Main Study 9X29 by Richard Pavlicek

Actual Play vs. Double-Dummy

How does actual play compare with double-dummy play? The question has often been asked, but concrete answers are rare because “actual play” is difficult to define. Clearly it implies imperfection to some degree, but exactly how much is unclear. Whatever the case, if both sides are equally imperfect, the errors should tend to cancel out in the long run, approaching the double-dummy state.

This study compares actual play from four major annual team events — Vanderbilt, Spingold, U.S. Championship and World Championship — with double-dummy play. The database from vugraph archives 1996-2014 consists of 80,138 results from 72 events, however 196 passouts are removed to leave 79,942 contracts. The playing field of “expert versus expert” is an ideal setting for comparison.

General Case After the Opening Lead Conclusion
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General Case

The first table shows various contract groups and the number of times each occurred. The remaining columns show the number of times made, percent made and average tricks won, both in actual play and at double-dummy. Corresponding values are placed side-by-side for comparison. The second table does the same for the 35 specific contracts. Rows tinted gold show contracts in which double-dummy play surpassed actual play in both percent made and average tricks won.

The overall picture is that actual declarer play does slightly better than double-dummy play except at the slam level where double-dummy play has a slight edge. The reason is apparent: The opening lead gives the defense a considerable advantage at double-dummy; e.g., the perfect lead will sometimes bury a contract before declarer has a chance. As the contract level increases, the opening lead tends to be less crucial, so the advantage tapers off, disappearing entirely from 5 NT upward. The narrow exception with 4 in the second table is probably a fluke that would reverse in a larger sample.

Contracts by Group
Group Times Times Made Percent Made Average Tricks
Played Actual DD Actual DD Actual DD
All contracts 79,942 51,448 49,585 64.36 62.03 9.28 9.21
Notrump 22,689 15,621 14,517 68.85 63.98 8.72 8.56
Suit 57,253 35,827 35,068 62.58 61.25 9.50 9.47
Major suit 42,130 27,316 26,780 64.84 63.57 9.50 9.47
Hearts 19,401 12,602 12,477 64.96 64.31 9.58 9.57
Spades 22,729 14,714 14,303 64.74 62.93 9.43 9.39
Minor suit 15,123 8511 8288 56.28 54.80 9.50 9.47
Clubs 7168 3912 3843 54.58 53.61 9.53 9.51
Diamonds 7955 4599 4445 57.81 55.88 9.47 9.43
Partscore 29,500 18,144 17,062 61.51 57.84 8.08 7.96
Game not slam 44,495 29,359 28,461 65.98 63.96 9.75 9.71
Slam (6 or 7) 5947 3945 4062 66.34 68.30 11.71 11.77
1 level 5786 3925 3546 67.84 61.29 7.11 6.84
2 level 11,771 7715 7356 65.54 62.49 7.95 7.84
3 level 25,844 16,528 15,558 63.95 60.20 8.94 8.85
4 level 24,312 16,202 16,030 66.64 65.93 9.93 9.93
5 level 6282 3133 3033 49.87 48.28 10.31 10.27
6 level 5152 3434 3503 66.65 67.99 11.63 11.68
7 level 795 511 559 64.28 70.31 12.26 12.37
1 of suit 851 583 560 68.51 65.80 7.25 7.10
2 of suit 10,314 6889 6624 66.79 64.22 8.00 7.91
3 of suit 10,459 5783 5472 55.29 52.32 8.58 8.52
4 of suit 23,976 15,919 15,757 66.40 65.72 9.92 9.92
5 of suit 6265 3123 3022 49.85 48.24 10.31 10.27
6 of suit 4690 3095 3153 65.99 67.23 11.61 11.66
7 of suit 698 435 480 62.32 68.77 12.20 12.32

Contracts by Group
Group	Times	Times Made	Percent Made	Average Tricks
Played	Actual	DD	Actual	DD	Actual	DD
All contracts	79,942	51,448	49,585	64.36	62.03	9.28	9.21
Notrump	22,689	15,621	14,517	68.85	63.98	8.72	8.56
Suit	57,253	35,827	35,068	62.58	61.25	9.50	9.47
Major suit	42,130	27,316	26,780	64.84	63.57	9.50	9.47
Hearts	19,401	12,602	12,477	64.96	64.31	9.58	9.57
Spades	22,729	14,714	14,303	64.74	62.93	9.43	9.39
Minor suit	15,123	8511	8288	56.28	54.80	9.50	9.47
Clubs	7168	3912	3843	54.58	53.61	9.53	9.51
Diamonds	7955	4599	4445	57.81	55.88	9.47	9.43
Partscore	29,500	18,144	17,062	61.51	57.84	8.08	7.96
Game not slam	44,495	29,359	28,461	65.98	63.96	9.75	9.71
Slam (6 or 7)	5947	3945	4062	66.34	68.30	11.71	11.77
1 level	5786	3925	3546	67.84	61.29	7.11	6.84
2 level	11,771	7715	7356	65.54	62.49	7.95	7.84
3 level	25,844	16,528	15,558	63.95	60.20	8.94	8.85
4 level	24,312	16,202	16,030	66.64	65.93	9.93	9.93
5 level	6282	3133	3033	49.87	48.28	10.31	10.27
6 level	5152	3434	3503	66.65	67.99	11.63	11.68
7 level	795	511	559	64.28	70.31	12.26	12.37
1 of suit	851	583	560	68.51	65.80	7.25	7.10
2 of suit	10,314	6889	6624	66.79	64.22	8.00	7.91
3 of suit	10,459	5783	5472	55.29	52.32	8.58	8.52
4 of suit	23,976	15,919	15,757	66.40	65.72	9.92	9.92
5 of suit	6265	3123	3022	49.85	48.24	10.31	10.27
6 of suit	4690	3095	3153	65.99	67.23	11.61	11.66
7 of suit	698	435	480	62.32	68.77	12.20	12.32

Specific Contracts
Contract Times Times Made Percent Made Average Tricks
Played Actual DD Actual DD Actual DD
1 45 25 28 55.56 62.22 6.53 6.53
1 72 39 31 54.17 43.06 6.74 6.38
1 230 153 153 66.52 66.52 7.29 7.23
1 504 366 348 72.62 69.05 7.38 7.20
1 NT 4935 3342 2986 67.72 60.51 7.09 6.79
2 847 505 484 59.62 57.14 7.84 7.72
2 1385 914 860 65.99 62.09 8.01 7.91
2 3297 2233 2187 67.73 66.33 8.06 7.98
2 4785 3237 3093 67.65 64.64 7.99 7.89
2 NT 1457 826 732 56.69 50.24 7.59 7.39
3 2303 1315 1271 57.10 55.19 8.62 8.59
3 2563 1527 1473 59.58 57.47 8.71 8.66
3 2704 1437 1329 53.14 49.15 8.49 8.42
3 2889 1504 1399 52.06 48.43 8.51 8.41
3 NT 15,385 10,745 10,086 69.84 65.56 9.19 9.07
4 782 374 360 47.83 46.04 9.36 9.25
4 702 347 328 49.43 46.72 9.32 9.26
4 10,406 7154 7204 68.75 69.23 10.00 10.03
4 12,086 8044 7865 66.56 65.08 9.92 9.91
4 NT 336 283 273 84.23 81.25 10.68 10.57
5 2110 1050 1027 49.76 48.67 10.28 10.26
5 2124 1059 1023 49.86 48.16 10.32 10.30
5 1183 529 490 44.72 41.42 10.19 10.08
5 848 485 482 57.19 56.84 10.55 10.50
5 NT 17 10 11 58.82 64.71 10.59 10.76
6 956 582 595 60.88 62.24 11.56 11.62
6 944 621 627 65.78 66.42 11.65 11.71
6 1371 945 958 68.93 69.88 11.66 11.70
6 1419 947 973 66.74 68.57 11.56 11.63
6 NT 462 339 350 73.38 75.76 11.79 11.87
7 125 61 78 48.80 62.40 11.91 12.14
7 165 92 103 55.76 62.42 11.93 12.04
7 210 151 156 71.90 74.29 12.40 12.45
7 198 131 143 66.16 72.22 12.40 12.53
7 NT 97 76 79 78.35 81.44 12.65 12.69

Specific Contracts
Contract	Times	Times Made	Percent Made	Average Tricks
Played	Actual	DD	Actual	DD	Actual	DD
1	45	25	28	55.56	62.22	6.53	6.53
1	72	39	31	54.17	43.06	6.74	6.38
1	230	153	153	66.52	66.52	7.29	7.23
1	504	366	348	72.62	69.05	7.38	7.20
1 NT	4935	3342	2986	67.72	60.51	7.09	6.79
2	847	505	484	59.62	57.14	7.84	7.72
2	1385	914	860	65.99	62.09	8.01	7.91
2	3297	2233	2187	67.73	66.33	8.06	7.98
2	4785	3237	3093	67.65	64.64	7.99	7.89
2 NT	1457	826	732	56.69	50.24	7.59	7.39
3	2303	1315	1271	57.10	55.19	8.62	8.59
3	2563	1527	1473	59.58	57.47	8.71	8.66
3	2704	1437	1329	53.14	49.15	8.49	8.42
3	2889	1504	1399	52.06	48.43	8.51	8.41
3 NT	15,385	10,745	10,086	69.84	65.56	9.19	9.07
4	782	374	360	47.83	46.04	9.36	9.25
4	702	347	328	49.43	46.72	9.32	9.26
4	10,406	7154	7204	68.75	69.23	10.00	10.03
4	12,086	8044	7865	66.56	65.08	9.92	9.91
4 NT	336	283	273	84.23	81.25	10.68	10.57
5	2110	1050	1027	49.76	48.67	10.28	10.26
5	2124	1059	1023	49.86	48.16	10.32	10.30
5	1183	529	490	44.72	41.42	10.19	10.08
5	848	485	482	57.19	56.84	10.55	10.50
5 NT	17	10	11	58.82	64.71	10.59	10.76
6	956	582	595	60.88	62.24	11.56	11.62
6	944	621	627	65.78	66.42	11.65	11.71
6	1371	945	958	68.93	69.88	11.66	11.70
6	1419	947	973	66.74	68.57	11.56	11.63
6 NT	462	339	350	73.38	75.76	11.79	11.87
7	125	61	78	48.80	62.40	11.91	12.14
7	165	92	103	55.76	62.42	11.93	12.04
7	210	151	156	71.90	74.29	12.40	12.45
7	198	131	143	66.16	72.22	12.40	12.53
7 NT	97	76	79	78.35	81.44	12.65	12.69

Top Main

After the Opening Lead

The next two tables show a comparison after the actual opening lead. That is, double-dummy play begins with the first play from dummy. (This reduced the database to 77,406 contracts, because some results did not include the play or opening lead.) Essentially, this removes the defensive advantage of the first strike, so double-dummy play surges to the front in each category — except for 1

(obviously unreliable based on little data) and 2

in percent made only, a curious mystery but probably a fluke. Another way of looking at it is that the actual declarer loses the advantage of a favorable lead; he may still get one but so will the double-dummy declarer.

Contracts by Group
Group Times Times Made Percent Made Average Tricks
Played Actual DD Actual DD Actual DD
All contracts 77,406 49,810 52,473 64.35 67.79 9.28 9.44
Notrump 21,955 15,113 15,769 68.84 71.82 8.72 8.92
Suit 55,451 34,697 36,704 62.57 66.19 9.50 9.65
Major suit 40,798 26,447 27,976 64.82 68.57 9.50 9.65
Hearts 18,809 12,222 13,036 64.98 69.31 9.58 9.75
Spades 21,989 14,225 14,940 64.69 67.94 9.42 9.57
Minor suit 14,653 8250 8728 56.30 59.56 9.50 9.63
Clubs 6943 3795 4056 54.66 58.42 9.54 9.67
Diamonds 7710 4455 4672 57.78 60.60 9.47 9.60
Partscore 28,560 17,562 18,116 61.49 63.43 8.08 8.17
Game not slam 43,129 28,449 30,157 65.96 69.92 9.75 9.96
Slam (6 or 7) 5717 3799 4200 66.45 73.47 11.71 11.91
1 level 5573 3788 3832 67.97 68.76 7.12 7.15
2 level 11,391 7471 7712 65.59 67.70 7.95 8.05
3 level 25,091 16,021 16,789 63.85 66.91 8.94 9.13
4 level 23,547 15,697 16,722 66.66 71.02 9.93 10.12
5 level 6087 3034 3218 49.84 52.87 10.31 10.44
6 level 4949 3301 3646 66.70 73.67 11.63 11.84
7 level 768 498 554 64.84 72.14 12.26 12.40
1 of suit 820 560 565 68.29 68.90 7.25 7.29
2 of suit 9996 6682 6875 66.85 68.78 8.01 8.11
3 of suit 10,168 5611 5853 55.18 57.56 8.58 8.69
4 of suit 23,220 15,422 16,441 66.42 70.81 9.92 10.11
5 of suit 6070 3024 3206 49.82 52.82 10.31 10.43
6 of suit 4504 2974 3288 66.03 73.00 11.61 11.82
7 of suit 673 424 476 63.00 70.73 12.20 12.35

Contracts by Group
Group	Times	Times Made	Percent Made	Average Tricks
Played	Actual	DD	Actual	DD	Actual	DD
All contracts	77,406	49,810	52,473	64.35	67.79	9.28	9.44
Notrump	21,955	15,113	15,769	68.84	71.82	8.72	8.92
Suit	55,451	34,697	36,704	62.57	66.19	9.50	9.65
Major suit	40,798	26,447	27,976	64.82	68.57	9.50	9.65
Hearts	18,809	12,222	13,036	64.98	69.31	9.58	9.75
Spades	21,989	14,225	14,940	64.69	67.94	9.42	9.57
Minor suit	14,653	8250	8728	56.30	59.56	9.50	9.63
Clubs	6943	3795	4056	54.66	58.42	9.54	9.67
Diamonds	7710	4455	4672	57.78	60.60	9.47	9.60
Partscore	28,560	17,562	18,116	61.49	63.43	8.08	8.17
Game not slam	43,129	28,449	30,157	65.96	69.92	9.75	9.96
Slam (6 or 7)	5717	3799	4200	66.45	73.47	11.71	11.91
1 level	5573	3788	3832	67.97	68.76	7.12	7.15
2 level	11,391	7471	7712	65.59	67.70	7.95	8.05
3 level	25,091	16,021	16,789	63.85	66.91	8.94	9.13
4 level	23,547	15,697	16,722	66.66	71.02	9.93	10.12
5 level	6087	3034	3218	49.84	52.87	10.31	10.44
6 level	4949	3301	3646	66.70	73.67	11.63	11.84
7 level	768	498	554	64.84	72.14	12.26	12.40
1 of suit	820	560	565	68.29	68.90	7.25	7.29
2 of suit	9996	6682	6875	66.85	68.78	8.01	8.11
3 of suit	10,168	5611	5853	55.18	57.56	8.58	8.69
4 of suit	23,220	15,422	16,441	66.42	70.81	9.92	10.11
5 of suit	6070	3024	3206	49.82	52.82	10.31	10.43
6 of suit	4504	2974	3288	66.03	73.00	11.61	11.82
7 of suit	673	424	476	63.00	70.73	12.20	12.35

Specific Contracts
Contract Times Times Made Percent Made Average Tricks
Played Actual DD Actual DD Actual DD
1 42 24 28 57.14 66.67 6.60 6.83
1 70 37 34 52.86 48.57 6.71 6.51
1 219 145 148 66.21 67.58 7.27 7.37
1 489 354 355 72.39 72.60 7.37 7.41
1 NT 4753 3228 3267 67.92 68.74 7.10 7.13
2 818 493 515 60.27 62.96 7.86 7.95
2 1341 885 875 66.00 65.25 8.01 8.11
2 3188 2159 2260 67.72 70.89 8.05 8.17
2 4649 3145 3225 67.65 69.37 8.00 8.09
2 NT 1395 789 837 56.56 60.00 7.59 7.68
3 2234 1270 1336 56.85 59.80 8.62 8.75
3 2496 1492 1559 59.78 62.46 8.72 8.84
3 2633 1396 1448 53.02 54.99 8.48 8.59
3 2805 1453 1510 51.80 53.83 8.50 8.59
3 NT 14,923 10,410 10,936 69.76 73.28 9.19 9.44
4 751 358 371 47.67 49.40 9.37 9.39
4 677 334 348 49.34 51.40 9.33 9.40
4 10,100 6950 7498 68.81 74.24 10.00 10.22
4 11,692 7780 8224 66.54 70.34 9.92 10.11
4 NT 327 275 281 84.10 85.93 10.66 10.87
5 2052 1023 1096 49.85 53.41 10.28 10.43
5 2054 1014 1089 49.37 53.02 10.31 10.45
5 1146 517 526 45.11 45.90 10.20 10.26
5 818 470 495 57.46 60.51 10.55 10.66
5 NT 17 10 12 58.82 70.59 10.59 11.00
6 924 567 633 61.36 68.51 11.57 11.77
6 911 602 664 66.08 72.89 11.67 11.89
6 1321 909 1001 68.81 75.78 11.66 11.85
6 1348 896 990 66.47 73.44 11.56 11.77
6 NT 445 327 358 73.48 80.45 11.79 12.04
7 122 60 77 49.18 63.11 11.91 12.16
7 161 91 103 56.52 63.98 11.94 12.09
7 202 146 155 72.28 76.73 12.39 12.48
7 188 127 141 67.55 75.00 12.41 12.56
7 NT 95 74 78 77.89 82.11 12.64 12.74

Specific Contracts
Contract	Times	Times Made	Percent Made	Average Tricks
Played	Actual	DD	Actual	DD	Actual	DD
1	42	24	28	57.14	66.67	6.60	6.83
1	70	37	34	52.86	48.57	6.71	6.51
1	219	145	148	66.21	67.58	7.27	7.37
1	489	354	355	72.39	72.60	7.37	7.41
1 NT	4753	3228	3267	67.92	68.74	7.10	7.13
2	818	493	515	60.27	62.96	7.86	7.95
2	1341	885	875	66.00	65.25	8.01	8.11
2	3188	2159	2260	67.72	70.89	8.05	8.17
2	4649	3145	3225	67.65	69.37	8.00	8.09
2 NT	1395	789	837	56.56	60.00	7.59	7.68
3	2234	1270	1336	56.85	59.80	8.62	8.75
3	2496	1492	1559	59.78	62.46	8.72	8.84
3	2633	1396	1448	53.02	54.99	8.48	8.59
3	2805	1453	1510	51.80	53.83	8.50	8.59
3 NT	14,923	10,410	10,936	69.76	73.28	9.19	9.44
4	751	358	371	47.67	49.40	9.37	9.39
4	677	334	348	49.34	51.40	9.33	9.40
4	10,100	6950	7498	68.81	74.24	10.00	10.22
4	11,692	7780	8224	66.54	70.34	9.92	10.11
4 NT	327	275	281	84.10	85.93	10.66	10.87
5	2052	1023	1096	49.85	53.41	10.28	10.43
5	2054	1014	1089	49.37	53.02	10.31	10.45
5	1146	517	526	45.11	45.90	10.20	10.26
5	818	470	495	57.46	60.51	10.55	10.66
5 NT	17	10	12	58.82	70.59	10.59	11.00
6	924	567	633	61.36	68.51	11.57	11.77
6	911	602	664	66.08	72.89	11.67	11.89
6	1321	909	1001	68.81	75.78	11.66	11.85
6	1348	896	990	66.47	73.44	11.56	11.77
6 NT	445	327	358	73.48	80.45	11.79	12.04
7	122	60	77	49.18	63.11	11.91	12.16
7	161	91	103	56.52	63.98	11.94	12.09
7	202	146	155	72.28	76.73	12.39	12.48
7	188	127	141	67.55	75.00	12.41	12.56
7 NT	95	74	78	77.89	82.11	12.64	12.74

Top Main

Conclusion

The overriding impact of the tables is that actual play versus double-dummy is pretty close, so analyses based on double-dummy play should generally be on track. The henchmen below don’t buy any of this, so please leave the building quietly and don’t make any quick moves.

Top Main