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

*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

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

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

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

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

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

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

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

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	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

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© 2022 Richard Pavlicek