one split except a singleton queen or jack on our right, and will yield four tricks better than 94% of the time.

That brings me to the first play problem:

 

You are in 3NT, after an uncontested auction (one table bid 1S – 2D – 2S – 3NT, the other South tried three clubs along the way). West leads the heart four, and we have the suit-choice problem I mentioned. If we decide to go after spades, we may need two entries to the table, and so should win the lead in hand. If we decide to play on diamonds, we can win the heart king, and start diamonds from the table, or win in hand, and start diamonds that way. Maybe we can combine our chances, testing one suit, and then the other. How would you play?

If we must rely entirely on one suit, then diamonds it is, for several reasons. First off, with the extra diamond spots, diamonds will come in more often than spades. Moreover, if spades are 4-2, we’ll have to lose two spade tricks along the way, and a club shift will likely set up three club winners for the opponents, one trick too many.

If we opt for diamonds, where should we win the opening lead?

We don’t have the entries to maximize the diamond suit itself – three to the nine. The best we can do is to start with the ace, and run the nine next, picking up four diamond tricks unless West has four or five diamonds to the queen and jack. That will give us four diamond tricks, three hearts, and two spades, provided we win the opening lead on dummy. If we win in hand, problems may arise. Suppose the diamond suit looks like this:

 

East may duck the diamond nine, and then we won’t have any sure entry to our diamonds.

What about combining our chances? Suppose we test diamonds first, and then go after spades if the diamonds don’t behave? That’s a nice idea, but we just don’t have the necessary entries for that. If we win the heart in hand, and cash two diamonds, we may not unblock the hearts, and if we win the heart king, North won’t have a reentry for those good spades.

Okay, how about testing spades first. Suppose we win the heart king, and lead out the spade ace next. If an honor (or the nine) drops, we can continue spades, hoping another big spade drops. Otherwise, go after diamonds.

That is interesting, but I don’t like it. What would we pitch on the second spade? If we throw a club, we might end up losing a spade and four clubs. If we throw a diamond, we are giving up on diamonds. There are other potential problems. Suppose the full hand looks like this:

 

We cash a high spade, then turn to diamonds, but East ducks the nine. Now, if we continue diamonds, we can never cash the other spade. If we cash it early, we set up five tricks for the defense.

Nope, simple is best here. Combining chances just makes our life too difficult – win the heart king, and pass the diamond nine.  If East shows out on the first diamond, we can win the king, and try spades.  Otherwise, we’ll make the hand unless West has QJxx in diamonds.

This was the full hand:

 

Our declarer correctly won the heart king, and ran the nine of diamonds. At the other table, declarer decided to win the heart in hand, and cash one high spade. When the queen appeared, the hope for two honors doubleton increased a lot, so declarer called for the other high spade, but didn’t know what to discard from hand. Hoping to develop spades, and keep a sure club stopper, South discarded a diamond, and the hand was over.

Then came this one:

Vulnerable against not, partner passes, and the auction proceeds:

 

Partner leads the heart three, and North plays the five. Lots of IMPs are riding on this play. Do you play the seven or the king?

What do we know? North has seventeen points, and we have a whopping five count. South bid only two clubs originally, so South will hold maybe six-to-nine, which leaves nine-to-twelve for partner. Of course, partner is a passed hand, so twelve is out, but we can place partner with nine-to-eleven. Partner’s double echoes that conclusion.

Could declarer have Ax in hearts on the auction? Maybe, with partner holding a hand like 10xxx Jxx AQx Kxx. However, South had two earlier chances to bid notrump, and didn’t. Furthermore, every declarer, every one, would call for the queen, not the five. So we can rule that one out. However, declarer might well hold a singleton ace of hearts, and partner 10xx Jxxx AQx Kxx. Declarer will have only eight tricks, unless we put up our heart king.

This is a very specific hand, and, holding a good hand with four trumps, partner might have bid more, so playing the king, and hoping declarer bid 3NT on that partial stopper, Jx, seems better. Still, losing a trick to the doubleton jack of hearts won’t cost the contract unless declarer also holds the diamond ace. Maybe partner doubled on a hand like 10xxx Axx Axx xxx, and we would still survive a misguess at trick one.

This is all very close, but it feels like the king is more likely to work, and letting them out for down one when partner has both red aces, rather than three down, doubled, would still be poor.
At the table, East tried the seven, only to find this full hand:

.

Not only did the heart play lose a trick, it gave declarer a second entry to pick up clubs (partner having four good clubs was a surprise on the auction). That turned +500 into -550.

By the way, West might well have led the heart ace. This would solve partner’s headache on a hand like this, and might help partner keep an entry on other hands, where partner had only five hearts to the king. Since West clearly holds the bulk of the defensive strength, West could afford to make the strange lead of the heart ace. Leading low, though normal, will only be necessary when South has a full stopper, like Kxx, almost impossible on the auction.