Chapter 11

03-20-2006 12:06:29

Chapter 11 Lead Tables

The computer bid these deals; they were analyzed by Gib, a double-dummy solver; and lead tables were generated. South dealt and opened a 15-17 notrump. North-South have about 25 points. The final contract is 2-, 3-, or 4-of-a-major, or 2- or 3NT. The East-West hands were not examined for overcalls. No attention was paid to the details of the auction in evaluating the opening lead. In the real world, partner might double or bid a suit, and South or North might show a second suit. The study would be more accurate if these details were included. Later, we may use these results for a guide to more specific problems.

In a Jacoby world, South declares. Results are for both West and East leading, and this gives a numerical value for the importance of transfers.

These sets of deals were generated with these requirements:

Final contract is 2NT or 3NT after Stayman, Jacoby, or whatever. North is limited to 12 HCP.
Final contract is 3 or 4 after Stayman, Jacoby, or Texas. North is limited to 12 HCP.
Final contract is 2 , 3 , or 4 after a transfer sequence. North has 6-12 HCP.

East-West averaged between 15 and 16 HCP. Heart and spade contracts were combined into suit results.

The results are for these assumptions. I believe defenders should be aggressive when there is a side-suit source-of-tricks. Since, North-South have not announced a second suit, a passive defense is more acceptable. Also, the North-South high card count is close to 25. Different assumptions, for example, a side source-of-tricks, or a different North-South count, will change the results.

I expect the lead tables to apply against weak notrumps, after a 2NT rebid, or a 2NT opening.

Importance of Transfers

I combined data into two categories - suit contracts and notrump contracts. I did a board-a-match scoring with double-dummy leads and North and South as declarer. The matchpoint score difference is 4.4% on 2000 notrump deals, and 3.0% on 5000 suit deals. About 90% of the time, the results do not depend on who declares. It is in this pure double-dummy mode that transfers do best. When you are more practical and choose the best lead from lead tables given below, the transfer gain is of the order of 1%.

Lead Tables

All other things being equal, what card combinations make the best leads? How does suit length affect the choice? Using the same deals as above, I used matchpoint scoring in an eight-table game with North and South declaring against leads in the four suits. Scores are low when leading small from one or more honors. For example, the experiment gives 55% for x-x-x-x and 45% for K-T-x-x. Before now, I would have led from the K-T-x-x. Scores are low for trump leads — the average trump lead scores 45% and the average side-suit lead is 52%. If we had only kept track of the effectiveness of leads in our bridge life, we would have known these things.

The lead chosen in each suit:

Top of touching honors.
From an interior sequence, (either ten or nine from K-T-9-x) else
Top from a doubleton, else
Low at notrump. At suit, lead the ace, rather than low.

Again, eighty to ninety percent of the time, a particular suit was equally good or bad from both sides of the table. At notrump, major leads were slightly better than minor leads. At suit, the message is to avoid trump leads, and the other major is slightly better than the minors. Choosing the wrong suit on any given hand costs about half a trick at notrump. Leading a trump costs about half a trick versus par. Leading a side-suit costs about one-quarter to one-third of a trick. If the lead was from what happens to be the best suit on each hand, tricks won are about one-hundredth of a trick higher than the double-dummy tricks won. Thus, there are not too many deals where the best card to lead in a suit is different from the card given by the above rules.

The Bridge Encyclopedia recommends low from K-Q-x-x, Q-J-x-x, and J-T-x-x. The computer recommends high from these combinations. The Encyclopedia looks askance at singleton leads. Anders Wirgen and the computer look favorably on these leads.

Next, the various suit combinations were ranked. To limit the number of numbers, I note that there are forty-two three-card or shorter combinations containing the nine or higher that can head a suit. To clarify, A, A-x, A-x-x .. is one combination; A-K-Q, A-K-Q-x, A-K-Q-x-x .. is a second combination; and x, x-x, x-x-x .. is a third combination of the forty-two combinations. Suits with more than six cards were treated as six-card suits. Trumps and side-suits were treated separately. There still are a lot of numbers for the computer to manipulate, and for some combinations there are not enough data.

Now the data. The first table separates the leads into percentage bands for notrump, for a side suit at trumps, and for trump leads. The second table shows leads versus suit length. The last three tables summarize sequence leads, broken sequences, one high-card, and no high cards as a function of suit length. Three cards and broken sequences do poorest.

Matchpoints for Leads at Suit and Notrump
Percent Notrump Side-Suit Trump
75- 77 AKQ
73- 75
71- 73
69- 71 KQJ
67- 69
65- 67 AKQ
63- 65 AKJ, KQT AK9, AKJ, AKT
61- 63 AKT AK
59- 61
57- 59 QJT, AK, JT9 KQJ, KQT AKQ
55- 57 AK9, KQ9 QJT
53- 55 T9, QJ9 x, JT9, 9, KQ9, JT, T, A, T9, KQ AKJ
51- 53 9, J9, JT, x, T, J J, AT, QJ9, J9, QJ, AT9
49- 51 QJ, QT9, KQ A9, Q, AJT, QT9, AJ9, Q9, QT AKT, x
47- 49 Q9, Q, A9, AT, A AJ, AQJ, AQT T, QJT, 9, AK, T9
45- 47 KT9, AJ, AJT, AQJ, K9 K, K9 A
43- 45 AT9, K, QT, KJT, AQ, KT KT, AQ9, KT9 J, JT9, A9, J9, KQJ, Q
41- 43 AQ9, AJ9 AQ, KJT, KJ9, KJ JT, AQJ, AQT, KQT, Q9
39- 41 KJ AT, AK9
37- 39 KJ9, AQT KQ9, K, AJ, QT
35- 37 K9, KJ9, AQ, QJ
33- 35 AJT, KQ, KT, QT9
31- 33 AQ9
29- 31 KT9, AJ9, KJ
27- 29 KJT
25- 27 QJ9
23- 25 AT9

Value of Leads as a Function of Suit Length
Length 1 2 3 4 5 6 Average
Notrump 49.81 48.76 48.45 50.92 52.97 53.93
Suit Non-trumps 59.23 53.07 50.35 50.79 50.99 53.80 51.67
Suit Trumps 49.65 44.73 43.66 41.51 45.31 47.22 44.89

**Matchpoints for Leads at Suit and Notrump**
Percent	Notrump	Side-Suit	Trump
75- 77	AKQ
73- 75
71- 73
69- 71	KQJ
67- 69
65- 67		AKQ
63- 65	AKJ, KQT	AK9, AKJ, AKT
61- 63	AKT	AK
59- 61
57- 59	QJT, AK, JT9	KQJ, KQT	AKQ
55- 57	AK9, KQ9	QJT
53- 55	T9, QJ9	x, JT9, 9, KQ9, JT, T, A, T9, KQ	AKJ
51- 53	9, J9, JT, x, T, J	J, AT, QJ9, J9, QJ, AT9
49- 51	QJ, QT9, KQ	A9, Q, AJT, QT9, AJ9, Q9, QT	AKT, x
47- 49	Q9, Q, A9, AT, A	AJ, AQJ, AQT	T, QJT, 9, AK, T9
45- 47	KT9, AJ, AJT, AQJ, K9	K, K9	A
43- 45	AT9, K, QT, KJT, AQ, KT	KT, AQ9, KT9	J, JT9, A9, J9, KQJ, Q
41- 43	AQ9, AJ9	AQ, KJT, KJ9, KJ	JT, AQJ, AQT, KQT, Q9
39- 41	KJ		AT, AK9
37- 39	KJ9, AQT		KQ9, K, AJ, QT
35- 37			K9, KJ9, AQ, QJ
33- 35			AJT, KQ, KT, QT9
31- 33			AQ9
29- 31			KT9, AJ9, KJ
27- 29			KJT
25- 27			QJ9
23- 25			AT9

Sequences vs Length at Suit and Notrump

**Rank Sequences at Notrump**
Length	1	2	3	4	5	6	Average
No high cards	49.4	51.9	52.6	54.8	58.3	66.7	51.9
One-high card	50.4	47.5	48.9	52.4	53.1	53.4	49.7
Broken sequence		42.9	42.1	46.9	49.8	48.6	46.0
2-card sequence		54.3	52.0	52.6	55.5	60.1	53.8
3-card sequence			59.4	60.4	63.5	63.4	62.1

**Rank side-suit Sequence Leads**
Length	1	2	3	4	5	6	Average
No high cards	59.1	54.8	52.8	54.0	51.5	54.2	54.8
One-high card	59.5	52.4	50.6	51.6	52.3	51.2	51.8
Broken sequence		49.7	46.0	46.8	47.2	51.3	47.4
2-card sequence		55.9	54.0	54.3	55.1	57.4	54.9
3-card sequence			55.8	58.1	57.3	57.9	57.6

**Rank Trump Sequence Leads**
Length	1	2	3	4	5	6	Average
No high cards	49.3	49.0	48.7	48.1	50.0		49.0
One-high card	50.1	43.0	45.4	46.2	54.7		45.3
Broken sequence		37.9	37.0	38.7	39.9	54.2	37.8
2-card sequence		49.4	41.7	34.9	49.5		41.7
3-card sequence			48.0	47.6	44.1	33.3	47.0

A-K-Q is the best side-suit lead, the best trump lead, and the best notrump lead. A-Q-T is poorest at notrump; K-J is the poorest side-suit lead; and A-T-9 is the poorest trump lead. The best side-suit length for a lead is a singleton, and then a doubleton, and this effect is significant. A three-card suit is poorest. At notrump, suits with up to three cards are poorest with three again being the worst, and then improve with length.

The message, that I do not want to believe, is Fourth highest from longest and strongest is wrong.

Lead high from two or three touching honors.
Lead passively, and
Avoid leading fourth highest from one or more honors.

First, go after a suit you have. Second, go after a suit that partner or declarer owns. This either finds partner's cards or does something for declarer that he can do for himself. Do not lead small from an honor and hope partner has help. (It might be right to lead small from an honor if they have a side source-of-tricks.) (Another interpretation is: The double-dummy solver has us make a lead that is not costly. Then, the solver takes over and saves the day. Real defenders, on the other hand, cannot recover after an uninformative lead such as small from air. )

To my partners: I do not promise to not lead small from an honor. I have been doing it for too long. I will think about it.

The next step used the tables to select a lead for West and for East on each deal. With no bidding clues to help in the choice of side-suit leads, you get a 6% improvement over the eight-table field average. The Jacoby effect reduces to about 1% (1.4% at suit and .7% at notrump.)

The full numerical bloodshed is relegated to Appendix 1.

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