Study 8J21   Main

Positional Advantage

by Richard Pavlicek

Which hand should be declarer?

As virtually all bridge players are aware, it sometimes matters which hand declares the partnership’s final contract — the difference being the opening lead, which may have a greater impact from one defender than the other. Most of the time it doesn’t matter, but when it does, it’s nice to have the positional advantage of declaring from the right side.

It is widely accepted, in general, that the stronger hand should be declarer, the logic being that its high-card abundance is spared from an immediate lead-through. This is the foundation for Jacoby transfers and various other conventions, such as the negative diamond response to forcing club bids so the weak hand will not be the first to name a major or notrump. But how much of an advantage is it? Is hand pattern also an issue? And how often does it matter? This study will provide answers.

Game in Notrump

Slam in Notrump

Game in a Major

Slam in a Suit

Honor Holdings

All statistics were derived from my database of 10,485,760 random solved deals. Partnerships of 21-35 HCP were appraised in two ways: (1) Notrump relevant if either hand is balanced or if longest fit is only eight cards, or (2) Suit relevant if both hands are unbalanced or if an 8+ card fit exists.* Note the overlap, so some partnerships were appraised both ways. Partnerships of 21-28 HCP were considered for game bidding (3 NT or four of a major), and partnerships of 29-35 HCP for slam bidding (6 NT or six of a suit).

*Where multiple fits exist, the longest was deemed to be trumps (even if play in another suit could win more tricks). In the event of a tie, the higher ranking was picked to emulate the usual practice of preferring a major.

Another factor that affects trick production and game or slam chances is the apportionment of a side’s HCP. Are the HCP evenly distributed? Or are they lopsided? To investigate this influence, each HCP total is not only shown in full but also broken down into its constituents, e.g., 25 HCP is shown for 13-12, 14-11, …, 25-0.

Study 8J21   Main

Top   Positional Advantage

Game in Notrump

The following tables show the positional advantage of declaring 3 NT for partnerships of 21-28 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which is the main concern at matchpoint scoring, and (2) the percent of cases 3 NT makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

An interesting observation is that, on average, it is better to choose the tamer (more balanced) hand as declarer than the stronger hand. As the HCP disparity increases, the advantage of the stronger hand also increases and eventually overtakes that of the tamer hand.

Perhaps the most astounding revelation is the effect of apportionment. For instance, with 24 HCP your chance of making 3 NT (assuming a fixed declarer) is 40.13 percent if the HCP are split 12-12, but only 25.12 percent if the HCP are split 21-3. We all know why this is true, but the difference of 15 percent is remarkable. The obvious implication is not to stretch for game when partner opens 2 NT or the like.

21 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1456537	8.91	6.55	5.13	6.57	5.22	6.57	5.30	6.61	5.63
11-10	320931	8.95	6.61	5.80	6.62	5.81	6.63	5.97	6.67	6.34
12-9	295450	8.94	6.60	5.64	6.61	5.70	6.61	5.84	6.65	6.19
13-8	256541	8.87	6.59	5.37	6.60	5.48	6.60	5.56	6.64	5.91
14-7	208253	8.96	6.56	5.12	6.58	5.26	6.58	5.30	6.61	5.62
15-6	148656	8.96	6.51	4.52	6.53	4.67	6.53	4.70	6.57	4.99
16-5	102116	8.77	6.46	4.06	6.48	4.21	6.47	4.20	6.51	4.47
17-4	64619	8.85	6.41	3.66	6.44	3.80	6.43	3.76	6.47	4.01
18-3	34686	8.68	6.32	3.19	6.35	3.36	6.34	3.32	6.37	3.48
19-2	15586	8.76	6.22	2.46	6.26	2.50	6.23	2.49	6.28	2.62
20-1	7090	8.70	6.18	2.69	6.22	2.76	6.19	2.74	6.23	2.81
21-0	2609	7.86	6.23	3.22	6.28	3.45	6.24	3.33	6.28	3.45

22 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1368958	9.63	7.08	11.57	7.09	11.76	7.09	11.89	7.14	12.61
11-11	150454	9.58	7.14	12.95	7.14	12.95	7.16	13.26	7.20	14.10
12-10	287161	9.72	7.12	12.64	7.13	12.71	7.14	12.99	7.18	13.78
13-9	257713	9.58	7.12	12.42	7.12	12.59	7.13	12.80	7.18	13.56
14-8	217156	9.63	7.10	11.91	7.12	12.16	7.12	12.26	7.16	13.00
15-7	168917	9.74	7.06	11.12	7.09	11.45	7.08	11.41	7.13	12.12
16-6	117889	9.64	7.01	10.11	7.03	10.41	7.02	10.37	7.07	11.03
17-5	78390	9.68	6.97	9.20	6.99	9.55	6.98	9.50	7.03	10.05
18-4	48257	9.23	6.91	8.25	6.95	8.58	6.93	8.51	6.97	8.94
19-3	25115	9.69	6.81	7.14	6.84	7.48	6.82	7.29	6.87	7.79
20-2	11187	9.48	6.74	5.79	6.78	6.05	6.75	5.91	6.79	6.27
21-1	5006	9.37	6.64	5.49	6.69	5.71	6.66	5.53	6.70	5.79
22-0	1713	8.58	6.61	5.14	6.66	5.60	6.63	5.49	6.67	5.72

23 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1237217	10.37	7.59	22.44	7.60	22.81	7.61	22.96	7.66	24.21
12-11	263598	10.43	7.65	24.32	7.65	24.41	7.67	24.85	7.71	26.19
13-10	244935	10.44	7.63	23.93	7.64	24.15	7.65	24.49	7.70	25.78
14-9	213485	10.41	7.62	23.43	7.63	23.80	7.64	24.00	7.69	25.28
15-8	173296	10.30	7.60	22.75	7.62	23.24	7.62	23.29	7.67	24.56
16-7	131906	10.37	7.56	21.40	7.58	21.97	7.58	21.92	7.63	23.12
17-6	89446	10.32	7.50	19.53	7.53	20.14	7.52	19.99	7.57	21.15
18-5	57500	10.36	7.46	18.21	7.50	18.92	7.48	18.65	7.53	19.75
19-4	34131	10.18	7.40	16.40	7.44	17.20	7.42	16.80	7.46	17.85
20-3	17290	9.75	7.28	13.47	7.32	14.16	7.30	13.95	7.34	14.62
21-2	7321	9.83	7.23	12.47	7.27	12.91	7.25	12.81	7.29	13.36
22-1	3233	10.05	7.10	10.18	7.15	10.70	7.11	10.21	7.16	10.92
23-0	1076	11.34	7.14	9.67	7.20	10.22	7.15	10.04	7.20	10.32

24 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1070924	11.19	8.10	37.71	8.12	38.22	8.13	38.38	8.18	40.18
12-12	112908	11.27	8.17	40.13	8.17	40.13	8.19	40.83	8.24	42.61
13-11	219494	11.35	8.16	40.05	8.17	40.24	8.19	40.72	8.24	42.56
14-10	198305	11.21	8.14	39.28	8.15	39.62	8.16	39.99	8.22	41.82
15-9	165822	11.20	8.13	38.71	8.14	39.21	8.15	39.34	8.20	41.17
16-8	131799	11.19	8.10	37.41	8.12	38.16	8.12	38.11	8.17	39.94
17-7	97099	11.21	8.05	35.45	8.08	36.38	8.07	36.17	8.13	37.92
18-6	64098	10.98	8.00	33.63	8.03	34.66	8.02	34.26	8.07	36.04
19-5	39660	10.80	7.94	31.05	7.98	32.19	7.96	31.76	8.01	33.34
20-4	23025	10.66	7.89	28.51	7.93	29.95	7.91	29.03	7.96	30.80
21-3	11427	10.83	7.78	25.12	7.82	26.46	7.80	25.83	7.84	27.06
22-2	4629	10.63	7.69	21.99	7.74	23.09	7.71	22.45	7.76	23.66
23-1	2014	10.87	7.58	18.02	7.65	19.07	7.61	18.47	7.66	19.41
24-0	644	9.01	7.59	17.55	7.63	19.25	7.60	17.70	7.64	19.25

25 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	889566	12.07	8.62	54.99	8.64	55.54	8.64	55.72	8.70	57.80
13-12	183242	12.28	8.68	57.18	8.68	57.23	8.70	57.97	8.76	60.01
14-11	174320	12.18	8.67	57.03	8.68	57.24	8.70	57.75	8.76	59.79
15-10	150241	12.11	8.65	56.18	8.67	56.64	8.68	56.86	8.74	58.98
16-9	123038	12.09	8.63	55.37	8.65	56.03	8.65	56.09	8.71	58.20
17-8	94687	11.84	8.60	54.52	8.62	55.35	8.62	55.19	8.68	57.31
18-7	68432	11.98	8.54	52.18	8.58	53.37	8.57	52.99	8.63	55.06
19-6	43423	11.69	8.49	49.90	8.53	51.04	8.52	50.66	8.57	52.71
20-5	26359	11.75	8.43	47.52	8.48	49.15	8.46	48.44	8.52	50.52
21-4	14444	11.32	8.37	45.22	8.42	46.89	8.39	45.84	8.45	48.01
22-3	7020	11.98	8.26	40.66	8.31	42.58	8.29	41.61	8.34	43.60
23-2	2909	12.55	8.15	36.34	8.21	38.43	8.17	37.16	8.23	39.33
24-1	1126	9.59	8.07	32.68	8.13	34.46	8.09	33.13	8.14	34.81
25-0	325	8.00	7.99	28.62	8.03	29.54	8.00	28.62	8.03	29.54

26 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	707022	12.91	9.13	70.29	9.15	70.81	9.16	70.97	9.22	72.94
13-13	72780	12.97	9.18	71.85	9.18	71.85	9.21	72.59	9.27	74.38
14-12	141341	13.01	9.19	71.93	9.19	72.01	9.22	72.59	9.28	74.51
15-11	127757	12.97	9.18	71.71	9.19	71.99	9.21	72.34	9.27	74.26
16-10	109480	13.11	9.15	70.85	9.17	71.40	9.18	71.61	9.24	73.55
17-9	86432	12.91	9.12	70.17	9.15	70.87	9.15	70.82	9.22	72.89
18-8	64798	12.74	9.09	69.43	9.12	70.25	9.12	70.03	9.18	72.08
19-7	44607	12.69	9.06	68.30	9.09	69.39	9.08	68.96	9.14	70.98
20-6	28034	12.77	8.96	65.30	9.00	66.65	8.99	66.09	9.05	68.20
21-5	16516	12.53	8.93	63.96	8.97	65.43	8.96	64.66	9.02	66.74
22-4	8717	11.71	8.83	61.14	8.89	63.35	8.86	62.04	8.92	64.31
23-3	4136	11.70	8.71	56.04	8.76	58.12	8.73	56.87	8.79	59.14
24-2	1622	11.16	8.64	52.96	8.69	54.50	8.66	53.39	8.71	55.24
25-1	629	11.92	8.42	43.08	8.51	44.83	8.46	43.40	8.52	45.15
26-0	173	9.25	8.56	47.98	8.65	49.13	8.61	47.98	8.65	49.13

27 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	538102	13.65	9.66	81.94	9.68	82.38	9.69	82.57	9.76	84.15
14-13	108930	13.85	9.71	82.92	9.71	82.94	9.74	83.52	9.81	85.03
15-12	101199	13.91	9.70	82.63	9.71	82.90	9.73	83.35	9.80	84.86
16-11	90164	13.81	9.69	82.36	9.70	82.66	9.72	82.92	9.79	84.52
17-10	75086	13.60	9.68	82.47	9.70	82.91	9.71	83.10	9.78	84.64
18-9	57439	13.37	9.64	81.72	9.67	82.41	9.67	82.38	9.74	83.97
19-8	41476	13.53	9.60	81.24	9.64	81.99	9.63	81.83	9.70	83.49
20-7	27996	13.41	9.56	80.45	9.60	81.41	9.59	81.04	9.66	82.79
21-6	17220	13.01	9.49	78.78	9.54	79.87	9.51	79.36	9.58	81.18
22-5	9776	12.78	9.42	77.70	9.48	79.35	9.45	78.47	9.52	80.29
23-4	5118	11.86	9.32	75.26	9.37	76.77	9.34	75.97	9.40	77.53
24-3	2401	12.49	9.21	72.39	9.28	74.59	9.25	73.47	9.30	75.39
25-2	908	13.33	9.09	69.16	9.16	71.15	9.12	69.82	9.19	71.81
26-1	304	13.16	8.97	63.49	9.02	64.47	8.98	63.16	9.03	65.13
27-0	85	10.59	9.02	61.18	9.11	65.88	9.11	65.88	9.11	65.88

28 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	388219	13.91	10.18	89.42	10.20	89.76	10.21	89.92	10.28	91.04
14-14	39633	14.14	10.24	90.06	10.24	90.06	10.27	90.50	10.35	91.57
15-13	75770	14.01	10.23	89.93	10.24	90.05	10.26	90.37	10.33	91.45
16-12	68675	14.12	10.21	89.61	10.22	89.80	10.24	90.13	10.32	91.21
17-11	59049	13.92	10.20	89.77	10.22	90.03	10.23	90.37	10.31	91.33
18-10	47960	13.84	10.19	89.46	10.22	89.96	10.21	89.95	10.29	91.11
19-9	35485	14.16	10.14	88.91	10.18	89.54	10.17	89.49	10.25	90.74
20-8	25331	13.27	10.12	88.95	10.15	89.56	10.14	89.39	10.22	90.57
21-7	16338	13.17	10.06	88.75	10.11	89.42	10.09	89.15	10.16	90.35
22-6	9689	13.45	10.00	87.38	10.05	88.28	10.03	87.93	10.10	89.21
23-5	5544	13.98	9.92	86.33	9.99	87.64	9.96	87.09	10.03	88.44
24-4	2827	12.91	9.87	86.70	9.93	87.80	9.89	86.84	9.96	88.61
25-3	1291	14.18	9.70	83.27	9.77	85.13	9.74	84.43	9.80	86.13
26-2	456	13.16	9.56	78.73	9.61	79.82	9.58	79.17	9.64	80.70
27-1	137	4.38	9.51	80.29	9.55	81.02	9.53	81.02	9.55	81.02
28-0	34	14.71	9.12	70.59	9.15	73.53	9.12	70.59	9.15	73.53

Study 8J21   Main

Top   Positional Advantage

Slam in Notrump

The following tables show the positional advantage of declaring 6 NT for partnerships of 29-35 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which may be of concern at matchpoint scoring, and (2) the percent of cases 6 NT makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

A curious observation is that the percent of sided cases (choice of declarer matters) peaks at 13.91 percent with 28 HCP then drops quite abruptly to only 0.52 percent with 35 HCP. Apparently, the super abundance of HCP leaves fewer weak spots and fewer resources for the opponents to avail an attack. Hence, declarer position is less important for slam bidding than for game — a concept that seems strange, since we tend to remember most the wrong-sided slams over the years.

29 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	270551	13.68	10.70	25.60	10.72	26.15	10.72	26.26	10.80	28.24
15-14	53370	13.93	10.75	27.13	10.76	27.34	10.78	27.86	10.86	30.07
16-13	50333	14.12	10.73	26.63	10.74	26.90	10.76	27.26	10.84	29.49
17-12	44529	13.78	10.72	26.22	10.73	26.62	10.74	26.86	10.82	28.96
18-11	37322	13.66	10.71	25.58	10.73	26.17	10.73	26.15	10.81	28.21
19-10	29247	13.57	10.69	25.32	10.73	26.39	10.72	26.19	10.80	27.97
20-9	21386	13.24	10.66	24.28	10.70	25.24	10.69	24.94	10.76	26.73
21-8	14669	13.22	10.62	23.39	10.67	24.41	10.65	24.10	10.72	25.54
22-7	9168	12.99	10.58	22.33	10.63	23.10	10.61	22.75	10.68	24.09
23-6	5396	13.03	10.54	21.78	10.59	22.79	10.56	22.15	10.63	23.41
24-5	2867	12.07	10.47	19.15	10.53	20.20	10.49	19.99	10.55	20.72
25-4	1359	12.21	10.31	16.34	10.37	17.59	10.34	16.92	10.40	17.81
26-3	587	11.58	10.19	13.80	10.23	14.48	10.21	14.48	10.27	14.65
27-2	223	9.87	10.06	14.80	10.14	16.14	10.12	15.70	10.15	16.14
28-1	74	10.81	10.05	16.22	10.11	16.22	10.07	16.22	10.11	16.22
29-0	21	9.52	9.57	4.76	9.71	4.76	9.67	4.76	9.71	4.76

30 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	176404	12.46	11.19	42.48	11.21	43.21	11.21	43.36	11.28	46.02
15-15	17377	12.79	11.21	43.21	11.21	43.21	11.23	43.85	11.30	46.84
16-14	33809	12.63	11.22	43.59	11.23	43.96	11.24	44.58	11.31	47.40
17-13	31025	12.86	11.21	43.63	11.23	44.11	11.24	44.47	11.31	47.41
18-12	26662	12.91	11.22	43.74	11.23	44.62	11.24	44.64	11.31	47.54
19-11	21625	12.24	11.19	42.62	11.22	43.54	11.22	43.53	11.28	45.99
20-10	16655	11.82	11.18	41.87	11.21	42.82	11.20	42.54	11.27	45.06
21-9	11711	11.92	11.15	41.12	11.19	42.30	11.18	42.15	11.24	44.32
22-8	7756	12.07	11.11	40.02	11.15	41.48	11.13	40.86	11.20	43.18
23-7	4714	11.90	11.04	37.38	11.09	39.01	11.07	38.61	11.14	40.37
24-6	2645	10.89	10.98	33.88	11.03	35.95	11.00	35.05	11.07	36.94
25-5	1348	10.68	10.95	31.82	11.02	33.38	10.98	32.34	11.04	34.05
26-4	664	10.69	10.80	28.16	10.85	29.82	10.83	29.37	10.87	30.12
27-3	297	13.47	10.68	28.62	10.76	29.29	10.71	28.96	10.80	29.63
28-2	77	6.49	10.61	24.68	10.75	25.97	10.74	25.97	10.75	25.97
29-1	30	10.00	10.20	10.00	10.20	10.00	10.20	10.00	10.20	10.00

31 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	109661	10.18	11.63	61.87	11.65	62.73	11.65	62.76	11.71	65.63
16-15	21371	10.12	11.66	63.25	11.67	63.37	11.68	63.98	11.73	66.97
17-14	20189	10.23	11.66	63.03	11.67	63.56	11.68	64.05	11.74	67.07
18-13	17983	10.29	11.65	63.00	11.66	63.83	11.67	63.75	11.72	66.74
19-12	14841	10.50	11.63	62.16	11.65	63.26	11.66	63.40	11.71	66.20
20-11	11980	10.44	11.62	61.30	11.64	62.54	11.64	62.20	11.70	65.15
21-10	8799	9.73	11.60	61.04	11.62	62.35	11.61	61.80	11.67	64.66
22-9	5959	9.95	11.59	59.81	11.62	61.05	11.60	60.51	11.66	62.98
23-8	3847	9.67	11.57	58.18	11.61	59.86	11.59	58.96	11.64	61.66
24-7	2327	9.02	11.53	57.07	11.57	58.66	11.55	57.54	11.60	59.82
25-6	1278	10.80	11.50	54.23	11.56	56.96	11.54	55.87	11.58	57.75
26-5	624	9.94	11.36	48.56	11.42	50.80	11.38	49.84	11.43	51.44
27-4	287	10.10	11.28	48.08	11.30	50.17	11.30	49.13	11.35	51.92
28-3	116	6.90	11.27	44.83	11.30	45.69	11.29	44.83	11.31	45.69
29-2	40	7.50	11.08	40.00	11.18	42.50	11.13	42.50	11.18	42.50
30-1	17	23.53	10.41	11.76	10.65	17.65	10.59	17.65	10.65	17.65

32 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	63851	7.42	12.00	79.70	12.01	80.44	12.02	80.44	12.05	82.88
16-16	6227	7.18	12.02	80.92	12.02	80.92	12.03	81.40	12.07	83.91
17-15	12249	7.71	12.02	80.88	12.03	81.21	12.04	81.57	12.08	84.24
18-14	11006	7.41	12.02	80.50	12.03	81.09	12.03	81.27	12.07	83.73
19-13	9622	7.35	12.01	80.19	12.03	81.12	12.03	81.12	12.07	83.40
20-12	7789	7.27	11.99	79.15	12.01	80.10	12.01	79.93	12.05	82.33
21-11	6003	7.98	11.99	79.39	12.01	80.89	12.01	80.51	12.05	83.06
22-10	4270	7.26	11.99	79.18	12.00	79.81	12.00	79.65	12.04	81.99
23-9	2962	7.22	11.97	77.45	11.99	78.53	11.98	77.92	12.01	80.18
24-8	1768	7.47	11.92	76.07	11.95	77.71	11.94	76.81	11.98	79.30
25-7	989	5.36	11.91	75.83	11.93	77.05	11.91	76.04	11.95	78.26
26-6	555	7.03	11.86	71.71	11.90	73.69	11.90	73.15	11.92	74.23
27-5	242	7.02	11.76	68.18	11.78	69.42	11.76	68.60	11.79	70.66
28-4	108	9.26	11.69	66.67	11.69	67.59	11.70	67.59	11.74	68.52
29-3	40	10.00	11.50	52.50	11.53	55.00	11.50	52.50	11.53	55.00
30-2	13	7.69	11.31	38.46	11.38	46.15	11.38	46.15	11.38	46.15

33 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	35128	3.90	12.31	91.96	12.32	92.31	12.32	92.32	12.34	93.61
17-16	6921	3.99	12.31	91.95	12.31	92.23	12.32	92.52	12.34	93.84
18-15	6335	3.77	12.32	92.85	12.32	92.99	12.32	92.99	12.34	94.38
19-14	5718	4.02	12.31	92.24	12.32	92.32	12.32	92.62	12.34	93.90
20-13	4825	3.98	12.33	92.41	12.33	92.99	12.33	92.85	12.35	94.07
21-12	3773	4.03	12.29	91.97	12.30	92.68	12.30	92.55	12.32	93.88
22-11	2759	3.95	12.33	92.03	12.33	92.42	12.34	92.28	12.35	93.48
23-10	1954	3.53	12.32	90.89	12.32	90.89	12.32	90.63	12.34	92.07
24-9	1229	3.74	12.28	89.83	12.28	89.99	12.28	89.99	12.29	90.97
25-8	784	3.44	12.25	89.03	12.28	90.69	12.26	90.05	12.28	91.07
26-7	445	3.15	12.27	90.56	12.28	91.01	12.28	90.34	12.29	91.24
27-6	196	4.08	12.23	91.33	12.26	92.86	12.21	91.33	12.27	93.37
28-5	123	4.88	12.15	82.93	12.18	84.55	12.18	84.55	12.19	84.55
29-4	41	0.00	12.12	87.80	12.12	87.80	12.12	87.80	12.12	87.80
30-3	20	15.00	11.80	70.00	11.80	70.00	11.75	65.00	11.80	70.00

34 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	17303	1.34	12.56	97.85	12.56	97.87	12.56	97.90	12.56	98.25
17-17	1656	1.39	12.58	97.89	12.58	97.89	12.58	97.89	12.58	98.31
18-16	3247	1.36	12.57	98.12	12.57	97.87	12.57	98.09	12.58	98.58
19-15	2993	0.94	12.57	98.36	12.57	98.23	12.57	98.40	12.58	98.60
20-14	2648	1.55	12.56	98.07	12.56	98.26	12.56	98.07	12.57	98.60
21-13	2144	1.03	12.55	97.57	12.56	97.71	12.55	97.67	12.56	97.95
22-12	1566	1.21	12.56	98.21	12.56	98.21	12.56	98.21	12.57	98.47
23-11	1203	1.66	12.52	97.09	12.53	97.34	12.53	97.26	12.53	97.59
24-10	759	1.71	12.53	98.29	12.53	98.42	12.53	98.42	12.54	98.68
25-9	502	1.99	12.52	96.22	12.53	96.61	12.52	96.41	12.53	96.81
26-8	288	1.04	12.52	96.53	12.52	96.53	12.52	96.53	12.52	96.53
27-7	169	2.96	12.53	95.27	12.53	96.45	12.53	95.86	12.54	96.45
28-6	71	4.23	12.35	91.55	12.34	91.55	12.37	92.96	12.37	92.96
29-5	38	2.63	12.55	100.00	12.58	100.00	12.58	100.00	12.58	100.00
30-4	12	0.00	11.92	83.33	11.92	83.33	11.92	83.33	11.92	83.33

35 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	7930	0.52	12.74	99.53	12.75	99.63	12.74	99.57	12.75	99.70
18-17	1536	0.46	12.76	99.80	12.76	99.93	12.76	99.80	12.76	99.93
19-16	1482	0.47	12.75	99.33	12.75	99.39	12.75	99.39	12.75	99.46
20-15	1235	0.24	12.75	99.60	12.75	99.76	12.75	99.68	12.75	99.76
21-14	995	0.90	12.74	99.30	12.74	99.40	12.74	99.40	12.75	99.70
22-13	843	0.71	12.74	99.53	12.74	99.64	12.73	99.53	12.74	99.64
23-12	683	0.00	12.77	99.85	12.77	99.85	12.77	99.85	12.77	99.85
24-11	459	0.22	12.73	99.56	12.73	99.56	12.73	99.56	12.73	99.56
25-10	307	0.98	12.69	99.67	12.69	99.67	12.69	99.67	12.69	100.00
26-9	205	0.98	12.70	99.02	12.71	99.02	12.71	99.02	12.71	99.02
27-8	97	2.06	12.67	97.94	12.67	98.97	12.66	97.94	12.68	98.97
28-7	49	2.04	12.80	100.00	12.80	100.00	12.80	100.00	12.82	100.00
29-6	31	0.00	12.65	100.00	12.65	100.00	12.65	100.00	12.65	100.00

HCP divisions with little data (fewer than 10 cases) are not shown.

Study 8J21   Main

Top   Positional Advantage

Game in a Major

The following tables show the positional advantage of declaring four of a major for partnerships of 21-28 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which is the main concern at matchpoint scoring, and (2) the percent of cases four of a major makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

Unlike the 3 NT scenario, the tamer hand is not the preferred declarer for game in a major. The stronger hand has a greater advantage for all HCP and splits, barring a few narrow exceptions. The stats run pretty close, however, so there’s little to gain or lose either way.

The percent of sided cases (choice of declarer matters) is much lower for suit contracts than at notrump, peaking at only 8.56 percent (27-28 HCP) versus 13.91 percent for 3 NT. Therefore, seeking to right-side suit contracts is less important, suggesting a rule of golf, “Play ‘em where they lie.”

Note that for the same HCP content, make percents are much higher for major-suit games than for 3 NT. This is because distributional factors are almost always present, sometimes extremely so, creating games out of thin air. Let this be a warning to anyone who evaluates a bridge hand by HCP alone. Distributional points must always be considered to bid accurately in a point-count system. Or as most experts would agree, shape rules as the greatest incentive to be aggressive.

Another difference is that the impact of apportionment is only slight. For instance, with 24 HCP your chance of making four of a major (assuming a fixed declarer) is 68.25 percent if the HCP are split 12-12, and 64.04 percent if the HCP are split 21-3. Quite a difference! A drop of only 4 percent, versus 15 in 3 NT. No doubt this is because ruffing ability often provides the needed communication.

21 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1498047	6.51	8.94	30.50	8.95	30.71	8.94	30.54	8.97	31.31
11-10	331572	6.37	8.96	31.08	8.96	31.13	8.96	31.10	8.99	31.92
12-9	304817	6.47	8.95	30.59	8.95	30.74	8.95	30.61	8.98	31.42
13-8	264684	6.48	8.96	30.89	8.97	31.11	8.96	30.91	8.99	31.72
14-7	214039	6.48	8.94	30.53	8.95	30.78	8.94	30.57	8.98	31.34
15-6	152238	6.64	8.93	30.04	8.94	30.40	8.93	30.12	8.96	30.85
16-5	104502	6.58	8.92	29.76	8.93	30.12	8.92	29.82	8.95	30.55
17-4	65522	6.87	8.90	29.52	8.92	29.94	8.91	29.59	8.94	30.28
18-3	35226	6.83	8.87	28.63	8.89	29.08	8.87	28.70	8.90	29.38
19-2	15712	7.05	8.86	28.45	8.88	28.90	8.86	28.53	8.89	29.19
20-1	7159	7.38	8.85	28.19	8.88	28.72	8.85	28.36	8.89	28.83
21-0	2576	6.48	8.86	28.65	8.89	29.00	8.86	28.73	8.89	29.08

22 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1405943	6.87	9.29	41.55	9.30	41.83	9.29	41.60	9.33	42.66
11-11	154954	6.83	9.31	42.27	9.31	42.27	9.31	42.27	9.35	43.41
12-10	296533	6.70	9.31	42.09	9.31	42.19	9.31	42.14	9.34	43.20
13-9	265872	6.78	9.30	41.85	9.31	42.08	9.30	41.91	9.33	42.98
14-8	222797	6.91	9.30	41.86	9.31	42.16	9.30	41.89	9.34	42.94
15-7	173094	6.97	9.29	41.40	9.30	41.86	9.29	41.49	9.33	42.56
16-6	120531	7.12	9.27	40.72	9.29	41.16	9.27	40.79	9.31	41.80
17-5	80004	6.93	9.26	40.36	9.28	41.01	9.26	40.43	9.30	41.44
18-4	48830	6.83	9.26	40.25	9.28	40.85	9.26	40.32	9.29	41.32
19-3	25447	7.50	9.22	38.69	9.24	39.29	9.22	38.95	9.25	39.76
20-2	11206	7.67	9.20	38.19	9.23	38.80	9.20	38.29	9.24	39.16
21-1	4992	7.07	9.19	37.50	9.22	38.44	9.19	37.86	9.22	38.58
22-0	1683	7.90	9.21	37.67	9.24	38.44	9.22	37.85	9.25	38.50

23 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1268504	7.29	9.64	54.36	9.65	54.73	9.64	54.45	9.68	55.76
12-11	270787	7.21	9.66	55.09	9.66	55.14	9.66	55.13	9.69	56.46
13-10	252844	7.18	9.65	54.86	9.66	55.08	9.65	54.92	9.69	56.26
14-9	219947	7.28	9.65	54.78	9.66	55.08	9.65	54.85	9.69	56.17
15-8	177426	7.26	9.65	54.52	9.66	54.94	9.65	54.56	9.68	55.91
16-7	135005	7.36	9.63	54.20	9.65	54.77	9.64	54.26	9.67	55.59
17-6	91106	7.37	9.61	53.18	9.63	53.92	9.61	53.35	9.65	54.59
18-5	58214	7.44	9.60	52.38	9.62	53.22	9.60	52.65	9.63	53.82
19-4	34191	7.70	9.59	51.97	9.61	52.83	9.59	52.27	9.63	53.40
20-3	17349	7.93	9.58	50.79	9.60	51.92	9.58	51.20	9.62	52.43
21-2	7320	7.42	9.54	50.40	9.57	51.30	9.55	50.86	9.58	51.64
22-1	3271	7.77	9.54	49.53	9.57	50.75	9.55	50.05	9.58	51.02
23-0	1044	7.28	9.52	48.18	9.56	49.43	9.53	48.95	9.56	49.52

24 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	1095315	7.72	9.99	67.66	10.00	68.08	9.99	67.74	10.03	69.22
12-12	115923	7.70	10.00	68.25	10.00	68.25	10.00	68.25	10.04	69.76
13-11	225080	7.70	10.00	68.45	10.00	68.59	10.00	68.46	10.04	69.98
14-10	203930	7.72	10.00	68.30	10.01	68.57	10.00	68.36	10.04	69.84
15-9	169936	7.69	9.99	67.64	10.00	68.14	9.99	67.76	10.03	69.27
16-8	134602	7.73	9.99	67.51	10.00	68.11	9.99	67.61	10.02	69.10
17-7	99122	7.89	9.98	67.08	9.99	67.78	9.98	67.18	10.02	68.66
18-6	64911	7.57	9.95	66.39	9.97	67.20	9.96	66.56	9.99	67.93
19-5	40076	7.77	9.94	65.74	9.97	66.61	9.95	65.92	9.98	67.24
20-4	23099	7.71	9.94	65.09	9.96	66.20	9.94	65.37	9.98	66.80
21-3	11429	7.97	9.91	64.04	9.94	65.26	9.92	64.43	9.95	65.70
22-2	4595	7.83	9.86	62.39	9.89	63.68	9.87	62.92	9.90	64.03
23-1	1996	7.92	9.87	62.78	9.92	64.78	9.89	63.68	9.92	64.88
24-0	616	7.95	9.88	63.31	9.93	65.26	9.90	64.29	9.93	65.42

25 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	906979	8.17	10.32	79.36	10.33	79.73	10.32	79.41	10.36	80.85
13-12	187674	8.30	10.33	79.66	10.33	79.73	10.33	79.70	10.37	81.13
14-11	178636	8.13	10.34	79.96	10.34	80.14	10.34	79.98	10.38	81.39
15-10	153887	8.02	10.33	79.79	10.34	80.07	10.33	79.78	10.37	81.23
16-9	125672	8.19	10.32	79.42	10.33	79.85	10.32	79.46	10.36	80.92
17-8	96014	8.12	10.31	79.04	10.32	79.58	10.31	79.08	10.35	80.54
18-7	69300	8.34	10.31	78.82	10.33	79.61	10.31	78.98	10.35	80.45
19-6	43583	8.12	10.28	78.21	10.30	79.04	10.28	78.29	10.32	79.79
20-5	26430	8.20	10.27	77.53	10.30	78.41	10.28	77.69	10.31	79.13
21-4	14546	7.93	10.27	77.90	10.30	78.83	10.28	77.97	10.31	79.41
22-3	6997	8.27	10.23	75.65	10.25	76.76	10.23	75.82	10.27	77.49
23-2	2822	8.04	10.17	74.45	10.20	75.66	10.18	74.81	10.21	76.26
24-1	1105	6.70	10.16	72.49	10.20	74.30	10.18	73.21	10.20	74.39
25-0	313	8.31	10.28	75.08	10.31	76.68	10.28	75.72	10.32	77.32

26 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	718659	8.42	10.64	88.34	10.65	88.61	10.65	88.38	10.69	89.49
13-13	74343	8.39	10.65	88.53	10.65	88.53	10.65	88.52	10.69	89.59
14-12	144238	8.44	10.66	88.61	10.66	88.68	10.66	88.62	10.70	89.73
15-11	130183	8.51	10.66	88.57	10.67	88.75	10.66	88.65	10.70	89.71
16-10	112007	8.34	10.64	88.55	10.65	88.80	10.65	88.58	10.69	89.66
17-9	87803	8.36	10.64	88.26	10.65	88.63	10.64	88.34	10.68	89.43
18-8	65401	8.24	10.63	88.17	10.65	88.60	10.64	88.18	10.68	89.35
19-7	45070	8.56	10.63	87.89	10.65	88.40	10.63	87.94	10.67	89.10
20-6	28093	8.50	10.61	87.58	10.63	88.31	10.61	87.64	10.65	88.90
21-5	16485	8.49	10.62	87.52	10.64	88.15	10.62	87.50	10.66	88.63
22-4	8638	8.52	10.59	86.84	10.61	87.71	10.59	87.01	10.63	88.23
23-3	4051	8.64	10.56	85.63	10.59	86.60	10.56	85.49	10.60	86.79
24-2	1563	8.51	10.55	84.33	10.58	85.35	10.56	84.64	10.59	85.73
25-1	615	10.08	10.53	85.04	10.58	86.34	10.54	84.88	10.59	86.50
26-0	169	5.33	10.64	85.80	10.66	86.98	10.64	85.80	10.66	86.98

27 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	543485	8.56	10.96	94.00	10.97	94.19	10.96	94.04	11.00	94.80
14-13	110868	8.57	10.97	94.14	10.97	94.19	10.97	94.17	11.02	94.92
15-12	102828	8.45	10.96	94.06	10.97	94.16	10.96	94.11	11.00	94.86
16-11	91400	8.77	10.97	94.19	10.97	94.32	10.97	94.25	11.01	94.99
17-10	75933	8.58	10.96	94.08	10.98	94.31	10.97	94.09	11.01	94.83
18-9	57677	8.55	10.95	94.05	10.97	94.26	10.95	94.03	11.00	94.82
19-8	41400	8.40	10.94	93.93	10.96	94.24	10.94	93.93	10.98	94.72
20-7	28026	8.46	10.94	93.64	10.96	94.08	10.94	93.67	10.98	94.46
21-6	17186	8.62	10.92	93.40	10.94	93.87	10.92	93.55	10.96	94.32
22-5	9664	8.36	10.90	93.09	10.93	93.78	10.91	93.25	10.95	94.06
23-4	4959	8.55	10.88	92.44	10.91	93.24	10.89	92.72	10.92	93.57
24-3	2295	7.89	10.84	91.98	10.87	92.55	10.85	92.29	10.88	92.94
25-2	879	11.95	10.80	91.92	10.85	92.83	10.81	91.24	10.86	93.29
26-1	286	6.99	10.83	90.56	10.86	91.61	10.84	91.26	10.86	91.96
27-0	84	3.57	11.00	96.43	11.02	97.62	11.02	97.62	11.04	97.62

28 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	390598	8.56	11.26	97.22	11.26	97.28	11.26	97.20	11.30	97.65
14-14	40131	8.64	11.27	97.29	11.27	97.29	11.27	97.22	11.31	97.67
15-13	76643	8.57	11.27	97.30	11.27	97.32	11.27	97.33	11.31	97.71
16-12	69152	8.61	11.26	97.30	11.27	97.30	11.26	97.28	11.31	97.70
17-11	59882	8.79	11.26	97.24	11.27	97.28	11.26	97.21	11.31	97.70
18-10	48212	8.50	11.26	97.28	11.27	97.39	11.26	97.24	11.31	97.71
19-9	35523	8.46	11.24	97.08	11.25	97.18	11.24	97.06	11.28	97.55
20-8	25359	8.25	11.24	97.02	11.26	97.23	11.24	97.07	11.28	97.50
21-7	16249	8.39	11.25	97.32	11.27	97.51	11.25	97.27	11.29	97.78
22-6	9496	8.57	11.21	96.68	11.24	96.94	11.22	96.67	11.26	97.27
23-5	5382	8.36	11.19	96.84	11.21	97.08	11.19	96.86	11.23	97.31
24-4	2744	7.58	11.21	96.43	11.24	96.68	11.22	96.50	11.25	97.05
25-3	1227	8.31	11.18	96.17	11.21	96.50	11.19	95.84	11.22	96.74
26-2	431	9.05	11.15	96.29	11.19	97.22	11.16	96.75	11.20	97.22
27-1	133	6.02	11.13	96.99	11.12	96.99	11.11	96.99	11.14	96.99
28-0	34	5.88	11.18	100.00	11.21	100.00	11.21	100.00	11.21	100.00

Study 8J21   Main

Top   Positional Advantage

Slam in a Suit

The following tables show the positional advantage of declaring six of a suit for partnerships of 29-35 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which may be of concern at matchpoint scoring, and (2) the percent of cases six of a suit makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

Stats for declaring six of a suit are pretty much as would be expected. The importance of sided consideration is reduced (as with 6 NT) and dwindles rapidly as the HCP total increases. Like major-suit games, the stronger hand is a better declarer choice than the tamer, high-card apportionment matters little, and make percents run high because of the likely distributional factors. Bid ‘em up!

29 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	270045	8.14	11.54	53.25	11.55	53.77	11.54	53.39	11.58	55.59
15-14	53650	8.15	11.55	54.15	11.56	54.30	11.56	54.30	11.60	56.50
16-13	50668	8.38	11.55	53.85	11.55	54.06	11.55	53.84	11.59	56.23
17-12	44512	8.06	11.54	52.94	11.55	53.50	11.54	53.15	11.58	55.40
18-11	37136	8.29	11.54	53.23	11.55	53.76	11.54	53.29	11.58	55.56
19-10	29159	8.09	11.54	53.35	11.56	54.17	11.55	53.58	11.58	55.76
20-9	21198	7.82	11.53	52.67	11.54	53.61	11.53	52.91	11.57	54.94
21-8	14531	8.18	11.52	52.07	11.54	52.99	11.52	52.21	11.56	54.28
22-7	8969	8.12	11.50	51.21	11.52	52.15	11.50	51.38	11.54	53.36
23-6	5289	7.75	11.51	51.81	11.53	53.13	11.52	52.30	11.55	54.04
24-5	2793	7.16	11.49	51.38	11.52	52.67	11.50	51.81	11.53	53.28
25-4	1297	7.56	11.48	51.12	11.50	52.58	11.49	51.81	11.52	53.12
26-3	554	5.96	11.40	48.19	11.42	49.10	11.41	48.56	11.43	49.28
27-2	205	10.73	11.38	45.37	11.41	46.83	11.40	46.34	11.43	47.32
28-1	65	3.08	11.52	47.69	11.54	47.69	11.51	47.69	11.54	47.69
29-0	19	5.26	11.47	57.89	11.53	57.89	11.53	57.89	11.53	57.89

30 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	174457	7.43	11.81	66.98	11.82	67.47	11.81	67.05	11.85	69.42
15-15	17251	7.23	11.81	66.80	11.81	66.80	11.81	66.66	11.85	69.14
16-14	33857	7.35	11.82	67.30	11.82	67.50	11.82	67.37	11.86	69.76
17-13	30834	7.70	11.82	67.31	11.82	67.61	11.82	67.35	11.86	69.88
18-12	26416	7.45	11.82	67.48	11.82	68.05	11.82	67.49	11.85	69.97
19-11	21280	7.63	11.81	67.14	11.81	67.79	11.81	67.21	11.84	69.59
20-10	16402	7.07	11.81	66.94	11.82	67.65	11.81	67.10	11.85	69.21
21-9	11362	7.23	11.80	66.69	11.82	67.66	11.80	66.80	11.84	69.05
22-8	7534	7.94	11.78	65.74	11.80	66.64	11.79	65.90	11.82	68.37
23-7	4650	7.05	11.80	66.67	11.82	67.53	11.81	66.99	11.84	68.80
24-6	2578	7.56	11.74	63.34	11.76	64.62	11.75	63.73	11.78	65.71
25-5	1267	6.95	11.76	64.01	11.78	65.11	11.78	64.56	11.80	66.14
26-4	636	7.39	11.73	61.16	11.75	62.74	11.73	61.16	11.76	63.52
27-3	283	8.13	11.71	59.72	11.74	62.19	11.71	60.07	11.76	62.90
28-2	71	7.04	11.68	61.97	11.70	63.38	11.68	63.38	11.70	63.38
29-1	28	3.57	11.68	57.14	11.68	57.14	11.68	57.14	11.68	57.14

31 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	107553	6.14	12.05	78.83	12.06	79.26	12.06	78.89	12.09	80.96
16-15	21111	6.23	12.06	79.05	12.06	79.12	12.06	79.06	12.09	81.14
17-14	19888	6.09	12.07	79.17	12.07	79.44	12.07	79.27	12.10	81.36
18-13	17696	6.17	12.06	79.27	12.06	79.60	12.06	79.30	12.09	81.43
19-12	14559	6.36	12.05	78.49	12.05	79.05	12.05	78.71	12.08	80.75
20-11	11676	6.15	12.05	78.49	12.06	79.14	12.05	78.55	12.08	80.68
21-10	8649	6.02	12.04	78.48	12.05	79.19	12.04	78.44	12.07	80.54
22-9	5824	6.15	12.05	78.88	12.06	79.74	12.05	78.76	12.08	80.98
23-8	3743	5.72	12.04	78.31	12.06	79.24	12.04	78.41	12.07	80.26
24-7	2227	5.84	12.04	78.13	12.05	78.58	12.04	78.13	12.07	79.61
25-6	1191	5.71	12.04	78.93	12.05	79.60	12.04	78.84	12.07	80.18
26-5	572	5.42	11.95	73.78	11.98	74.83	11.96	73.95	11.98	75.35
27-4	260	5.38	11.98	77.31	11.99	78.46	11.98	77.31	12.01	79.23
28-3	100	6.00	12.15	83.00	12.19	86.00	12.17	84.00	12.20	86.00
29-2	39	5.13	11.79	69.23	11.82	71.79	11.85	71.79	11.85	71.79
30-1	15	13.33	11.53	46.67	11.67	53.33	11.60	46.67	11.67	53.33

32 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	62195	5.09	12.27	87.78	12.27	88.10	12.27	87.78	12.29	89.36
16-16	6151	5.23	12.27	87.53	12.27	87.53	12.27	87.51	12.29	89.06
17-15	12086	5.03	12.28	88.25	12.28	88.50	12.28	88.20	12.30	90.00
18-14	10799	4.69	12.28	87.92	12.28	88.15	12.28	87.95	12.30	89.42
19-13	9352	5.07	12.27	88.01	12.27	88.16	12.27	87.95	12.30	89.48
20-12	7588	5.05	12.27	87.26	12.27	87.60	12.26	87.19	12.29	88.72
21-11	5810	5.52	12.26	87.57	12.27	88.23	12.26	87.78	12.29	89.33
22-10	4082	5.32	12.26	88.05	12.27	88.46	12.26	87.95	12.28	89.64
23-9	2790	5.05	12.26	87.74	12.27	87.99	12.26	87.56	12.28	89.00
24-8	1692	5.67	12.23	86.29	12.24	87.35	12.23	86.58	12.26	88.30
25-7	956	4.92	12.27	88.81	12.28	89.85	12.26	88.70	12.29	90.48
26-6	504	6.55	12.20	85.91	12.22	87.50	12.21	87.10	12.23	88.29
27-5	230	4.78	12.20	86.96	12.20	87.83	12.20	86.96	12.22	87.83
28-4	96	5.21	12.25	86.46	12.26	87.50	12.24	86.46	12.27	87.50
29-3	40	2.50	12.20	82.50	12.20	82.50	12.20	82.50	12.20	82.50
30-2	11	0.00	11.91	54.55	11.91	54.55	11.91	54.55	11.91	54.55

33 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	33685	3.70	12.47	93.57	12.47	93.78	12.47	93.68	12.49	94.48
17-16	6598	3.82	12.47	93.50	12.47	93.59	12.47	93.60	12.49	94.39
18-15	6125	3.18	12.48	94.27	12.48	94.42	12.48	94.22	12.49	95.05
19-14	5503	3.42	12.46	93.28	12.46	93.51	12.46	93.48	12.47	94.15
20-13	4617	3.68	12.46	93.52	12.47	93.65	12.47	93.65	12.48	94.41
21-12	3620	3.87	12.46	93.43	12.46	93.70	12.46	93.65	12.47	94.56
22-11	2669	3.78	12.48	93.59	12.49	93.93	12.49	93.97	12.50	94.79
23-10	1859	4.57	12.49	93.11	12.49	93.33	12.49	93.01	12.51	93.92
24-9	1186	3.63	12.46	93.51	12.46	93.51	12.46	93.17	12.48	94.01
25-8	737	4.48	12.45	94.17	12.47	94.98	12.46	94.44	12.47	95.12
26-7	417	4.80	12.44	92.09	12.44	92.57	12.44	92.09	12.46	93.29
27-6	184	4.89	12.44	93.48	12.46	94.57	12.44	92.93	12.47	94.57
28-5	110	5.45	12.49	91.82	12.51	93.64	12.51	93.64	12.53	94.55
29-4	37	0.00	12.46	94.59	12.46	94.59	12.46	94.59	12.46	94.59
30-3	19	15.79	12.16	89.47	12.21	89.47	12.16	84.21	12.21	89.47

34 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	16483	2.61	12.63	96.78	12.63	96.81	12.63	96.77	12.64	97.17
17-17	1606	2.68	12.64	97.20	12.64	97.20	12.64	97.32	12.65	97.51
18-16	3093	2.72	12.64	96.93	12.64	96.77	12.64	96.86	12.65	97.22
19-15	2850	2.21	12.64	97.05	12.64	96.88	12.64	96.88	12.65	97.23
20-14	2539	3.35	12.62	96.46	12.63	96.57	12.62	96.22	12.64	97.12
21-13	2037	2.99	12.61	96.37	12.62	96.61	12.62	96.37	12.63	96.81
22-12	1510	2.25	12.63	97.09	12.63	97.09	12.63	97.22	12.64	97.42
23-11	1124	2.49	12.61	96.62	12.62	96.89	12.62	96.89	12.63	97.15
24-10	707	1.56	12.65	96.46	12.66	96.75	12.66	96.89	12.66	97.17
25-9	469	2.77	12.60	95.95	12.60	96.38	12.60	96.16	12.61	96.38
26-8	269	1.49	12.65	97.40	12.65	97.40	12.65	97.40	12.67	97.40
27-7	154	2.60	12.66	97.40	12.66	98.05	12.67	98.05	12.67	98.05
28-6	70	0.00	12.53	94.29	12.53	94.29	12.53	94.29	12.53	94.29
29-5	37	2.70	12.65	100.00	12.68	100.00	12.68	100.00	12.68	100.00
30-4	11	0.00	12.55	90.91	12.55	90.91	12.55	90.91	12.55	90.91

35 HCP	Cases	Sided	Fixed		Stronger		Tamer		Utopian
All ways	7452	2.28	12.75	98.32	12.76	98.36	12.76	98.42	12.77	98.64
18-17	1460	2.33	12.77	98.90	12.78	99.04	12.78	98.90	12.79	99.18
19-16	1408	2.56	12.74	97.94	12.74	97.80	12.74	97.94	12.75	98.22
20-15	1181	2.20	12.75	98.31	12.76	98.39	12.76	98.31	12.76	98.48
21-14	950	2.53	12.76	98.00	12.75	98.00	12.75	98.21	12.77	98.53
22-13	776	3.09	12.78	98.84	12.78	98.97	12.78	99.10	12.80	99.36
23-12	624	1.76	12.76	98.40	12.76	98.24	12.76	98.56	12.77	98.56
24-11	420	1.19	12.71	98.57	12.71	98.57	12.71	98.57	12.72	98.81
25-10	281	1.07	12.74	97.86	12.75	98.22	12.74	97.86	12.75	98.22
26-9	187	1.60	12.75	96.26	12.76	96.79	12.76	97.33	12.77	97.33
27-8	86	3.49	12.74	97.67	12.76	97.67	12.76	97.67	12.76	97.67
28-7	44	0.00	12.82	100.00	12.82	100.00	12.82	100.00	12.82	100.00
29-6	27	3.70	12.63	96.30	12.63	96.30	12.67	96.30	12.67	96.30

HCP divisions with little data (fewer than 10 cases) are not shown.

Study 8J21   Main

Top   Positional Advantage

Honor Holdings

I thought it would be interesting to examine the specific honor holdings in each case that was sided (choice of declarer matters). The data source seems large enough for this to provide a meaningful ranking of the positional value of each holding. More specifically, the frequency in which a holding appears in the optimal declaring hand would be a grading scale; the more frequent, the greater its positional value.

I decided to limit the scope to notrump cases, not only because positional values are more prominent there but to eliminate ruffing ability as a factor. A suit contract is sometimes right-sided because the opening leader cannot deliver a ruff, which is irrelevant to this issue.

Doubletons and tripletons are the obvious candidates. Singleton honors may have positional value in actual play but not at double-dummy. On this farm, you can run but you can’t hide; bid 3 NT with a stiff king, and the ace will be led every time. Honors in 4+ card suits also have positional value, but it’s less crucial, and the ranking would almost surely mirror the 3-card holdings.

The following table lists each doubleton or tripleton honor holding. Occurrence is the number of times the holding appeared in sided notrump contracts. Declarer shows the percent of time the holding was in the hand of the optimal declarer.

Holding	Occurrence	Declarer
A-Q	41826	79.05
K-10	26458	73.49
A-J	28495	72.64
K-x	215485	71.98
A-Q-10	14474	70.84
A-J-x	106624	70.20
K-J	25529	69.55
A-Q-x	114424	68.89
K-J-x	91113	68.48
A-10	25104	68.19
A-J-10	11518	66.10
A-K-10	13474	65.40
K-10-x	77233	63.90
A-K-J	13951	63.74
A-Q-J	13181	62.80
K-x-x	274144	62.20
Q-x-x	251854	61.75
K-J-10	9636	61.19
Q-x	181145	60.18
K-Q-x	85845	60.06
Q-10-x	63275	59.84
A-10-x	71056	59.10
K-Q-10	10590	59.10
Q-10	20362	55.43
K-Q	19371	55.27
A-K-x	89949	55.08
Q-J-x	65779	54.66
A-K	22962	54.48
A-x	210591	54.16
K-Q-J	9823	50.74
A-K-Q	12300	49.61
J-x	121731	49.47
J-x-x	175518	48.79
A-x-x	241120	48.68
Q-J-10	7256	47.97
Q-J	18688	45.37
J-10	14255	43.95
J-10-x	51873	42.28
10-x-x	141225	40.54
10-x	116680	38.31
x-x-x	284195	37.41
x-x	432237	33.43

For the most part the list flows as expected, save a few oddball results. Why would A-K and K-Q doubleton appear significantly more often in the optimal declaring hand? Strange, since the only possible positional advantage would be if the opening leader were void, which seems too remote to account for the percentage. This prompted me to recheck the numbers via different software, but the results were the same. Something to think about, though I’ll pass on examining 40,000+ deals individually.

[Addendum] I think I understand the above anomaly. If one hand has A-K or K-Q doubleton, that suit is eliminated from having positional value in either hand (barring voids). The hand with A-K or K-Q doubleton has 11 available spaces for positional holdings in the other suits. The opposite hand, however, rates to have 3+ cards (3.67 on average) facing the A-K or K-Q doubleton, hence fewer available spaces for positional holdings in the other suits.

Study 8J21   Main

Top   Positional Advantage

© 2014 Richard Pavlicek