by Matthew Kidd

♠KQ84
K32
AQ753
♣Q

Nice hand. The auction has gone 1♣ Dbl (you) Pass 1; 1NT. Opener’s rebid promises the balanced 18-19 that a 2NT rebid would normally promise—opener would pass with a minimum. What’s your lead? It's matchpoints if you care.

Aaargh! Leading into a strong notrump hand from a strong hand is always frustrating. Partner can't have more than 6 HCP here and will average 2½. So what’s it going to be? A lead away from a tenace in your longest suit? Or maybe partner’s suit, even though you have almost no expectation of finding him with ace or queen-jack, let alone an entry? And he might have bid on a three card suit with 3=3=3=4 or even 2=3=3=5 given the 12 clubs out. Perhaps a spade? Is it so much to ask him for a jack?

My instinct is a diamond. Perhaps you can catch partner with a jack or king. Still it seems like a good moment for an opening lead simulation as in the Two-Six Dream.

Here are the assumptions that we will put into the simulation:

1. South is a balanced 18-19 without a five card major.
2. South will open 1♣ with 3-3 in the minors but would open 1 with 4-4, planning to rebid 2NT. (We don’t have to consider 5-4 or longer in the minors because the balanced requirement will always give South at least five cards in the majors.)
3. North would either make a weak jump shift or jump in clubs with a six card or longer suit, regardless of point count.
4. East will bid his longest suit (except clubs), and in the case of a tie, choose a major over diamonds, or the major with the most HCP in it. Note: East will never be strong enough for a 1NT bid.

The Tcl code for the Thomas Andrews’ Deal program is below.

Let’s generate 3000 deals with the Deal program using the code above, save them in PBN format, and run Lead Solver on the batch.

Total Hands = 3000
East Spades = 2.44 +- 0.87
East Hearts = 4.04 +- 0.84
East Diamonds = 2.34 +- 0.87
East Clubs = 4.19 +- 1.07

Here are the results:

```Double dummy analysis completed for 3000 deals in 2 m 59 s (0.06 sec/deal ave)

Frequency of Tricks Taken
Ld   Avg  %Set     0 1   2   3   4   5   6   7   8   9  10
CQ  5.58  27.93* [ 0 0  10 211 524 690 727 553 251  33   1  … ]
D5  5.47  24.53  [ 0 0  16 277 511 703 757 476 240  20   0  … ]
D3  5.47  24.53  [ 0 0  16 277 511 703 757 476 240  20   0  … ]
D7  5.46  24.50  [ 0 0  17 278 512 701 757 476 239  20   0  … ]
DA  5.45  23.47  [ 0 0  19 262 490 787 738 449 236  19   0  … ]
H3  5.37  22.83  [ 0 1  24 307 569 681 733 461 186  36   2  … ]
SK  5.33  23.03  [ 0 0  45 302 606 631 725 485 180  24   2  … ]
S4  5.28  20.43  [ 0 0  40 301 634 651 761 435 153  25   0  … ]
S8  5.25  19.73  [ 0 0  41 322 630 643 772 422 146  24   0  … ]
HK  5.06  19.57  [ 0 8 105 425 637 605 633 397 163  27   0  … ]
DQ  5.03  16.50  [ 0 6  96 386 644 756 617 315 164  16   0  … ]
```

Diamond leads, except the Q, work well. But the surprise winner is the ♣Q! Why is this so? Partner rates to have some club length but only 4.19 on average for a combined defensive length of 5.19. By contrast the defense averages 6.44 spades, 7.04 hearts, and 7.34 diamonds. Maybe the lead gives little away without helping declarer because a 4-4 or 4-5 club fit is most declarer can expect with a significant chance of losing one round to an intermediate in East’s hand.

Incidentally, East ends up having to bid 1 on a three card suit 25% of the time.

Double dummy lines in 1NT can be awfully strange. Consider this hand from the batch where a low diamond is a trick worse than either diamond honor.

On a low diamond lead, declarer’s double dummy line is to win, cash the ♣A (cashing A first is okay too, the Qx still endplaying the Kx), and play a diamond. West can cash out the suit but is then endplayed. On a heart to the 7, 10, and Q, a low spade give declarer another trick in additional to the major suit aces to escape for down one. But on the lead of high diamond, followed by the Q, either East gets in once to lead a spade (or run clubs if the ♣A is cashed), or declarer ducks, West continues diamonds and the timing shifts because after cashing out diamonds West is down to ♠K84 against declarer’s tightened ♠AJ instead of ♠KQ84 against declarer’s looser ♠AJ2, holding K32 against declarer’s AQ5 in either case.

Let’s pull a hand from the simulation where the ♣Q lead works better than other leads.

Only the ♣Q holds declarer to nine tricks, any other lead gives him ten. Declarer can win give West a spade, endplaying him. Say he returns a spade and declarer runs clubs. West safely pitches three diamonds, collects a K or A and exits safely with the Q to declarer’s now bare K, and waits for a second spade. On a low spade lead, West doesn’t get his second spade and a low diamond gives declarer a cheap trick. It's the offensive intermediates that made the ♣Q the safe lead.

But this hand is the exception rather than the rule. Most of the time the ♣Q succeeds not by being the sole winning lead but rather by being one of the multiple leads that do not give up a trick.

However, the ♣Q might be overrated by the simulation. The double dummy analysis always knows to drop the singleton ♣Q but real declarers will sometimes lose a finesse to it, a possibility that is surrendered if it is led. This is a stronger argument for a stiff king because against a queen, declarer will often be able to play off an honor before finessing. But on the present hand, this may be impossible or awkward given the very limited entries to dummy. On the actual hand, board 8 (rotated below) from the November 27, 2016 La Jolla Unit game, I led a low diamond which was won in dummy. Declarer immediately finessed into my ♣Q, whereupon I cashed diamonds and when the smoke cleared the contract was down one.