Study AB01 Main

Opening Bid Stats

by Richard Pavlicek

The purpose of this study is to determine statistics for opening bids based on the Pavlicek methods. System structure includes five-card majors, strong notrumps (15-17 HCP) and convenient minors (longer or stronger) which is always 3+ cards. Further, when a choice exists between 1 NT and a major, 1 NT requires no doubleton worse than Q-x.

Suit Lengths Hand Strength Hand Pattern

For each of the five one-bids, random hands were dealt until 100,000 fitting examples were found. The following table shows the empirical frequency of each opening bid. This assumes opener is the dealer, as after one hand passes, the frequency of the next hand opening would be greater; and in third and fourth seat, requirements are often shaded for tactical benefit.

Frequency
Opening Percent of Hands
1 9.3094
1 9.4789
1 6.2499
1 6.5183
1 NT* 4.6877
Any one-bid 36.2442

Frequency
Opening	Percent of Hands
1	9.3094
1	9.4789
1	6.2499
1	6.5183
1 NT*	4.6877
Any one-bid	36.2442

*In practice this would be slightly higher because off-shape 1 NT bids were ignored.
Hence 1 and 1 would be slightly lower to compensate.

Each of the tables that follow summarize a specific statistic for each opening bid. Each table cell shows the number of hands out of 100,000 which fit that criterion. The numbers are easily converted to percent by placing a decimal point three digits from the right.

Suit Lengths

Club Length
Opening 0 1 2 3 4 5 6 7 8 9 10
1 0 0 0 8901 31,862 35,127 18,807 4533 696 70 4
1 1833 12,832 29,579 32,883 18,703 4085 80 5 0 0 0
1 3432 16,322 29,553 26,459 18,049 6076 106 3 0 0 0
1 4022 17,760 29,606 25,522 17,241 5738 108 3 0 0 0
1 NT 0 0 18,959 43,516 29,226 8299 0 0 0 0 0

Club Length
Opening	0	1	2	3	4	5	6	7	8	9	10
1	0	0	0	8901	31,862	35,127	18,807	4533	696	70	4
1	1833	12,832	29,579	32,883	18,703	4085	80	5	0	0	0
1	3432	16,322	29,553	26,459	18,049	6076	106	3	0	0	0
1	4022	17,760	29,606	25,522	17,241	5738	108	3	0	0	0
1 NT	0	0	18,959	43,516	29,226	8299	0	0	0	0	0

Diamond Length
Opening 0 1 2 3 4 5 6 7 8 9 10
1 1878 13,038 30,495 34,231 19,626 732 0 0 0 0 0
1 0 0 0 8295 30,149 37,835 18,623 4347 700 49 2
1 3358 16,560 29,430 26,489 18,161 5874 126 2 0 0 0
1 3960 17,520 29,693 25,626 17,277 5802 120 2 0 0 0
1 NT 0 0 18,951 43,561 29,194 8294 0 0 0 0 0

Diamond Length
Opening	0	1	2	3	4	5	6	7	8	9	10
1	1878	13,038	30,495	34,231	19,626	732	0	0	0	0	0
1	0	0	0	8295	30,149	37,835	18,623	4347	700	49	2
1	3358	16,560	29,430	26,489	18,161	5874	126	2	0	0	0
1	3960	17,520	29,693	25,626	17,277	5802	120	2	0	0	0
1 NT	0	0	18,951	43,561	29,194	8294	0	0	0	0	0

Heart Length
Opening 0 1 2 3 4 5 6 7 8 9 10
1 1944 11,354 24,465 29,795 31,714 728 0 0 0 0 0
1 2267 12,583 24,859 29,046 30,558 687 0 0 0 0 0
1 0 0 0 0 0 63,882 28,370 6659 980 105 4
1 3901 17,356 29,955 25,500 17,352 5822 108 6 0 0 0
1 NT 0 0 19,440 44,744 29,240 6576 0 0 0 0 0

Heart Length
Opening	0	1	2	3	4	5	6	7	8	9	10
1	1944	11,354	24,465	29,795	31,714	728	0	0	0	0	0
1	2267	12,583	24,859	29,046	30,558	687	0	0	0	0	0
1	0	0	0	0	0	63,882	28,370	6659	980	105	4
1	3901	17,356	29,955	25,500	17,352	5822	108	6	0	0	0
1 NT	0	0	19,440	44,744	29,240	6576	0	0	0	0	0

Spade Length
Opening 0 1 2 3 4 5 6 7 8 9 10
1 1860 11,466 24,359 29,814 31,778 723 0 0 0 0 0
1 2300 12,340 24,732 29,377 30,571 680 0 0 0 0 0
1 4131 18,713 31,192 26,756 18,182 1026 0 0 0 0 0
1 0 0 0 0 0 65,886 26,798 6308 918 89 1
1 NT 0 0 19,249 44,582 29,737 6432 0 0 0 0 0

Spade Length
Opening	0	1	2	3	4	5	6	7	8	9	10
1	1860	11,466	24,359	29,814	31,778	723	0	0	0	0	0
1	2300	12,340	24,732	29,377	30,571	680	0	0	0	0	0
1	4131	18,713	31,192	26,756	18,182	1026	0	0	0	0	0
1	0	0	0	0	0	65,886	26,798	6308	918	89	1
1 NT	0	0	19,249	44,582	29,737	6432	0	0	0	0	0

Study AB01 Main Top Opening Bid Stats

Hand Strength

For explanations of any statistic see Hand Evaluation Stats.

Controls
Opening 0 1 2 3 4 5 6 7 8 9
1 0 4 856 17,817 32,910 29,019 12,771 5021 1486 116
1 0 6 908 17,839 33,081 28,619 12,902 5080 1451 114
1 0 3 859 19,452 32,424 27,446 13,286 5284 1173 73
1 0 2 907 19,678 32,268 27,601 13,145 5189 1117 93
1 NT 0 2 206 3250 17,139 36,237 31,372 11,367 427 0

Controls
Opening	1	2	3	4	5	6	7	8	9
1	4	856	17,817	32,910	29,019	12,771	5021	1486	116
1	6	908	17,839	33,081	28,619	12,902	5080	1451	114
1	3	859	19,452	32,424	27,446	13,286	5284	1173	73
1	2	907	19,678	32,268	27,601	13,145	5189	1117	93
1 NT	2	206	3250	17,139	36,237	31,372	11,367	427	0

High-Card Points
Opening 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1 0 48 486 2567 9493 19,132 23,806 20,268 5906 4521 3206 5722 3680 777 301 87
1 1 40 437 2915 9694 18,898 23,522 19,607 6146 4775 3282 5747 3718 785 337 96
1 1 55 734 4772 12,718 18,128 18,198 15,235 9677 7163 4932 4088 2615 1123 453 108
1 2 57 703 5213 13,191 17,933 17,765 15,121 9693 7165 4892 4044 2604 1127 374 116
1 NT 0 0 0 0 0 0 0 0 43,186 33,105 23,709 0 0 0 0 0

High-Card Points
Opening	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
1	0	48	486	2567	9493	19,132	23,806	20,268	5906	4521	3206	5722	3680	777	301	87
1	1	40	437	2915	9694	18,898	23,522	19,607	6146	4775	3282	5747	3718	785	337	96
1	1	55	734	4772	12,718	18,128	18,198	15,235	9677	7163	4932	4088	2615	1123	453	108
1	2	57	703	5213	13,191	17,933	17,765	15,121	9693	7165	4892	4044	2604	1127	374	116
1 NT	0	0	0	0	0	0	0	0	43,186	33,105	23,709	0	0	0	0	0

Revalued Points
Opening 13 14 15 16 17 18 19 20 21 22 23
1 26,088 24,248 16,484 8728 5930 5604 5656 3938 1910 876 538
1 25,667 23,654 16,356 8986 6171 5893 5782 3966 2002 987 536
1 20,259 19,887 16,245 12,568 9530 7425 5614 3821 2388 1424 839
1 20,214 19,429 16,619 12,505 9619 7406 5640 3934 2393 1396 845
1 NT 0 0 16,955 33,536 29,903 15,845 3760 1 0 0 0

Revalued Points
Opening	13	14	15	16	17	18	19	20	21	22	23
1	26,088	24,248	16,484	8728	5930	5604	5656	3938	1910	876	538
1	25,667	23,654	16,356	8986	6171	5893	5782	3966	2002	987	536
1	20,259	19,887	16,245	12,568	9530	7425	5614	3821	2388	1424	839
1	20,214	19,429	16,619	12,505	9619	7406	5640	3934	2393	1396	845
1 NT	0	0	16,955	33,536	29,903	15,845	3760	1	0	0	0

Playing Tricks
Opening 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
1 443 3483 9118 15,651 16,783 14,255 14,012 11,154 7129 4068 2283 998 436 144 33 7 3
1 414 3325 8543 14,844 15,953 14,146 14,691 11,720 7584 4525 2435 1134 475 137 55 18 1
1 0 88 2172 6684 13,108 17,556 19,381 15,847 11,221 6964 4019 1843 787 234 69 23 4
1 0 98 2093 6427 12,479 16,572 19,762 16,408 11,643 7268 4102 1933 858 252 83 17 5
1 NT 0 270 5901 13,530 29,972 34,888 13,977 1441 21 0 0 0 0 0 0 0 0

Playing Tricks
Opening	4	4.5	5	5.5	6	6.5	7	7.5	8	8.5	9	9.5	10	10.5	11	11.5	12
1	443	3483	9118	15,651	16,783	14,255	14,012	11,154	7129	4068	2283	998	436	144	33	7	3
1	414	3325	8543	14,844	15,953	14,146	14,691	11,720	7584	4525	2435	1134	475	137	55	18	1
1	0	88	2172	6684	13,108	17,556	19,381	15,847	11,221	6964	4019	1843	787	234	69	23	4
1	0	98	2093	6427	12,479	16,572	19,762	16,408	11,643	7268	4102	1933	858	252	83	17	5
1 NT	0	270	5901	13,530	29,972	34,888	13,977	1441	21	0	0	0	0	0	0	0	0

Defensive Tricks
Opening 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
1 21 16 1031 3498 20,921 29,032 24,875 9580 6959 3044 966 54 3
1 15 14 971 3441 21,038 28,939 24,518 9947 6985 3129 960 40 3
1 39 26 1410 4078 21,925 26,506 23,663 11,160 7507 2762 843 77 4
1 28 16 1379 4117 22,142 26,448 23,563 11,327 7402 2671 843 58 6
1 NT 0 0 2 65 1992 12,501 33,531 34,098 16,323 1488 0 0 0

Defensive Tricks
Opening	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6
1	21	16	1031	3498	20,921	29,032	24,875	9580	6959	3044	966	54	3
1	15	14	971	3441	21,038	28,939	24,518	9947	6985	3129	960	40	3
1	39	26	1410	4078	21,925	26,506	23,663	11,160	7507	2762	843	77	4
1	28	16	1379	4117	22,142	26,448	23,563	11,327	7402	2671	843	58	6
1 NT	0	0	2	65	1992	12,501	33,531	34,098	16,323	1488	0	0	0

Losing Tricks
Opening 0 1 2 3 4 5 6 7 8 9
1 0 1 67 846 4627 15,108 28,517 33,626 15,836 1372
1 0 4 98 919 4975 16,150 29,446 32,420 14,671 1317
1 0 7 117 1470 8002 22,897 37,675 25,343 4436 53
1 0 4 142 1615 8131 23,639 38,096 23,945 4380 48
1 NT 0 0 0 0 0 2167 38,436 49,408 9873 116

Losing Tricks
Opening	1	2	3	4	5	6	7	8	9
1	1	67	846	4627	15,108	28,517	33,626	15,836	1372
1	4	98	919	4975	16,150	29,446	32,420	14,671	1317
1	7	117	1470	8002	22,897	37,675	25,343	4436	53
1	4	142	1615	8131	23,639	38,096	23,945	4380	48
1 NT	0	0	0	0	2167	38,436	49,408	9873	116

Study AB01 Main Top Opening Bid Stats

Hand Pattern

Freakness
Opening 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 9294 25,034 9131 17,196 19,285 3607 8015 4044 1929 1987 173 265 31 5 4
1 8656 23,705 8848 16,662 19,032 3688 10,399 4728 1866 1848 158 375 20 13 2
1 0 0 14,767 16,351 29,070 5632 19,412 8278 2782 2751 237 634 59 23 4
1 0 0 14,222 15,475 27,471 5076 22,342 9051 2657 2720 211 697 48 29 1
1 NT 23,401 46,998 29,601 0 0 0 0 0 0 0 0 0 0 0 0

Freakness
Opening	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	9294	25,034	9131	17,196	19,285	3607	8015	4044	1929	1987	173	265	31	5	4
1	8656	23,705	8848	16,662	19,032	3688	10,399	4728	1866	1848	158	375	20	13	2
1	0	0	14,767	16,351	29,070	5632	19,412	8278	2782	2751	237	634	59	23	4
1	0	0	14,222	15,475	27,471	5076	22,342	9051	2657	2720	211	697	48	29	1
1 NT	23,401	46,998	29,601	0	0	0	0	0	0	0	0	0	0	0	0

Generic Shape
Opening 4432 5332 5431 5422 4333 6322 6421 6331 5521 4441 7321
1 25,034 9131 13,592 10,761 9294 5693 5756 3607 0 6435 2316
1 23,705 8848 13,451 10,579 8656 5581 5680 3688 2596 6083 2218
1 0 14,767 20,405 16,351 0 8665 8587 5632 7546 0 3317
1 0 14,222 19,430 15,475 0 8041 8052 5076 11,066 0 3148
1 NT 46,998 29,601 0 0 23,401 0 0 0 0 0 0

Generic Shape
Opening	4432	5332	5431	5422	4333	6322	6421	6331	5521	4441	7321
1	25,034	9131	13,592	10,761	9294	5693	5756	3607	0	6435	2316
1	23,705	8848	13,451	10,579	8656	5581	5680	3688	2596	6083	2218
1	0	14,767	20,405	16,351	0	8665	8587	5632	7546	0	3317
1	0	14,222	19,430	15,475	0	8041	8052	5076	11,066	0	3148
1 NT	46,998	29,601	0	0	23,401	0	0	0	0	0	0

Opening 6430 5440 5530 6511 6520 7222 7411 7420 7330 8221 8311
1 1728 1643 0 1046 977 616 556 563 327 273 174
1 1715 1566 795 932 944 557 563 457 371 263 184
1 2528 2380 2433 1390 1337 899 870 783 522 385 246
1 2569 2359 3334 1379 1344 865 751 775 527 362 239

Opening	6430	5440	5530	6511	6520	7222	7411	7420	7330	8221	8311
1	1728	1643	0	1046	977	616	556	563	327	273	174
1	1715	1566	795	932	944	557	563	457	371	263	184
1	2528	2380	2433	1390	1337	899	870	783	522	385	246
1	2569	2359	3334	1379	1344	865	751	775	527	362	239

Opening 7510 8320 6610 8410 9211 9310 9220 7600 8500 A210 9400
1 155 173 0 71 39 19 12 0 5 4 0
1 179 158 78 89 29 12 8 7 6 2 0
1 262 237 226 104 42 31 28 11 8 4 4
1 232 211 326 99 40 26 22 21 7 1 1

Opening	7510	8320	6610	8410	9211	9310	9220	7600	8500	A210	9400
1	155	173	0	71	39	19	12	0	5	4	0
1	179	158	78	89	29	12	8	7	6	2	0
1	262	237	226	104	42	31	28	11	8	4	4
1	232	211	326	99	40	26	22	21	7	1	1

Study AB01 Main Top Opening Bid Stats

Opening	7510	8320	6610	8410	9211	9310	9220	7600	8500	A210	9400
1	155	173	0	71	39	19	12	0	5	4	0
1	179	158	78	89	29	12	8	7	6	2	0
1	262	237	226	104	42	31	28	11	8	4	4
1	232	211	326	99	40	26	22	21	7	1	1

Opening	7510	8320	6610	8410	9211	9310	9220	7600	8500	A210	9400
1	155	173	0	71	39	19	12	0	5	4	0
1	179	158	78	89	29	12	8	7	6	2	0
1	262	237	226	104	42	31	28	11	8	4	4
1	232	211	326	99	40	26	22	21	7	1	1

Opening	7510	8320	6610	8410	9211	9310	9220	7600	8500	A210	9400
1	155	173	0	71	39	19	12	0	5	4	0
1	179	158	78	89	29	12	8	7	6	2	0
1	262	237	226	104	42	31	28	11	8	4	4
1	232	211	326	99	40	26	22	21	7	1	1