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	31862	35127	18807	4533	696	70	4
1	1833	12832	29579	32883	18703	4085	80	5	0	0	0
1	3432	16322	29553	26459	18049	6076	106	3	0	0	0
1	4022	17760	29606	25522	17241	5738	108	3	0	0	0
1 NT	0	0	18959	43516	29226	8299	0	0	0	0	0

Diamond Length

Opening	0	1	2	3	4	5	6	7	8	9	10
1	1878	13038	30495	34231	19626	732	0	0	0	0	0
1	0	0	0	8295	30149	37835	18623	4347	700	49	2
1	3358	16560	29430	26489	18161	5874	126	2	0	0	0
1	3960	17520	29693	25626	17277	5802	120	2	0	0	0
1 NT	0	0	18951	43561	29194	8294	0	0	0	0	0

Heart Length

Opening	0	1	2	3	4	5	6	7	8	9	10
1	1944	11354	24465	29795	31714	728	0	0	0	0	0
1	2267	12583	24859	29046	30558	687	0	0	0	0	0
1	0	0	0	0	0	63882	28370	6659	980	105	4
1	3901	17356	29955	25500	17352	5822	108	6	0	0	0
1 NT	0	0	19440	44744	29240	6576	0	0	0	0	0

Spade Length

Opening	0	1	2	3	4	5	6	7	8	9	10
1	1860	11466	24359	29814	31778	723	0	0	0	0	0
1	2300	12340	24732	29377	30571	680	0	0	0	0	0
1	4131	18713	31192	26756	18182	1026	0	0	0	0	0
1	0	0	0	0	0	65886	26798	6308	918	89	1
1 NT	0	0	19249	44582	29737	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	17817	32910	29019	12771	5021	1486	116
1	0	6	908	17839	33081	28619	12902	5080	1451	114
1	0	3	859	19452	32424	27446	13286	5284	1173	73
1	0	2	907	19678	32268	27601	13145	5189	1117	93
1 NT	0	2	206	3250	17139	36237	31372	11367	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	19132	23806	20268	5906	4521	3206	5722	3680	777	301	87
1	1	40	437	2915	9694	18898	23522	19607	6146	4775	3282	5747	3718	785	337	96
1	1	55	734	4772	12718	18128	18198	15235	9677	7163	4932	4088	2615	1123	453	108
1	2	57	703	5213	13191	17933	17765	15121	9693	7165	4892	4044	2604	1127	374	116
1 NT	0	0	0	0	0	0	0	0	43186	33105	23709	0	0	0	0	0

Revalued Points

Opening	13	14	15	16	17	18	19	20	21	22	23
1	26088	24248	16484	8728	5930	5604	5656	3938	1910	876	538
1	25667	23654	16356	8986	6171	5893	5782	3966	2002	987	536
1	20259	19887	16245	12568	9530	7425	5614	3821	2388	1424	839
1	20214	19429	16619	12505	9619	7406	5640	3934	2393	1396	845
1 NT	0	0	16955	33536	29903	15845	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	15651	16783	14255	14012	11154	7129	4068	2283	998	436	144	33	7	3
1	414	3325	8543	14844	15953	14146	14691	11720	7584	4525	2435	1134	475	137	55	18	1
1	0	88	2172	6684	13108	17556	19381	15847	11221	6964	4019	1843	787	234	69	23	4
1	0	98	2093	6427	12479	16572	19762	16408	11643	7268	4102	1933	858	252	83	17	5
1 NT	0	270	5901	13530	29972	34888	13977	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	20921	29032	24875	9580	6959	3044	966	54	3
1	15	14	971	3441	21038	28939	24518	9947	6985	3129	960	40	3
1	39	26	1410	4078	21925	26506	23663	11160	7507	2762	843	77	4
1	28	16	1379	4117	22142	26448	23563	11327	7402	2671	843	58	6
1 NT	0	0	2	65	1992	12501	33531	34098	16323	1488	0	0	0

Losing Tricks

Opening	0	1	2	3	4	5	6	7	8	9
1	0	1	67	846	4627	15108	28517	33626	15836	1372
1	0	4	98	919	4975	16150	29446	32420	14671	1317
1	0	7	117	1470	8002	22897	37675	25343	4436	53
1	0	4	142	1615	8131	23639	38096	23945	4380	48
1 NT	0	0	0	0	0	2167	38436	49408	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	25034	9131	17196	19285	3607	8015	4044	1929	1987	173	265	31	5	4
1	8656	23705	8848	16662	19032	3688	10399	4728	1866	1848	158	375	20	13	2
1	0	0	14767	16351	29070	5632	19412	8278	2782	2751	237	634	59	23	4
1	0	0	14222	15475	27471	5076	22342	9051	2657	2720	211	697	48	29	1
1 NT	23401	46998	29601	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	25034	9131	13592	10761	9294	5693	5756	3607	0	6435	2316
1	23705	8848	13451	10579	8656	5581	5680	3688	2596	6083	2218
1	0	14767	20405	16351	0	8665	8587	5632	7546	0	3317
1	0	14222	19430	15475	0	8041	8052	5076	11066	0	3148
1 NT	46998	29601	0	0	23401	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

Top   Opening Bid Stats

© 2022 Richard Pavlicek