First, Do No Harm

 Continuing with our hand from a recent Wydaho online pairs game:

♠ A 8 4
♥ J 10 8
♦ Q 10 8
♣ A Q 9 7

You are on lead against 1 NT; declarer opened 1 NT (15-17) after partner passed.

THE PRINCIPLE: Think of notrump contracts as a race: Can the defenders set up and cash their winning tricks before declarer crosses the finish line? 

We saw that a fourth-best club lead from this hand -- underleading the ace-queen -- has about a 70% chance of blowing a trick, giving declarer a trick she cannot get on her own. (To be precise, 71.2%, considering declarer could have 16 or 17 points.) Let's not give declarer a one-trick headstart 😝

We usually want a lead that will help establish our winning tricks, without giving away too much in the process. Against a notrump contract, finding and establishing five-card (or longer) suits is usually the winning strategy. If you don't have a five-card suit that looks worthwhile, maybe partner does; your two- and three-card holdings might be where partner has some length.

Where might partner have a long suit?  Note that if partner has a six-card (or longer) suit, she might well have opened a weak two or a higher preempt instead of passing. But we can still hope for a five-card suit in her hand. But which suit?

• Note that dummy did not transfer to a major over her partner's 1 NT; dummy does not have a five-card (or longer) major. 
• If dummy was 4-4 in the majors -- or even 4-3 -- she might have bid Stayman even with a very weak hand, planning to pass any response by opener

So if partner has a five-card suit, it is somewhat more likely to be a major suit because the opponents haven't peeped about the majors.

When leading against notrump, three-card honor sequences are always a good choice: king-queen-jack, queen-jack-ten, jack-ten-nine.  There is almost no danger of setting up a trick for declarer in those suits. Two-and-a-half honor sequences are almost as good -- king-queen-ten, queen-jack-nine, jack-ten-eight -- because there is only a very slight chance of giving up a trick. A suit with only two touching honors (and no supporting card one step below) is still a reasonable choice; the standard lead is low from honor-honor-fourth or fifth, but lead the top honor from honor-honor-third.

In this hand, then, the ♥ J is the standout lead. We hope to find partner with heart length, and not blow a trick on the opening lead. Our club tricks can wait patiently for somebody else to lead that suit.

Bonus Minute
When I started to play bridge, the standard advice for notrump leads was "fourth best from your longest and strongest." That was a long time ago; in those days it was dummy's job to go stand watch against dinosaur attacks. 😏  A lot has changed; much of what I learned back then turned out to be wrong (and not just the bridge bits, hmm).

If you are interested in more effective defense against notrump contracts, I highly recommend Winning Notrump Leads by David Bird and Taf Anthias. The authors created several hundred thousand computer-generated hands matching up with various notrump auctions, and did the double-dummy analyses to determine which leads were most effective in various situations. One key takeaway: Fourth-best from four is probably a waste of time. I specifically owe my first Regional Knockout Team win to the advice in that book. It is not an easy read, but well worth some patient effort by intermediate-to-advanced players; the book truly is a game-changer.

-- Ray
Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)

Playing The Odds

From a recent Wydaho online pairs game:

♠ A 8 4
♥ J 10 8
♦ Q 10 8
♣ A Q 9 7

Partner passes as dealer, then the auction proceeds 1 NT (15-17) on your right, all pass.
What do you lead? Since this is featured in a blog post, it must be some sort of "problem hand"; take an extra moment to think it over.

If you are like most players in that event, your fingers (or mouse) are hovering over the ♣ 7. Let's take a closer look at the ♣ 7 lead.

Whether the ♣ 7 is an effective lead depends on where the ♣ K is!

• If partner has the ♣ K, wonderful, you struck gold: At least three, possibly four club tricks for our side.
• If dummy has the ♣ K it will always win a trick, but the question is who has the ♣ J? If the king is in dummy and declarer has the jack, declarer will play low from dummy and win with the jack. That's not so good for you; declarer will score two club tricks, and your queen is in jeopardy. Ugh.
• If declarer has the ♣ K, ugh! The club lead lets declarer score a trick with the king, a trick that she cannot win without your help. Consider instead that if declarer has to lead clubs, or if partner leads clubs, your ace-queen will trap declarer's king; two club tricks for you, zero for declarer.

We don't know where the king is (without peeking, anyway); the best we can do is estimate what the chances are. Here's how:

There are 40 high card points in every deal: the AKQJ in each of four suits. The relative odds of any particular honor card in any particular hand roughly correspond to the relative distribution of high-card points in the four hands. (It gets more complicated if you know anything about the suit distributions.) 

Here you have 13 points, which leaves 27 points in the other three hands. Declarer has at least 15 points for her 1NT opening. So there is a 15 of 27 chance that declarer has the king; that's more than a 50-50 chance that the club lead will blow a trick (55.5% to be exact, but who wants to be exact with bad news like that).

But partner could have the king; what are the chances of that?  We don't know partner's point count, but we can make a rough estimate. There are at most 12 HCP outstanding (you have 13, declarer has 15-17). If dummy had 8 or 9 points, dummy would have bid over 1NT; so dummy is limited to 7 points. If partner had all the missing honors, partner might have bid over 1NT. So we guess to call it even, 6 points for dummy, 6 points for partner. A 6 in 27 chance is a bit less than 1 in 4, 22% to be exact. 

So, our chances on a club lead are:

• Partner has the king, 6 in 27 chances. 
• Dummy has the king, 6 in 27 chances. And if so, then 15 of 24 that declarer has the jack.(That works out to roughly 2 in 27 are break-even, 4 in 27 blow a trick).  Ugh. 
• Declarer has the king, 15 in 27 chances. Ugh.

If we lead a club, we have a 22% chance of something good, 8% of breaking even (king in dummy, partner or dummy has the jack), and a 70% chance of blowing a trick to declarer's king or jack.

PRINCIPLES:

• The distribution of high card points around the table is a rough estimate for the chances of any specific honor being in any particular hand.
• When most of the high cards are on your right, leading fourth-best from a broken honor holding is likely to lose a trick that you could win by just waiting.

Still want to lead the ♣ 7?  No, I didn't think so. Me neither. So what should we lead? Stay tuned...

Bonus Minute:  If you had a weaker hand, the chances of finding the ♣ K (or any other honor) in partner's hand are greater because partner will have a share of more missing high cards. Declarer will have a correspondingly lower chance of holding the ♣ K. Even so, the ace-queen holding is almost always dangerous to lead from when declarer has the strongest hand; with a 1NT opener, declarer will have at least 15 of 34 chances to hold the king. Figuring out why would be a good homework exercise...

-- Ray
Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)