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 1,456,537 8.91 6.55 5.13 6.57 5.22 6.57 5.30 6.61 5.63
11-10 320,931 8.95 6.61 5.80 6.62 5.81 6.63 5.97 6.67 6.34
12-9 295,450 8.94 6.60 5.64 6.61 5.70 6.61 5.84 6.65 6.19
13-8 256,541 8.87 6.59 5.37 6.60 5.48 6.60 5.56 6.64 5.91
14-7 208,253 8.96 6.56 5.12 6.58 5.26 6.58 5.30 6.61 5.62
15-6 148,656 8.96 6.51 4.52 6.53 4.67 6.53 4.70 6.57 4.99
16-5 102,116 8.77 6.46 4.06 6.48 4.21 6.47 4.20 6.51 4.47
17-4 64,619 8.85 6.41 3.66 6.44 3.80 6.43 3.76 6.47 4.01
18-3 34,686 8.68 6.32 3.19 6.35 3.36 6.34 3.32 6.37 3.48
19-2 15,586 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

21 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,456,537	8.91	6.55	5.13	6.57	5.22	6.57	5.30	6.61	5.63
11-10	320,931	8.95	6.61	5.80	6.62	5.81	6.63	5.97	6.67	6.34
12-9	295,450	8.94	6.60	5.64	6.61	5.70	6.61	5.84	6.65	6.19
13-8	256,541	8.87	6.59	5.37	6.60	5.48	6.60	5.56	6.64	5.91
14-7	208,253	8.96	6.56	5.12	6.58	5.26	6.58	5.30	6.61	5.62
15-6	148,656	8.96	6.51	4.52	6.53	4.67	6.53	4.70	6.57	4.99
16-5	102,116	8.77	6.46	4.06	6.48	4.21	6.47	4.20	6.51	4.47
17-4	64,619	8.85	6.41	3.66	6.44	3.80	6.43	3.76	6.47	4.01
18-3	34,686	8.68	6.32	3.19	6.35	3.36	6.34	3.32	6.37	3.48
19-2	15,586	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 1,368,958 9.63 7.08 11.57 7.09 11.76 7.09 11.89 7.14 12.61
11-11 150,454 9.58 7.14 12.95 7.14 12.95 7.16 13.26 7.20 14.10
12-10 287,161 9.72 7.12 12.64 7.13 12.71 7.14 12.99 7.18 13.78
13-9 257,713 9.58 7.12 12.42 7.12 12.59 7.13 12.80 7.18 13.56
14-8 217,156 9.63 7.10 11.91 7.12 12.16 7.12 12.26 7.16 13.00
15-7 168,917 9.74 7.06 11.12 7.09 11.45 7.08 11.41 7.13 12.12
16-6 117,889 9.64 7.01 10.11 7.03 10.41 7.02 10.37 7.07 11.03
17-5 78,390 9.68 6.97 9.20 6.99 9.55 6.98 9.50 7.03 10.05
18-4 48,257 9.23 6.91 8.25 6.95 8.58 6.93 8.51 6.97 8.94
19-3 25,115 9.69 6.81 7.14 6.84 7.48 6.82 7.29 6.87 7.79
20-2 11,187 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

22 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,368,958	9.63	7.08	11.57	7.09	11.76	7.09	11.89	7.14	12.61
11-11	150,454	9.58	7.14	12.95	7.14	12.95	7.16	13.26	7.20	14.10
12-10	287,161	9.72	7.12	12.64	7.13	12.71	7.14	12.99	7.18	13.78
13-9	257,713	9.58	7.12	12.42	7.12	12.59	7.13	12.80	7.18	13.56
14-8	217,156	9.63	7.10	11.91	7.12	12.16	7.12	12.26	7.16	13.00
15-7	168,917	9.74	7.06	11.12	7.09	11.45	7.08	11.41	7.13	12.12
16-6	117,889	9.64	7.01	10.11	7.03	10.41	7.02	10.37	7.07	11.03
17-5	78,390	9.68	6.97	9.20	6.99	9.55	6.98	9.50	7.03	10.05
18-4	48,257	9.23	6.91	8.25	6.95	8.58	6.93	8.51	6.97	8.94
19-3	25,115	9.69	6.81	7.14	6.84	7.48	6.82	7.29	6.87	7.79
20-2	11,187	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 1,237,217 10.37 7.59 22.44 7.60 22.81 7.61 22.96 7.66 24.21
12-11 263,598 10.43 7.65 24.32 7.65 24.41 7.67 24.85 7.71 26.19
13-10 244,935 10.44 7.63 23.93 7.64 24.15 7.65 24.49 7.70 25.78
14-9 213,485 10.41 7.62 23.43 7.63 23.80 7.64 24.00 7.69 25.28
15-8 173,296 10.30 7.60 22.75 7.62 23.24 7.62 23.29 7.67 24.56
16-7 131,906 10.37 7.56 21.40 7.58 21.97 7.58 21.92 7.63 23.12
17-6 89,446 10.32 7.50 19.53 7.53 20.14 7.52 19.99 7.57 21.15
18-5 57,500 10.36 7.46 18.21 7.50 18.92 7.48 18.65 7.53 19.75
19-4 34,131 10.18 7.40 16.40 7.44 17.20 7.42 16.80 7.46 17.85
20-3 17,290 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

23 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,237,217	10.37	7.59	22.44	7.60	22.81	7.61	22.96	7.66	24.21
12-11	263,598	10.43	7.65	24.32	7.65	24.41	7.67	24.85	7.71	26.19
13-10	244,935	10.44	7.63	23.93	7.64	24.15	7.65	24.49	7.70	25.78
14-9	213,485	10.41	7.62	23.43	7.63	23.80	7.64	24.00	7.69	25.28
15-8	173,296	10.30	7.60	22.75	7.62	23.24	7.62	23.29	7.67	24.56
16-7	131,906	10.37	7.56	21.40	7.58	21.97	7.58	21.92	7.63	23.12
17-6	89,446	10.32	7.50	19.53	7.53	20.14	7.52	19.99	7.57	21.15
18-5	57,500	10.36	7.46	18.21	7.50	18.92	7.48	18.65	7.53	19.75
19-4	34,131	10.18	7.40	16.40	7.44	17.20	7.42	16.80	7.46	17.85
20-3	17,290	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 1,070,924 11.19 8.10 37.71 8.12 38.22 8.13 38.38 8.18 40.18
12-12 112,908 11.27 8.17 40.13 8.17 40.13 8.19 40.83 8.24 42.61
13-11 219,494 11.35 8.16 40.05 8.17 40.24 8.19 40.72 8.24 42.56
14-10 198,305 11.21 8.14 39.28 8.15 39.62 8.16 39.99 8.22 41.82
15-9 165,822 11.20 8.13 38.71 8.14 39.21 8.15 39.34 8.20 41.17
16-8 131,799 11.19 8.10 37.41 8.12 38.16 8.12 38.11 8.17 39.94
17-7 97,099 11.21 8.05 35.45 8.08 36.38 8.07 36.17 8.13 37.92
18-6 64,098 10.98 8.00 33.63 8.03 34.66 8.02 34.26 8.07 36.04
19-5 39,660 10.80 7.94 31.05 7.98 32.19 7.96 31.76 8.01 33.34
20-4 23,025 10.66 7.89 28.51 7.93 29.95 7.91 29.03 7.96 30.80
21-3 11,427 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

24 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,070,924	11.19	8.10	37.71	8.12	38.22	8.13	38.38	8.18	40.18
12-12	112,908	11.27	8.17	40.13	8.17	40.13	8.19	40.83	8.24	42.61
13-11	219,494	11.35	8.16	40.05	8.17	40.24	8.19	40.72	8.24	42.56
14-10	198,305	11.21	8.14	39.28	8.15	39.62	8.16	39.99	8.22	41.82
15-9	165,822	11.20	8.13	38.71	8.14	39.21	8.15	39.34	8.20	41.17
16-8	131,799	11.19	8.10	37.41	8.12	38.16	8.12	38.11	8.17	39.94
17-7	97,099	11.21	8.05	35.45	8.08	36.38	8.07	36.17	8.13	37.92
18-6	64,098	10.98	8.00	33.63	8.03	34.66	8.02	34.26	8.07	36.04
19-5	39,660	10.80	7.94	31.05	7.98	32.19	7.96	31.76	8.01	33.34
20-4	23,025	10.66	7.89	28.51	7.93	29.95	7.91	29.03	7.96	30.80
21-3	11,427	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 889,566 12.07 8.62 54.99 8.64 55.54 8.64 55.72 8.70 57.80
13-12 183,242 12.28 8.68 57.18 8.68 57.23 8.70 57.97 8.76 60.01
14-11 174,320 12.18 8.67 57.03 8.68 57.24 8.70 57.75 8.76 59.79
15-10 150,241 12.11 8.65 56.18 8.67 56.64 8.68 56.86 8.74 58.98
16-9 123,038 12.09 8.63 55.37 8.65 56.03 8.65 56.09 8.71 58.20
17-8 94,687 11.84 8.60 54.52 8.62 55.35 8.62 55.19 8.68 57.31
18-7 68,432 11.98 8.54 52.18 8.58 53.37 8.57 52.99 8.63 55.06
19-6 43,423 11.69 8.49 49.90 8.53 51.04 8.52 50.66 8.57 52.71
20-5 26,359 11.75 8.43 47.52 8.48 49.15 8.46 48.44 8.52 50.52
21-4 14,444 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

25 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	889,566	12.07	8.62	54.99	8.64	55.54	8.64	55.72	8.70	57.80
13-12	183,242	12.28	8.68	57.18	8.68	57.23	8.70	57.97	8.76	60.01
14-11	174,320	12.18	8.67	57.03	8.68	57.24	8.70	57.75	8.76	59.79
15-10	150,241	12.11	8.65	56.18	8.67	56.64	8.68	56.86	8.74	58.98
16-9	123,038	12.09	8.63	55.37	8.65	56.03	8.65	56.09	8.71	58.20
17-8	94,687	11.84	8.60	54.52	8.62	55.35	8.62	55.19	8.68	57.31
18-7	68,432	11.98	8.54	52.18	8.58	53.37	8.57	52.99	8.63	55.06
19-6	43,423	11.69	8.49	49.90	8.53	51.04	8.52	50.66	8.57	52.71
20-5	26,359	11.75	8.43	47.52	8.48	49.15	8.46	48.44	8.52	50.52
21-4	14,444	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 707,022 12.91 9.13 70.29 9.15 70.81 9.16 70.97 9.22 72.94
13-13 72,780 12.97 9.18 71.85 9.18 71.85 9.21 72.59 9.27 74.38
14-12 141,341 13.01 9.19 71.93 9.19 72.01 9.22 72.59 9.28 74.51
15-11 127,757 12.97 9.18 71.71 9.19 71.99 9.21 72.34 9.27 74.26
16-10 109,480 13.11 9.15 70.85 9.17 71.40 9.18 71.61 9.24 73.55
17-9 86,432 12.91 9.12 70.17 9.15 70.87 9.15 70.82 9.22 72.89
18-8 64,798 12.74 9.09 69.43 9.12 70.25 9.12 70.03 9.18 72.08
19-7 44,607 12.69 9.06 68.30 9.09 69.39 9.08 68.96 9.14 70.98
20-6 28,034 12.77 8.96 65.30 9.00 66.65 8.99 66.09 9.05 68.20
21-5 16,516 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

26 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	707,022	12.91	9.13	70.29	9.15	70.81	9.16	70.97	9.22	72.94
13-13	72,780	12.97	9.18	71.85	9.18	71.85	9.21	72.59	9.27	74.38
14-12	141,341	13.01	9.19	71.93	9.19	72.01	9.22	72.59	9.28	74.51
15-11	127,757	12.97	9.18	71.71	9.19	71.99	9.21	72.34	9.27	74.26
16-10	109,480	13.11	9.15	70.85	9.17	71.40	9.18	71.61	9.24	73.55
17-9	86,432	12.91	9.12	70.17	9.15	70.87	9.15	70.82	9.22	72.89
18-8	64,798	12.74	9.09	69.43	9.12	70.25	9.12	70.03	9.18	72.08
19-7	44,607	12.69	9.06	68.30	9.09	69.39	9.08	68.96	9.14	70.98
20-6	28,034	12.77	8.96	65.30	9.00	66.65	8.99	66.09	9.05	68.20
21-5	16,516	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 538,102 13.65 9.66 81.94 9.68 82.38 9.69 82.57 9.76 84.15
14-13 108,930 13.85 9.71 82.92 9.71 82.94 9.74 83.52 9.81 85.03
15-12 101,199 13.91 9.70 82.63 9.71 82.90 9.73 83.35 9.80 84.86
16-11 90,164 13.81 9.69 82.36 9.70 82.66 9.72 82.92 9.79 84.52
17-10 75,086 13.60 9.68 82.47 9.70 82.91 9.71 83.10 9.78 84.64
18-9 57,439 13.37 9.64 81.72 9.67 82.41 9.67 82.38 9.74 83.97
19-8 41,476 13.53 9.60 81.24 9.64 81.99 9.63 81.83 9.70 83.49
20-7 27,996 13.41 9.56 80.45 9.60 81.41 9.59 81.04 9.66 82.79
21-6 17,220 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

27 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	538,102	13.65	9.66	81.94	9.68	82.38	9.69	82.57	9.76	84.15
14-13	108,930	13.85	9.71	82.92	9.71	82.94	9.74	83.52	9.81	85.03
15-12	101,199	13.91	9.70	82.63	9.71	82.90	9.73	83.35	9.80	84.86
16-11	90,164	13.81	9.69	82.36	9.70	82.66	9.72	82.92	9.79	84.52
17-10	75,086	13.60	9.68	82.47	9.70	82.91	9.71	83.10	9.78	84.64
18-9	57,439	13.37	9.64	81.72	9.67	82.41	9.67	82.38	9.74	83.97
19-8	41,476	13.53	9.60	81.24	9.64	81.99	9.63	81.83	9.70	83.49
20-7	27,996	13.41	9.56	80.45	9.60	81.41	9.59	81.04	9.66	82.79
21-6	17,220	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 388,219 13.91 10.18 89.42 10.20 89.76 10.21 89.92 10.28 91.04
14-14 39,633 14.14 10.24 90.06 10.24 90.06 10.27 90.50 10.35 91.57
15-13 75,770 14.01 10.23 89.93 10.24 90.05 10.26 90.37 10.33 91.45
16-12 68,675 14.12 10.21 89.61 10.22 89.80 10.24 90.13 10.32 91.21
17-11 59,049 13.92 10.20 89.77 10.22 90.03 10.23 90.37 10.31 91.33
18-10 47,960 13.84 10.19 89.46 10.22 89.96 10.21 89.95 10.29 91.11
19-9 35,485 14.16 10.14 88.91 10.18 89.54 10.17 89.49 10.25 90.74
20-8 25,331 13.27 10.12 88.95 10.15 89.56 10.14 89.39 10.22 90.57
21-7 16,338 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

28 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	388,219	13.91	10.18	89.42	10.20	89.76	10.21	89.92	10.28	91.04
14-14	39,633	14.14	10.24	90.06	10.24	90.06	10.27	90.50	10.35	91.57
15-13	75,770	14.01	10.23	89.93	10.24	90.05	10.26	90.37	10.33	91.45
16-12	68,675	14.12	10.21	89.61	10.22	89.80	10.24	90.13	10.32	91.21
17-11	59,049	13.92	10.20	89.77	10.22	90.03	10.23	90.37	10.31	91.33
18-10	47,960	13.84	10.19	89.46	10.22	89.96	10.21	89.95	10.29	91.11
19-9	35,485	14.16	10.14	88.91	10.18	89.54	10.17	89.49	10.25	90.74
20-8	25,331	13.27	10.12	88.95	10.15	89.56	10.14	89.39	10.22	90.57
21-7	16,338	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 270,551 13.68 10.70 25.60 10.72 26.15 10.72 26.26 10.80 28.24
15-14 53,370 13.93 10.75 27.13 10.76 27.34 10.78 27.86 10.86 30.07
16-13 50,333 14.12 10.73 26.63 10.74 26.90 10.76 27.26 10.84 29.49
17-12 44,529 13.78 10.72 26.22 10.73 26.62 10.74 26.86 10.82 28.96
18-11 37,322 13.66 10.71 25.58 10.73 26.17 10.73 26.15 10.81 28.21
19-10 29,247 13.57 10.69 25.32 10.73 26.39 10.72 26.19 10.80 27.97
20-9 21,386 13.24 10.66 24.28 10.70 25.24 10.69 24.94 10.76 26.73
21-8 14,669 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

29 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	270,551	13.68	10.70	25.60	10.72	26.15	10.72	26.26	10.80	28.24
15-14	53,370	13.93	10.75	27.13	10.76	27.34	10.78	27.86	10.86	30.07
16-13	50,333	14.12	10.73	26.63	10.74	26.90	10.76	27.26	10.84	29.49
17-12	44,529	13.78	10.72	26.22	10.73	26.62	10.74	26.86	10.82	28.96
18-11	37,322	13.66	10.71	25.58	10.73	26.17	10.73	26.15	10.81	28.21
19-10	29,247	13.57	10.69	25.32	10.73	26.39	10.72	26.19	10.80	27.97
20-9	21,386	13.24	10.66	24.28	10.70	25.24	10.69	24.94	10.76	26.73
21-8	14,669	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 176,404 12.46 11.19 42.48 11.21 43.21 11.21 43.36 11.28 46.02
15-15 17,377 12.79 11.21 43.21 11.21 43.21 11.23 43.85 11.30 46.84
16-14 33,809 12.63 11.22 43.59 11.23 43.96 11.24 44.58 11.31 47.40
17-13 31,025 12.86 11.21 43.63 11.23 44.11 11.24 44.47 11.31 47.41
18-12 26,662 12.91 11.22 43.74 11.23 44.62 11.24 44.64 11.31 47.54
19-11 21,625 12.24 11.19 42.62 11.22 43.54 11.22 43.53 11.28 45.99
20-10 16,655 11.82 11.18 41.87 11.21 42.82 11.20 42.54 11.27 45.06
21-9 11,711 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

30 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	176,404	12.46	11.19	42.48	11.21	43.21	11.21	43.36	11.28	46.02
15-15	17,377	12.79	11.21	43.21	11.21	43.21	11.23	43.85	11.30	46.84
16-14	33,809	12.63	11.22	43.59	11.23	43.96	11.24	44.58	11.31	47.40
17-13	31,025	12.86	11.21	43.63	11.23	44.11	11.24	44.47	11.31	47.41
18-12	26,662	12.91	11.22	43.74	11.23	44.62	11.24	44.64	11.31	47.54
19-11	21,625	12.24	11.19	42.62	11.22	43.54	11.22	43.53	11.28	45.99
20-10	16,655	11.82	11.18	41.87	11.21	42.82	11.20	42.54	11.27	45.06
21-9	11,711	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 109,661 10.18 11.63 61.87 11.65 62.73 11.65 62.76 11.71 65.63
16-15 21,371 10.12 11.66 63.25 11.67 63.37 11.68 63.98 11.73 66.97
17-14 20,189 10.23 11.66 63.03 11.67 63.56 11.68 64.05 11.74 67.07
18-13 17,983 10.29 11.65 63.00 11.66 63.83 11.67 63.75 11.72 66.74
19-12 14,841 10.50 11.63 62.16 11.65 63.26 11.66 63.40 11.71 66.20
20-11 11,980 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

31 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	109,661	10.18	11.63	61.87	11.65	62.73	11.65	62.76	11.71	65.63
16-15	21,371	10.12	11.66	63.25	11.67	63.37	11.68	63.98	11.73	66.97
17-14	20,189	10.23	11.66	63.03	11.67	63.56	11.68	64.05	11.74	67.07
18-13	17,983	10.29	11.65	63.00	11.66	63.83	11.67	63.75	11.72	66.74
19-12	14,841	10.50	11.63	62.16	11.65	63.26	11.66	63.40	11.71	66.20
20-11	11,980	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 63,851 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 12,249 7.71 12.02 80.88 12.03 81.21 12.04 81.57 12.08 84.24
18-14 11,006 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

32 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	63,851	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	12,249	7.71	12.02	80.88	12.03	81.21	12.04	81.57	12.08	84.24
18-14	11,006	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 35,128 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

33 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	35,128	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 17,303 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

34 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	17,303	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

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 1,498,047 6.51 8.94 30.50 8.95 30.71 8.94 30.54 8.97 31.31
11-10 331,572 6.37 8.96 31.08 8.96 31.13 8.96 31.10 8.99 31.92
12-9 304,817 6.47 8.95 30.59 8.95 30.74 8.95 30.61 8.98 31.42
13-8 264,684 6.48 8.96 30.89 8.97 31.11 8.96 30.91 8.99 31.72
14-7 214,039 6.48 8.94 30.53 8.95 30.78 8.94 30.57 8.98 31.34
15-6 152,238 6.64 8.93 30.04 8.94 30.40 8.93 30.12 8.96 30.85
16-5 104,502 6.58 8.92 29.76 8.93 30.12 8.92 29.82 8.95 30.55
17-4 65,522 6.87 8.90 29.52 8.92 29.94 8.91 29.59 8.94 30.28
18-3 35,226 6.83 8.87 28.63 8.89 29.08 8.87 28.70 8.90 29.38
19-2 15,712 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

21 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,498,047	6.51	8.94	30.50	8.95	30.71	8.94	30.54	8.97	31.31
11-10	331,572	6.37	8.96	31.08	8.96	31.13	8.96	31.10	8.99	31.92
12-9	304,817	6.47	8.95	30.59	8.95	30.74	8.95	30.61	8.98	31.42
13-8	264,684	6.48	8.96	30.89	8.97	31.11	8.96	30.91	8.99	31.72
14-7	214,039	6.48	8.94	30.53	8.95	30.78	8.94	30.57	8.98	31.34
15-6	152,238	6.64	8.93	30.04	8.94	30.40	8.93	30.12	8.96	30.85
16-5	104,502	6.58	8.92	29.76	8.93	30.12	8.92	29.82	8.95	30.55
17-4	65,522	6.87	8.90	29.52	8.92	29.94	8.91	29.59	8.94	30.28
18-3	35,226	6.83	8.87	28.63	8.89	29.08	8.87	28.70	8.90	29.38
19-2	15,712	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 1,405,943 6.87 9.29 41.55 9.30 41.83 9.29 41.60 9.33 42.66
11-11 154,954 6.83 9.31 42.27 9.31 42.27 9.31 42.27 9.35 43.41
12-10 296,533 6.70 9.31 42.09 9.31 42.19 9.31 42.14 9.34 43.20
13-9 265,872 6.78 9.30 41.85 9.31 42.08 9.30 41.91 9.33 42.98
14-8 222,797 6.91 9.30 41.86 9.31 42.16 9.30 41.89 9.34 42.94
15-7 173,094 6.97 9.29 41.40 9.30 41.86 9.29 41.49 9.33 42.56
16-6 120,531 7.12 9.27 40.72 9.29 41.16 9.27 40.79 9.31 41.80
17-5 80,004 6.93 9.26 40.36 9.28 41.01 9.26 40.43 9.30 41.44
18-4 48,830 6.83 9.26 40.25 9.28 40.85 9.26 40.32 9.29 41.32
19-3 25,447 7.50 9.22 38.69 9.24 39.29 9.22 38.95 9.25 39.76
20-2 11,206 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

22 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,405,943	6.87	9.29	41.55	9.30	41.83	9.29	41.60	9.33	42.66
11-11	154,954	6.83	9.31	42.27	9.31	42.27	9.31	42.27	9.35	43.41
12-10	296,533	6.70	9.31	42.09	9.31	42.19	9.31	42.14	9.34	43.20
13-9	265,872	6.78	9.30	41.85	9.31	42.08	9.30	41.91	9.33	42.98
14-8	222,797	6.91	9.30	41.86	9.31	42.16	9.30	41.89	9.34	42.94
15-7	173,094	6.97	9.29	41.40	9.30	41.86	9.29	41.49	9.33	42.56
16-6	120,531	7.12	9.27	40.72	9.29	41.16	9.27	40.79	9.31	41.80
17-5	80,004	6.93	9.26	40.36	9.28	41.01	9.26	40.43	9.30	41.44
18-4	48,830	6.83	9.26	40.25	9.28	40.85	9.26	40.32	9.29	41.32
19-3	25,447	7.50	9.22	38.69	9.24	39.29	9.22	38.95	9.25	39.76
20-2	11,206	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 1,268,504 7.29 9.64 54.36 9.65 54.73 9.64 54.45 9.68 55.76
12-11 270,787 7.21 9.66 55.09 9.66 55.14 9.66 55.13 9.69 56.46
13-10 252,844 7.18 9.65 54.86 9.66 55.08 9.65 54.92 9.69 56.26
14-9 219,947 7.28 9.65 54.78 9.66 55.08 9.65 54.85 9.69 56.17
15-8 177,426 7.26 9.65 54.52 9.66 54.94 9.65 54.56 9.68 55.91
16-7 135,005 7.36 9.63 54.20 9.65 54.77 9.64 54.26 9.67 55.59
17-6 91,106 7.37 9.61 53.18 9.63 53.92 9.61 53.35 9.65 54.59
18-5 58,214 7.44 9.60 52.38 9.62 53.22 9.60 52.65 9.63 53.82
19-4 34,191 7.70 9.59 51.97 9.61 52.83 9.59 52.27 9.63 53.40
20-3 17,349 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

23 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,268,504	7.29	9.64	54.36	9.65	54.73	9.64	54.45	9.68	55.76
12-11	270,787	7.21	9.66	55.09	9.66	55.14	9.66	55.13	9.69	56.46
13-10	252,844	7.18	9.65	54.86	9.66	55.08	9.65	54.92	9.69	56.26
14-9	219,947	7.28	9.65	54.78	9.66	55.08	9.65	54.85	9.69	56.17
15-8	177,426	7.26	9.65	54.52	9.66	54.94	9.65	54.56	9.68	55.91
16-7	135,005	7.36	9.63	54.20	9.65	54.77	9.64	54.26	9.67	55.59
17-6	91,106	7.37	9.61	53.18	9.63	53.92	9.61	53.35	9.65	54.59
18-5	58,214	7.44	9.60	52.38	9.62	53.22	9.60	52.65	9.63	53.82
19-4	34,191	7.70	9.59	51.97	9.61	52.83	9.59	52.27	9.63	53.40
20-3	17,349	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 1,095,315 7.72 9.99 67.66 10.00 68.08 9.99 67.74 10.03 69.22
12-12 115,923 7.70 10.00 68.25 10.00 68.25 10.00 68.25 10.04 69.76
13-11 225,080 7.70 10.00 68.45 10.00 68.59 10.00 68.46 10.04 69.98
14-10 203,930 7.72 10.00 68.30 10.01 68.57 10.00 68.36 10.04 69.84
15-9 169,936 7.69 9.99 67.64 10.00 68.14 9.99 67.76 10.03 69.27
16-8 134,602 7.73 9.99 67.51 10.00 68.11 9.99 67.61 10.02 69.10
17-7 99,122 7.89 9.98 67.08 9.99 67.78 9.98 67.18 10.02 68.66
18-6 64,911 7.57 9.95 66.39 9.97 67.20 9.96 66.56 9.99 67.93
19-5 40,076 7.77 9.94 65.74 9.97 66.61 9.95 65.92 9.98 67.24
20-4 23,099 7.71 9.94 65.09 9.96 66.20 9.94 65.37 9.98 66.80
21-3 11,429 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

24 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	1,095,315	7.72	9.99	67.66	10.00	68.08	9.99	67.74	10.03	69.22
12-12	115,923	7.70	10.00	68.25	10.00	68.25	10.00	68.25	10.04	69.76
13-11	225,080	7.70	10.00	68.45	10.00	68.59	10.00	68.46	10.04	69.98
14-10	203,930	7.72	10.00	68.30	10.01	68.57	10.00	68.36	10.04	69.84
15-9	169,936	7.69	9.99	67.64	10.00	68.14	9.99	67.76	10.03	69.27
16-8	134,602	7.73	9.99	67.51	10.00	68.11	9.99	67.61	10.02	69.10
17-7	99,122	7.89	9.98	67.08	9.99	67.78	9.98	67.18	10.02	68.66
18-6	64,911	7.57	9.95	66.39	9.97	67.20	9.96	66.56	9.99	67.93
19-5	40,076	7.77	9.94	65.74	9.97	66.61	9.95	65.92	9.98	67.24
20-4	23,099	7.71	9.94	65.09	9.96	66.20	9.94	65.37	9.98	66.80
21-3	11,429	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 906,979 8.17 10.32 79.36 10.33 79.73 10.32 79.41 10.36 80.85
13-12 187,674 8.30 10.33 79.66 10.33 79.73 10.33 79.70 10.37 81.13
14-11 178,636 8.13 10.34 79.96 10.34 80.14 10.34 79.98 10.38 81.39
15-10 153,887 8.02 10.33 79.79 10.34 80.07 10.33 79.78 10.37 81.23
16-9 125,672 8.19 10.32 79.42 10.33 79.85 10.32 79.46 10.36 80.92
17-8 96,014 8.12 10.31 79.04 10.32 79.58 10.31 79.08 10.35 80.54
18-7 69,300 8.34 10.31 78.82 10.33 79.61 10.31 78.98 10.35 80.45
19-6 43,583 8.12 10.28 78.21 10.30 79.04 10.28 78.29 10.32 79.79
20-5 26,430 8.20 10.27 77.53 10.30 78.41 10.28 77.69 10.31 79.13
21-4 14,546 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

25 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	906,979	8.17	10.32	79.36	10.33	79.73	10.32	79.41	10.36	80.85
13-12	187,674	8.30	10.33	79.66	10.33	79.73	10.33	79.70	10.37	81.13
14-11	178,636	8.13	10.34	79.96	10.34	80.14	10.34	79.98	10.38	81.39
15-10	153,887	8.02	10.33	79.79	10.34	80.07	10.33	79.78	10.37	81.23
16-9	125,672	8.19	10.32	79.42	10.33	79.85	10.32	79.46	10.36	80.92
17-8	96,014	8.12	10.31	79.04	10.32	79.58	10.31	79.08	10.35	80.54
18-7	69,300	8.34	10.31	78.82	10.33	79.61	10.31	78.98	10.35	80.45
19-6	43,583	8.12	10.28	78.21	10.30	79.04	10.28	78.29	10.32	79.79
20-5	26,430	8.20	10.27	77.53	10.30	78.41	10.28	77.69	10.31	79.13
21-4	14,546	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 718,659 8.42 10.64 88.34 10.65 88.61 10.65 88.38 10.69 89.49
13-13 74,343 8.39 10.65 88.53 10.65 88.53 10.65 88.52 10.69 89.59
14-12 144,238 8.44 10.66 88.61 10.66 88.68 10.66 88.62 10.70 89.73
15-11 130,183 8.51 10.66 88.57 10.67 88.75 10.66 88.65 10.70 89.71
16-10 112,007 8.34 10.64 88.55 10.65 88.80 10.65 88.58 10.69 89.66
17-9 87,803 8.36 10.64 88.26 10.65 88.63 10.64 88.34 10.68 89.43
18-8 65,401 8.24 10.63 88.17 10.65 88.60 10.64 88.18 10.68 89.35
19-7 45,070 8.56 10.63 87.89 10.65 88.40 10.63 87.94 10.67 89.10
20-6 28,093 8.50 10.61 87.58 10.63 88.31 10.61 87.64 10.65 88.90
21-5 16,485 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

26 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	718,659	8.42	10.64	88.34	10.65	88.61	10.65	88.38	10.69	89.49
13-13	74,343	8.39	10.65	88.53	10.65	88.53	10.65	88.52	10.69	89.59
14-12	144,238	8.44	10.66	88.61	10.66	88.68	10.66	88.62	10.70	89.73
15-11	130,183	8.51	10.66	88.57	10.67	88.75	10.66	88.65	10.70	89.71
16-10	112,007	8.34	10.64	88.55	10.65	88.80	10.65	88.58	10.69	89.66
17-9	87,803	8.36	10.64	88.26	10.65	88.63	10.64	88.34	10.68	89.43
18-8	65,401	8.24	10.63	88.17	10.65	88.60	10.64	88.18	10.68	89.35
19-7	45,070	8.56	10.63	87.89	10.65	88.40	10.63	87.94	10.67	89.10
20-6	28,093	8.50	10.61	87.58	10.63	88.31	10.61	87.64	10.65	88.90
21-5	16,485	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 543,485 8.56 10.96 94.00 10.97 94.19 10.96 94.04 11.00 94.80
14-13 110,868 8.57 10.97 94.14 10.97 94.19 10.97 94.17 11.02 94.92
15-12 102,828 8.45 10.96 94.06 10.97 94.16 10.96 94.11 11.00 94.86
16-11 91,400 8.77 10.97 94.19 10.97 94.32 10.97 94.25 11.01 94.99
17-10 75,933 8.58 10.96 94.08 10.98 94.31 10.97 94.09 11.01 94.83
18-9 57,677 8.55 10.95 94.05 10.97 94.26 10.95 94.03 11.00 94.82
19-8 41,400 8.40 10.94 93.93 10.96 94.24 10.94 93.93 10.98 94.72
20-7 28,026 8.46 10.94 93.64 10.96 94.08 10.94 93.67 10.98 94.46
21-6 17,186 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

27 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	543,485	8.56	10.96	94.00	10.97	94.19	10.96	94.04	11.00	94.80
14-13	110,868	8.57	10.97	94.14	10.97	94.19	10.97	94.17	11.02	94.92
15-12	102,828	8.45	10.96	94.06	10.97	94.16	10.96	94.11	11.00	94.86
16-11	91,400	8.77	10.97	94.19	10.97	94.32	10.97	94.25	11.01	94.99
17-10	75,933	8.58	10.96	94.08	10.98	94.31	10.97	94.09	11.01	94.83
18-9	57,677	8.55	10.95	94.05	10.97	94.26	10.95	94.03	11.00	94.82
19-8	41,400	8.40	10.94	93.93	10.96	94.24	10.94	93.93	10.98	94.72
20-7	28,026	8.46	10.94	93.64	10.96	94.08	10.94	93.67	10.98	94.46
21-6	17,186	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 390,598 8.56 11.26 97.22 11.26 97.28 11.26 97.20 11.30 97.65
14-14 40,131 8.64 11.27 97.29 11.27 97.29 11.27 97.22 11.31 97.67
15-13 76,643 8.57 11.27 97.30 11.27 97.32 11.27 97.33 11.31 97.71
16-12 69,152 8.61 11.26 97.30 11.27 97.30 11.26 97.28 11.31 97.70
17-11 59,882 8.79 11.26 97.24 11.27 97.28 11.26 97.21 11.31 97.70
18-10 48,212 8.50 11.26 97.28 11.27 97.39 11.26 97.24 11.31 97.71
19-9 35,523 8.46 11.24 97.08 11.25 97.18 11.24 97.06 11.28 97.55
20-8 25,359 8.25 11.24 97.02 11.26 97.23 11.24 97.07 11.28 97.50
21-7 16,249 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

28 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	390,598	8.56	11.26	97.22	11.26	97.28	11.26	97.20	11.30	97.65
14-14	40,131	8.64	11.27	97.29	11.27	97.29	11.27	97.22	11.31	97.67
15-13	76,643	8.57	11.27	97.30	11.27	97.32	11.27	97.33	11.31	97.71
16-12	69,152	8.61	11.26	97.30	11.27	97.30	11.26	97.28	11.31	97.70
17-11	59,882	8.79	11.26	97.24	11.27	97.28	11.26	97.21	11.31	97.70
18-10	48,212	8.50	11.26	97.28	11.27	97.39	11.26	97.24	11.31	97.71
19-9	35,523	8.46	11.24	97.08	11.25	97.18	11.24	97.06	11.28	97.55
20-8	25,359	8.25	11.24	97.02	11.26	97.23	11.24	97.07	11.28	97.50
21-7	16,249	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 270,045 8.14 11.54 53.25 11.55 53.77 11.54 53.39 11.58 55.59
15-14 53,650 8.15 11.55 54.15 11.56 54.30 11.56 54.30 11.60 56.50
16-13 50,668 8.38 11.55 53.85 11.55 54.06 11.55 53.84 11.59 56.23
17-12 44,512 8.06 11.54 52.94 11.55 53.50 11.54 53.15 11.58 55.40
18-11 37,136 8.29 11.54 53.23 11.55 53.76 11.54 53.29 11.58 55.56
19-10 29,159 8.09 11.54 53.35 11.56 54.17 11.55 53.58 11.58 55.76
20-9 21,198 7.82 11.53 52.67 11.54 53.61 11.53 52.91 11.57 54.94
21-8 14,531 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

29 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	270,045	8.14	11.54	53.25	11.55	53.77	11.54	53.39	11.58	55.59
15-14	53,650	8.15	11.55	54.15	11.56	54.30	11.56	54.30	11.60	56.50
16-13	50,668	8.38	11.55	53.85	11.55	54.06	11.55	53.84	11.59	56.23
17-12	44,512	8.06	11.54	52.94	11.55	53.50	11.54	53.15	11.58	55.40
18-11	37,136	8.29	11.54	53.23	11.55	53.76	11.54	53.29	11.58	55.56
19-10	29,159	8.09	11.54	53.35	11.56	54.17	11.55	53.58	11.58	55.76
20-9	21,198	7.82	11.53	52.67	11.54	53.61	11.53	52.91	11.57	54.94
21-8	14,531	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 174,457 7.43 11.81 66.98 11.82 67.47 11.81 67.05 11.85 69.42
15-15 17,251 7.23 11.81 66.80 11.81 66.80 11.81 66.66 11.85 69.14
16-14 33,857 7.35 11.82 67.30 11.82 67.50 11.82 67.37 11.86 69.76
17-13 30,834 7.70 11.82 67.31 11.82 67.61 11.82 67.35 11.86 69.88
18-12 26,416 7.45 11.82 67.48 11.82 68.05 11.82 67.49 11.85 69.97
19-11 21,280 7.63 11.81 67.14 11.81 67.79 11.81 67.21 11.84 69.59
20-10 16,402 7.07 11.81 66.94 11.82 67.65 11.81 67.10 11.85 69.21
21-9 11,362 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

30 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	174,457	7.43	11.81	66.98	11.82	67.47	11.81	67.05	11.85	69.42
15-15	17,251	7.23	11.81	66.80	11.81	66.80	11.81	66.66	11.85	69.14
16-14	33,857	7.35	11.82	67.30	11.82	67.50	11.82	67.37	11.86	69.76
17-13	30,834	7.70	11.82	67.31	11.82	67.61	11.82	67.35	11.86	69.88
18-12	26,416	7.45	11.82	67.48	11.82	68.05	11.82	67.49	11.85	69.97
19-11	21,280	7.63	11.81	67.14	11.81	67.79	11.81	67.21	11.84	69.59
20-10	16,402	7.07	11.81	66.94	11.82	67.65	11.81	67.10	11.85	69.21
21-9	11,362	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 107,553 6.14 12.05 78.83 12.06 79.26 12.06 78.89 12.09 80.96
16-15 21,111 6.23 12.06 79.05 12.06 79.12 12.06 79.06 12.09 81.14
17-14 19,888 6.09 12.07 79.17 12.07 79.44 12.07 79.27 12.10 81.36
18-13 17,696 6.17 12.06 79.27 12.06 79.60 12.06 79.30 12.09 81.43
19-12 14,559 6.36 12.05 78.49 12.05 79.05 12.05 78.71 12.08 80.75
20-11 11,676 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

31 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	107,553	6.14	12.05	78.83	12.06	79.26	12.06	78.89	12.09	80.96
16-15	21,111	6.23	12.06	79.05	12.06	79.12	12.06	79.06	12.09	81.14
17-14	19,888	6.09	12.07	79.17	12.07	79.44	12.07	79.27	12.10	81.36
18-13	17,696	6.17	12.06	79.27	12.06	79.60	12.06	79.30	12.09	81.43
19-12	14,559	6.36	12.05	78.49	12.05	79.05	12.05	78.71	12.08	80.75
20-11	11,676	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 62,195 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 12,086 5.03 12.28 88.25 12.28 88.50 12.28 88.20 12.30 90.00
18-14 10,799 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

32 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	62,195	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	12,086	5.03	12.28	88.25	12.28	88.50	12.28	88.20	12.30	90.00
18-14	10,799	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 33,685 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

33 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	33,685	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 16,483 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

34 HCP	Cases	Sided	Fixed	Stronger	Tamer	Utopian
All ways	16,483	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

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 41,826 79.05
K-10 26,458 73.49
A-J 28,495 72.64
K-x 215,485 71.98
A-Q-10 14,474 70.84
A-J-x 106,624 70.20
K-J 25,529 69.55
A-Q-x 114,424 68.89
K-J-x 91,113 68.48
A-10 25,104 68.19
A-J-10 11,518 66.10
A-K-10 13,474 65.40
K-10-x 77,233 63.90
A-K-J 13,951 63.74
A-Q-J 13,181 62.80
K-x-x 274,144 62.20
Q-x-x 251,854 61.75
K-J-10 9636 61.19
Q-x 181,145 60.18
K-Q-x 85,845 60.06
Q-10-x 63,275 59.84
A-10-x 71,056 59.10
K-Q-10 10,590 59.10
Q-10 20,362 55.43
K-Q 19,371 55.27
A-K-x 89,949 55.08
Q-J-x 65,779 54.66
A-K 22,962 54.48
A-x 210,591 54.16
K-Q-J 9823 50.74
A-K-Q 12,300 49.61
J-x 121,731 49.47
J-x-x 175,518 48.79
A-x-x 241,120 48.68
Q-J-10 7256 47.97
Q-J 18,688 45.37
J-10 14,255 43.95
J-10-x 51,873 42.28
10-x-x 141,225 40.54
10-x 116,680 38.31
x-x-x 284,195 37.41
x-x 432,237 33.43

Holding	Occurrence	Declarer
A-Q	41,826	79.05
K-10	26,458	73.49
A-J	28,495	72.64
K-x	215,485	71.98
A-Q-10	14,474	70.84
A-J-x	106,624	70.20
K-J	25,529	69.55
A-Q-x	114,424	68.89
K-J-x	91,113	68.48
A-10	25,104	68.19
A-J-10	11,518	66.10
A-K-10	13,474	65.40
K-10-x	77,233	63.90
A-K-J	13,951	63.74
A-Q-J	13,181	62.80
K-x-x	274,144	62.20
Q-x-x	251,854	61.75
K-J-10	9636	61.19
Q-x	181,145	60.18
K-Q-x	85,845	60.06
Q-10-x	63,275	59.84
A-10-x	71,056	59.10
K-Q-10	10,590	59.10
Q-10	20,362	55.43
K-Q	19,371	55.27
A-K-x	89,949	55.08
Q-J-x	65,779	54.66
A-K	22,962	54.48
A-x	210,591	54.16
K-Q-J	9823	50.74
A-K-Q	12,300	49.61
J-x	121,731	49.47
J-x-x	175,518	48.79
A-x-x	241,120	48.68
Q-J-10	7256	47.97
Q-J	18,688	45.37
J-10	14,255	43.95
J-10-x	51,873	42.28
10-x-x	141,225	40.54
10-x	116,680	38.31
x-x-x	284,195	37.41
x-x	432,237	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