Stats 8H29 Main

RP BBO Matches

by Richard Pavlicek

General stats for 61,228 deals

Each table lists all possible values of each statistic in decimal (or binary if a bitmap) with the number of occurrences and percent for North, South, West and East. The last column shows the theoretical expectation, which is mathematically determined and exact. The bottom line shows the number of unique values (table rows), the total number of occurrences, and the average (mean) value.

F

Gs

C

Hp

Rp

Pt

Dt

Lt

Ls

Ss

Rs

S

H

D

C

St

Ht

Dt

Ct

Sc

Hc

Dc

Cc

Sq

Hq

Dq

Cq

Sx

Hx

Dx

Cx

Percents and averages are rounded to four places (unless zero which is shown as a single digit). The most frequent occurrence (mode) is tinted gold, the second-most a paler gold, and the third-most even paler.

Freakness

0-20 scale: 4333 = 0 4432 = 1 5332 = 2 4441 5422 = 3 5431 6322 = 4
6331 = 5 5440 5521 6421 7222 = 6 5530 6430 7321 = 7 6511 7330 7411 = 8
6520 7420 8221 8311 = 9 8320 = 10 6610 7510 8410 9211 = 11 9220 9310 = 12
7600 8500 9400 A110 = 13 A210 A300 = 14 B110 B200 = 16 C100 = 18 D000 = 20

Freakness	North		South		West		East		Theoretical
0	6522	10.6520	6519	10.6471	6473	10.5720	6434	10.5083	66905856160	10.5361
1	13381	21.8544	13147	21.4722	13203	21.5637	13131	21.4461	136852887600	21.5512
2	9473	15.4717	9767	15.9519	9403	15.3574	9547	15.5925	98534079072	15.5168
3	8343	13.6261	8283	13.5281	8333	13.6098	8335	13.6131	86189672140	13.5729
4	11196	18.2858	11128	18.1747	11498	18.7790	11353	18.5422	117942306768	18.5732
5	2154	3.5180	2180	3.5605	2104	3.4363	2118	3.4592	21896462016	3.4482
6	5837	9.5332	5969	9.7488	5826	9.5153	5916	9.6622	61166193660	9.6323
7	2419	3.9508	2405	3.9279	2500	4.0831	2503	4.0880	26049899304	4.1023
8	843	1.3768	811	1.3246	848	1.3850	834	1.3621	8651399328	1.3624
9	833	1.3605	779	1.2723	773	1.2625	825	1.3474	8399095848	1.3227
10	45	0.0735	68	0.1111	62	0.1013	59	0.0964	689049504	0.1085
11	163	0.2662	153	0.2499	174	0.2842	152	0.2483	1548621360	0.2439
12	14	0.0229	13	0.0212	18	0.0294	16	0.0261	116001600	0.0183
13	4	0.0065	4	0.0065	11	0.0180	3	0.0049	63860368	0.0101
14	1	0.0016	2	0.0033	2	0.0033	2	0.0033	7941648	0.0013
16	0	0	0	0	0	0	0	0	231192	0.0000
18	0	0	0	0	0	0	0	0	2028	0.0000
20	0	0	0	0	0	0	0	0	4	0.0000
18	61228	2.9657	61228	2.9674	61228	2.9829	61228	2.9867	635013559600	2.9829

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Generic shape

39 generic hand patterns in order of theoretical frequency

Shape	North		South		West		East		Theoretical
4432	13381	21.8544	13147	21.4722	13203	21.5637	13131	21.4461	136852887600	21.5512
5332	9473	15.4717	9767	15.9519	9403	15.3574	9547	15.5925	98534079072	15.5168
5431	7769	12.6886	7696	12.5694	8086	13.2064	7807	12.7507	82111732560	12.9307
5422	6518	10.6455	6501	10.6177	6442	10.5213	6486	10.5932	67182326640	10.5797
4333	6522	10.6520	6519	10.6471	6473	10.5720	6434	10.5083	66905856160	10.5361
6322	3427	5.5971	3432	5.6053	3412	5.5726	3546	5.7915	35830574208	5.6425
6421	2839	4.6368	2974	4.8573	2915	4.7609	2864	4.6776	29858811840	4.7021
6331	2154	3.5180	2180	3.5605	2104	3.4363	2118	3.4592	21896462016	3.4482
5521	1921	3.1375	1983	3.2387	1901	3.1048	1964	3.2077	20154697992	3.1739
4441	1825	2.9807	1782	2.9104	1891	3.0885	1849	3.0199	19007345500	2.9932
7321	1070	1.7476	1126	1.8390	1107	1.8080	1161	1.8962	11943524736	1.8808
6430	776	1.2674	752	1.2282	819	1.3376	815	1.3311	8421716160	1.3262
5440	761	1.2429	706	1.1531	715	1.1678	742	1.2119	7895358900	1.2433
5530	573	0.9358	527	0.8607	574	0.9375	527	0.8607	5684658408	0.8952
6511	445	0.7268	422	0.6892	459	0.7497	431	0.7039	4478821776	0.7053
6520	398	0.6500	382	0.6239	378	0.6174	392	0.6402	4134297024	0.6511
7222	316	0.5161	306	0.4998	295	0.4818	346	0.5651	3257324928	0.5130
7411	228	0.3724	228	0.3724	237	0.3871	238	0.3887	2488234320	0.3918
7420	244	0.3985	214	0.3495	194	0.3168	224	0.3658	2296831680	0.3617
7330	170	0.2777	161	0.2630	152	0.2483	165	0.2695	1684343232	0.2652
8221	126	0.2058	108	0.1764	129	0.2107	121	0.1976	1221496848	0.1924
8311	65	0.1062	75	0.1225	72	0.1176	88	0.1437	746470296	0.1176
7510	65	0.1062	59	0.0964	90	0.1470	72	0.1176	689049504	0.1085
8320	45	0.0735	68	0.1111	62	0.1013	59	0.0964	689049504	0.1085
6610	57	0.0931	49	0.0800	42	0.0686	36	0.0588	459366336	0.0723
8410	24	0.0392	36	0.0588	34	0.0555	24	0.0392	287103960	0.0452
9211	17	0.0278	9	0.0147	8	0.0131	20	0.0327	113101560	0.0178
9310	7	0.0114	8	0.0131	10	0.0163	11	0.0180	63800880	0.0100
9220	7	0.0114	5	0.0082	8	0.0131	5	0.0082	52200720	0.0082
7600	0	0	1	0.0016	4	0.0065	2	0.0033	35335872	0.0056
8500	4	0.0065	3	0.0049	7	0.0114	1	0.0016	19876428	0.0031
A210	1	0.0016	2	0.0033	1	0.0016	2	0.0033	6960096	0.0011
9400	0	0	0	0	0	0	0	0	6134700	0.0010
A111	0	0	0	0	0	0	0	0	2513368	0.0004
A300	0	0	0	0	1	0.0016	0	0	981552	0.0002
B110	0	0	0	0	0	0	0	0	158184	0.0000
B200	0	0	0	0	0	0	0	0	73008	0.0000
C100	0	0	0	0	0	0	0	0	2028	0.0000
D000	0	0	0	0	0	0	0	0	4	0.0000
39	61228	3.6839	61228	3.6670	61228	3.6926	61228	3.7111	635013559600	3.6954

Mean is calculated with shapes valued from 0 to 38, so 3.xxxx falls between “5422” and “4333”

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Controls

Ace = 2 King = 1

Controls	North		South		West		East		Theoretical
0	5041	8.2332	5236	8.5516	4934	8.0584	4973	8.1221	51915526432	8.1755
1	8016	13.0920	8331	13.6065	8157	13.3223	8100	13.2292	84362730452	13.2852
2	12701	20.7438	12478	20.3796	12384	20.2260	12581	20.5478	130378765244	20.5317
3	12716	20.7683	12673	20.6980	12685	20.7176	12770	20.8565	132634453224	20.8869
4	10236	16.7178	10236	16.7178	10342	16.8910	10294	16.8126	106275127972	16.7359
5	6934	11.3249	6776	11.0668	6846	11.1812	6798	11.1028	70893050800	11.1640
6	3386	5.5301	3441	5.6200	3597	5.8748	3570	5.8307	36155455908	5.6937
7	1534	2.5054	1448	2.3649	1569	2.5626	1526	2.4923	15596471176	2.4561
8	500	0.8166	467	0.7627	516	0.8428	473	0.7725	5192436964	0.8177
9	121	0.1976	119	0.1944	164	0.2679	119	0.1944	1322059596	0.2082
10	39	0.0637	20	0.0327	31	0.0506	22	0.0359	258159616	0.0407
11	4	0.0065	3	0.0049	3	0.0049	2	0.0033	28236208	0.0044
12	0	0	0	0	0	0	0	0	1086008	0.0002
13	61228	3.0012	61228	2.9717	61228	3.0230	61228	3.0041	635013559600	3.0000

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High-card points

Ace = 4 King = 3 Queen = 2 Jack = 1

HCP	North		South		West		East		Theoretical
0	222	0.3626	227	0.3707	200	0.3266	225	0.3675	2310789600	0.3639
1	505	0.8248	524	0.8558	476	0.7774	538	0.8787	5006710800	0.7884
2	823	1.3442	858	1.4013	886	1.4471	827	1.3507	8611542576	1.3561
3	1488	2.4303	1569	2.5626	1517	2.4776	1560	2.5479	15636342960	2.4624
4	2402	3.9230	2418	3.9492	2291	3.7418	2373	3.8757	24419055136	3.8454
5	3062	5.0010	3190	5.2100	3108	5.0761	3190	5.2100	32933031040	5.1862
6	4041	6.5999	4053	6.6195	3980	6.5003	3956	6.4611	41619399184	6.5541
7	4904	8.0094	4953	8.0894	4817	7.8673	4988	8.1466	50979441968	8.0281
8	5495	8.9747	5398	8.8162	5375	8.7787	5253	8.5794	56466608128	8.8922
9	5723	9.3470	5714	9.3323	5639	9.2098	5770	9.4238	59413313872	9.3562
10	5824	9.5120	5703	9.3144	5772	9.4271	5681	9.2784	59723754816	9.4051
11	5494	8.9730	5481	8.9518	5452	8.9044	5398	8.8162	56799933520	8.9447
12	4888	7.9833	4822	7.8755	4913	8.0241	5027	8.2103	50971682080	8.0269
13	4273	6.9788	4260	6.9576	4321	7.0572	4212	6.8792	43906944752	6.9143
14	3419	5.5840	3481	5.6853	3550	5.7980	3481	5.6853	36153374224	5.6933
15	2708	4.4228	2686	4.3869	2750	4.4914	2784	4.5469	28090962724	4.4237
16	2023	3.3040	2052	3.3514	2047	3.3432	2035	3.3236	21024781756	3.3109
17	1426	2.3290	1454	2.3747	1450	2.3682	1473	2.4058	14997082848	2.3617
18	1000	1.6332	941	1.5369	1050	1.7149	967	1.5793	10192504020	1.6051
19	640	1.0453	627	1.0240	681	1.1122	653	1.0665	6579838440	1.0362
20	388	0.6337	391	0.6386	451	0.7366	353	0.5765	4086538404	0.6435
21	225	0.3675	190	0.3103	237	0.3871	244	0.3985	2399507844	0.3779
22	129	0.2107	116	0.1895	132	0.2156	131	0.2140	1333800036	0.2100
23	55	0.0898	63	0.1029	74	0.1209	56	0.0915	710603628	0.1119
24	41	0.0670	28	0.0457	31	0.0506	32	0.0523	354993864	0.0559
25	13	0.0212	20	0.0327	17	0.0278	17	0.0278	167819892	0.0264
26	11	0.0180	7	0.0114	6	0.0098	2	0.0033	74095248	0.0117
27	4	0.0065	1	0.0016	1	0.0016	1	0.0016	31157940	0.0049
28	1	0.0016	0	0	4	0.0065	0	0	11790760	0.0019
29	1	0.0016	1	0.0016	0	0	0	0	4236588	0.0007
30	0	0	0	0	0	0	1	0.0016	1396068	0.0002
31	0	0	0	0	0	0	0	0	388196	0.0001
32	0	0	0	0	0	0	0	0	109156	0.0000
33	0	0	0	0	0	0	0	0	22360	0.0000
34	0	0	0	0	0	0	0	0	4484	0.0000
35	0	0	0	0	0	0	0	0	624	0.0000
36	0	0	0	0	0	0	0	0	60	0.0000
37	0	0	0	0	0	0	0	0	4	0.0000
38	61228	9.9964	61228	9.9526	61228	10.0596	61228	9.9914	635013559600	10.0000

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Revalued points

Per RP method (reference)

HCP each void +3 each singleton (except K Q J) +2 singleton J +1
each doubleton (except KQ KJ QJ Qx Jx) +1 four aces and/or tens +1

Points	North		South		West		East		Theoretical
0	28	0.0457	33	0.0539	21	0.0343	29	0.0474	293805568	0.0463
1	177	0.2891	165	0.2695	165	0.2695	184	0.3005	1766279872	0.2781
2	433	0.7072	465	0.7595	467	0.7627	447	0.7301	4460756944	0.7025
3	826	1.3491	824	1.3458	799	1.3050	789	1.2886	8243807120	1.2982
4	1374	2.2441	1424	2.3257	1315	2.1477	1422	2.3225	13933491492	2.1942
5	2055	3.3563	2113	3.4510	2089	3.4118	2147	3.5066	21764214176	3.4274
6	2891	4.7217	3043	4.9699	2903	4.7413	2904	4.7429	30423163944	4.7909
7	3706	6.0528	3784	6.1802	3718	6.0724	3755	6.1328	38944701748	6.1329
8	4531	7.4002	4552	7.4345	4434	7.2418	4475	7.3087	47115157372	7.4196
9	5228	8.5386	5196	8.4863	5061	8.2658	5127	8.3736	53631235236	8.4457
10	5558	9.0775	5608	9.1592	5498	8.9796	5396	8.8130	57295091856	9.0227
11	5603	9.1510	5482	8.9534	5504	8.9894	5601	9.1478	58143902808	9.1563
12	5495	8.9747	5391	8.8048	5420	8.8522	5474	8.9404	56245617636	8.8574
13	5001	8.1678	4961	8.1025	5008	8.1793	4843	7.9098	51805296432	8.1581
14	4362	7.1242	4325	7.0638	4495	7.3414	4531	7.4002	45528936116	7.1698
15	3689	6.0250	3712	6.0626	3771	6.1589	3745	6.1165	38297308552	6.0309
16	2903	4.7413	2905	4.7446	2993	4.8883	2975	4.8589	30847863460	4.8578
17	2340	3.8218	2370	3.8708	2334	3.8120	2341	3.8234	23818563824	3.7509
18	1671	2.7291	1655	2.7030	1707	2.7879	1730	2.8255	17638216924	2.7776
19	1195	1.9517	1175	1.9191	1226	2.0024	1171	1.9125	12512959412	1.9705
20	828	1.3523	776	1.2674	854	1.3948	820	1.3393	8546506844	1.3459
21	549	0.8966	555	0.9064	623	1.0175	556	0.9081	5599172640	0.8817
22	340	0.5553	306	0.4998	336	0.5488	325	0.5308	3509161412	0.5526
23	204	0.3332	192	0.3136	208	0.3397	211	0.3446	2112451680	0.3327
24	114	0.1862	98	0.1601	147	0.2401	118	0.1927	1215549644	0.1914
25	64	0.1045	59	0.0964	63	0.1029	62	0.1013	665258884	0.1048
26	33	0.0539	31	0.0506	42	0.0686	22	0.0359	346309380	0.0545
27	17	0.0278	20	0.0327	14	0.0229	21	0.0343	171594884	0.0270
28	7	0.0114	4	0.0065	6	0.0098	6	0.0098	79694360	0.0126
29	4	0.0065	2	0.0033	4	0.0065	0	0	35006360	0.0055
30	1	0.0016	2	0.0033	3	0.0049	0	0	14392632	0.0023
31	1	0.0016	0	0	0	0	1	0.0016	5429168	0.0009
32	0	0	0	0	0	0	0	0	1895604	0.0003
33	0	0	0	0	0	0	0	0	574548	0.0001
34	0	0	0	0	0	0	0	0	153448	0.0000
35	0	0	0	0	0	0	0	0	31924	0.0000
36	0	0	0	0	0	0	0	0	5172	0.0000
37	0	0	0	0	0	0	0	0	508	0.0000
38	0	0	0	0	0	0	0	0	16	0.0000
39	61228	11.3632	61228	11.3047	61228	11.4278	61228	11.3662	635013559600	11.3682

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Playing tricks

Evaluated in half-tricks (refinements)

K Qx Kx JTx Qxx = 1 A KJ KQ Ax QJx Kxx Axx = 2
AJ AQ KJT KQx AJx AQx = 3 AK KQJ AQT AKx = 4
AQJ AKJ = 5 AKQ = 6 Each suit card over three = 2

Half-tricks	North		South		West		East		Theoretical
2	93	0.1519	106	0.1731	109	0.1780	113	0.1846	1022787584	0.1611
3	180	0.2940	163	0.2662	192	0.3136	168	0.2744	1834835968	0.2889
4	821	1.3409	845	1.3801	785	1.2821	797	1.3017	8288385280	1.3052
5	1360	2.2212	1388	2.2669	1300	2.1232	1360	2.2212	13587961408	2.1398
6	2846	4.6482	2959	4.8328	2900	4.7364	2900	4.7364	29907404912	4.7097
7	4051	6.6163	4053	6.6195	3895	6.3615	4038	6.5950	41453445520	6.5280
8	5965	9.7423	5962	9.7374	5854	9.5610	5890	9.6198	61513033480	9.6869
9	6823	11.1436	6935	11.3265	6706	10.9525	6724	10.9819	70986532496	11.1787
10	7731	12.6266	7695	12.5678	7638	12.4747	7602	12.4159	80169517920	12.6249
11	7438	12.1480	7427	12.1301	7316	11.9488	7632	12.4649	77238005980	12.1632
12	6810	11.1224	6880	11.2367	7155	11.6858	6796	11.0995	70723648784	11.1373
13	5547	9.0596	5404	8.8260	5473	8.9387	5494	8.9730	57473116632	9.0507
14	4323	7.0605	4234	6.9151	4409	7.2010	4309	7.0376	44455847496	7.0008
15	2880	4.7037	2875	4.6956	2934	4.7919	2997	4.8948	30812461108	4.8523
16	1978	3.2305	1986	3.2436	2013	3.2877	1993	3.2550	20488020544	3.2264
17	1141	1.8635	1123	1.8341	1220	1.9926	1161	1.8962	12080979332	1.9025
18	656	1.0714	619	1.0110	683	1.1155	662	1.0812	6865130592	1.0811
19	322	0.5259	312	0.5096	333	0.5439	344	0.5618	3412850548	0.5374
20	174	0.2842	154	0.2515	192	0.3136	159	0.2597	1635279380	0.2575
21	64	0.1045	78	0.1274	84	0.1372	54	0.0882	673249156	0.1060
22	21	0.0343	18	0.0294	27	0.0441	24	0.0392	269155616	0.0424
23	3	0.0049	7	0.0114	5	0.0082	5	0.0082	86893416	0.0137
24	1	0.0016	5	0.0082	4	0.0065	3	0.0049	27926304	0.0044
25	0	0	0	0	1	0.0016	3	0.0049	5652256	0.0009
26	0	0	0	0	0	0	0	0	1437888	0.0002
25	61228	10.7206	61228	10.6887	61228	10.7776	61228	10.7374	635013559600	10.7371

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Defensive tricks

Evaluated in half-tricks (refinements)

AK = 4 AQ = 3 A = 2 KQ = 2 K = 1

Half-tricks	North		South		West		East		Theoretical
0	5261	8.5925	5481	8.9518	5181	8.4618	5213	8.5141	54389790360	8.5651
1	5852	9.5577	6063	9.9023	5939	9.6998	5871	9.5888	61602628572	9.7010
2	11049	18.0457	10921	17.8366	10770	17.5900	11018	17.9950	113660108928	17.8988
3	9337	15.2496	9246	15.1009	9163	14.9654	9336	15.2479	96416902372	15.1834
4	10612	17.3319	10651	17.3956	10675	17.4348	10636	17.3711	111050090784	17.4878
5	7009	11.4474	7032	11.4849	7122	11.6319	7052	11.5176	72935403696	11.4856
6	5778	9.4369	5688	9.2899	5877	9.5985	5783	9.4450	59887556392	9.4309
7	3054	4.9879	2958	4.8311	3052	4.9846	3028	4.9454	31112636760	4.8995
8	1906	3.1130	1935	3.1603	2010	3.2828	1980	3.2338	20067427740	3.1602
9	777	1.2690	727	1.1874	829	1.3540	751	1.2266	7980162216	1.2567
10	403	0.6582	360	0.5880	417	0.6811	401	0.6549	4055992444	0.6387
11	119	0.1944	111	0.1813	114	0.1862	102	0.1666	1214000280	0.1912
12	49	0.0800	40	0.0653	65	0.1062	46	0.0751	502896536	0.0792
13	16	0.0261	10	0.0163	11	0.0180	8	0.0131	99889520	0.0157
14	6	0.0098	5	0.0082	2	0.0033	3	0.0049	33145000	0.0052
15	0	0	0	0	1	0.0016	0	0	3843840	0.0006
16	0	0	0	0	0	0	0	0	1084160	0.0002
17	61228	3.5598	61228	3.5240	61228	3.5904	61228	3.5611	635013559600	3.5563

Stats 8H29 Main

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Losing tricks

Evaluated for each suit (refinements)

AKQ AK A void = 0 AKx AQx KQx Ax Kx x = 1
Axx Kxx Qxx xx = 2 Jxx or worse = 3

Losers	North		South		West		East		Theoretical
0	0	0	0	0	0	0	0	0	1611768	0.0003
1	3	0.0049	6	0.0098	5	0.0082	6	0.0098	39329036	0.0062
2	37	0.0604	37	0.0604	49	0.0800	48	0.0784	454375244	0.0716
3	306	0.4998	299	0.4883	318	0.5194	279	0.4557	3126502788	0.4924
4	1365	2.2294	1305	2.1314	1387	2.2653	1361	2.2228	14069567832	2.2156
5	4168	6.8073	4074	6.6538	4297	7.0180	4239	6.9233	43541225304	6.8567
6	9187	15.0046	9064	14.8037	9322	15.2251	9086	14.8396	94901190408	14.9448
7	13860	22.6367	13953	22.7886	14158	23.1234	14199	23.1904	145807470468	22.9613
8	15214	24.8481	15076	24.6227	14746	24.0838	14898	24.3320	155515164912	24.4901
9	10686	17.4528	10949	17.8823	10543	17.2192	10696	17.4691	111719209440	17.5932
10	4926	8.0453	4988	8.1466	4979	8.1319	4963	8.1058	51111464400	8.0489
11	1342	2.1918	1338	2.1853	1264	2.0644	1308	2.1363	13274928000	2.0905
12	134	0.2189	139	0.2270	160	0.2613	145	0.2368	1451520000	0.2286
13	61228	7.5611	61228	7.5788	61228	7.5390	61228	7.5569	635013559600	7.5566

Stats 8H29 Main

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Longest suit

Number of cards in longest suit

Length	North		South		West		East		Theoretical
4	21728	35.4870	21448	35.0297	21567	35.2241	21414	34.9742	222766089260	35.0805
5	27015	44.1220	27180	44.3915	27121	44.2951	27073	44.2167	281562853572	44.3397
6	10096	16.4892	10191	16.6443	10129	16.5431	10202	16.6623	105080049360	16.5477
7	2093	3.4184	2095	3.4216	2079	3.3955	2208	3.6062	22394644272	3.5266
8	264	0.4312	290	0.4736	304	0.4965	293	0.4785	2963997036	0.4668
9	31	0.0506	22	0.0359	26	0.0425	36	0.0588	235237860	0.0370
10	1	0.0016	2	0.0033	2	0.0033	2	0.0033	10455016	0.0016
11	0	0	0	0	0	0	0	0	231192	0.0000
12	0	0	0	0	0	0	0	0	2028	0.0000
13	0	0	0	0	0	0	0	0	4	0.0000
10	61228	4.8934	61228	4.9004	61228	4.8979	61228	4.9059	635013559600	4.9008

Stats 8H29 Main

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Shortest suit

Number of cards in shortest suit

Length	North		South		West		East		Theoretical
0	3132	5.1153	2973	4.8556	3091	5.0483	3077	5.0255	32427298180	5.1066
1	18459	30.1480	18583	30.3505	18909	30.8829	18661	30.4779	194023212812	30.5542
2	33115	54.0847	33153	54.1468	32755	53.4968	33056	53.9884	341657192448	53.8031
3	6522	10.6520	6519	10.6471	6473	10.5720	6434	10.5083	66905856160	10.5361
4	61228	1.7027	61228	1.7059	61228	1.6959	61228	1.6998	635013559600	1.6977

Stats 8H29 Main

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Rank sum

Ace = 14 King = 13 Queen = 12 Jack = 11 Ten = 10 … Two = 2

Sum	North		South		West		East		Theoretical
41	0	0	0	0	0	0	0	0	4	0.0000
42	0	0	0	0	0	0	0	0	28	0.0000
43	0	0	0	0	0	0	0	0	116	0.0000
44	0	0	0	0	0	0	0	0	392	0.0000
45	0	0	0	0	0	0	0	0	1132	0.0000
46	0	0	0	0	0	0	0	0	2928	0.0000
47	0	0	0	0	0	0	0	0	6916	0.0000
48	0	0	0	0	0	0	0	0	15308	0.0000
49	0	0	0	0	0	0	0	0	31884	0.0000
50	0	0	0	0	0	0	0	0	63344	0.0000
51	0	0	0	0	0	0	0	0	120504	0.0000
52	0	0	0	0	0	0	0	0	221128	0.0000
53	0	0	0	0	0	0	0	0	392460	0.0001
54	1	0.0016	0	0	0	0	0	0	676704	0.0001
55	0	0	0	0	0	0	0	0	1135720	0.0002
56	0	0	0	0	1	0.0016	1	0.0016	1860884	0.0003
57	0	0	0	0	0	0	0	0	2980992	0.0005
58	0	0	0	0	0	0	0	0	4678132	0.0007
59	0	0	0	0	0	0	0	0	7200352	0.0011
60	0	0	1	0.0016	1	0.0016	0	0	10885276	0.0017
61	0	0	2	0.0033	2	0.0033	0	0	16177656	0.0025
62	1	0.0016	3	0.0049	0	0	2	0.0033	23662872	0.0037
63	2	0.0033	3	0.0049	6	0.0098	4	0.0065	34088292	0.0054
64	1	0.0016	10	0.0163	7	0.0114	3	0.0049	48406056	0.0076
65	8	0.0131	2	0.0033	6	0.0098	5	0.0082	67796512	0.0107
66	3	0.0049	12	0.0196	6	0.0098	6	0.0098	93717520	0.0148
67	15	0.0245	20	0.0327	12	0.0196	9	0.0147	127923728	0.0201
68	15	0.0245	10	0.0163	8	0.0131	20	0.0327	172518652	0.0272
69	25	0.0408	15	0.0245	21	0.0343	32	0.0523	229959256	0.0362
70	30	0.0490	28	0.0457	20	0.0327	21	0.0343	303102568	0.0477
71	44	0.0719	42	0.0686	32	0.0523	36	0.0588	395185876	0.0622
72	62	0.1013	45	0.0735	58	0.0947	55	0.0898	509855124	0.0803
73	60	0.0980	75	0.1225	68	0.1111	69	0.1127	651106144	0.1025
74	86	0.1405	89	0.1454	75	0.1225	77	0.1258	823287808	0.1296
75	98	0.1601	107	0.1748	92	0.1503	104	0.1699	1030988200	0.1624
76	137	0.2238	136	0.2221	143	0.2336	122	0.1993	1279004300	0.2014
77	160	0.2613	157	0.2564	157	0.2564	159	0.2597	1572168200	0.2476
78	193	0.3152	199	0.3250	171	0.2793	194	0.3168	1915276928	0.3016
79	198	0.3234	207	0.3381	214	0.3495	226	0.3691	2312858508	0.3642
80	261	0.4263	284	0.4638	287	0.4687	260	0.4246	2769074104	0.4361
81	284	0.4638	314	0.5128	300	0.4900	322	0.5259	3287427876	0.5177
82	373	0.6092	376	0.6141	336	0.5488	392	0.6402	3870662368	0.6095
83	434	0.7088	459	0.7497	440	0.7186	419	0.6843	4520438996	0.7119
84	498	0.8134	519	0.8477	506	0.8264	537	0.8770	5237248656	0.8247
85	549	0.8966	570	0.9309	556	0.9081	572	0.9342	6020098480	0.9480
86	675	1.1024	665	1.0861	651	1.0632	694	1.1335	6866482488	1.0813
87	788	1.2870	767	1.2527	704	1.1498	769	1.2560	7772102604	1.2239
88	859	1.4030	863	1.4095	848	1.3850	863	1.4095	8730942544	1.3749
89	955	1.5597	921	1.5042	897	1.4650	928	1.5156	9735066676	1.5330
90	1059	1.7296	989	1.6153	1072	1.7508	1066	1.7410	10774819856	1.6968
91	1117	1.8243	1161	1.8962	1115	1.8211	1157	1.8897	11838737216	1.8643
92	1223	1.9975	1268	2.0709	1238	2.0220	1278	2.0873	12913893708	2.0336
93	1349	2.2032	1351	2.2065	1343	2.1934	1337	2.1836	13985920668	2.2025
94	1467	2.3960	1427	2.3306	1470	2.4009	1403	2.2914	15039510420	2.3684
95	1555	2.5397	1595	2.6050	1473	2.4058	1525	2.4907	16058532536	2.5288
96	1652	2.6981	1664	2.7177	1641	2.6801	1666	2.7210	17026650064	2.6813
97	1770	2.8908	1682	2.7471	1718	2.8059	1729	2.8239	17927508472	2.8232
98	1767	2.8859	1885	3.0787	1734	2.8320	1808	2.9529	18745417740	2.9520
99	1868	3.0509	1946	3.1783	1906	3.1130	1878	3.0672	19465543056	3.0654
100	1927	3.1473	1927	3.1473	1924	3.1424	1948	3.1816	20074598356	3.1613
101	2027	3.3106	2013	3.2877	1994	3.2567	1941	3.1701	20560978696	3.2379
102	2046	3.3416	2051	3.3498	1983	3.2387	1944	3.1750	20915379072	3.2937
103	2024	3.3057	2040	3.3318	2104	3.4363	2011	3.2844	21130820080	3.3276
104	2000	3.2665	2005	3.2746	2005	3.2746	2048	3.3449	21203133328	3.3390
105	2117	3.4576	2033	3.3204	2030	3.3155	2039	3.3302	21130820080	3.3276
106	2007	3.2779	2017	3.2942	1991	3.2518	1971	3.2191	20915379072	3.2937
107	2004	3.2730	1981	3.2354	1976	3.2273	1983	3.2387	20560978696	3.2379
108	1863	3.0427	1839	3.0035	1905	3.1113	1889	3.0852	20074598356	3.1613
109	1817	2.9676	1907	3.1146	1930	3.1522	1918	3.1326	19465543056	3.0654
110	1830	2.9888	1727	2.8206	1769	2.8892	1782	2.9104	18745417740	2.9520
111	1695	2.7683	1727	2.8206	1727	2.8206	1628	2.6589	17927508472	2.8232
112	1632	2.6654	1661	2.7128	1697	2.7716	1652	2.6981	17026650064	2.6813
113	1569	2.5626	1506	2.4597	1560	2.5479	1612	2.6328	16058532536	2.5288
114	1428	2.3323	1510	2.4662	1467	2.3960	1529	2.4972	15039510420	2.3684
115	1371	2.2392	1318	2.1526	1369	2.2359	1336	2.1820	13985920668	2.2025
116	1263	2.0628	1276	2.0840	1291	2.1085	1280	2.0905	12913893708	2.0336
117	1124	1.8358	1125	1.8374	1154	1.8848	1126	1.8390	11838737216	1.8643
118	1081	1.7655	1029	1.6806	1074	1.7541	1065	1.7394	10774819856	1.6968
119	965	1.5761	913	1.4911	994	1.6234	908	1.4830	9735066676	1.5330
120	830	1.3556	828	1.3523	845	1.3801	898	1.4666	8730942544	1.3749
121	737	1.2037	728	1.1890	749	1.2233	737	1.2037	7772102604	1.2239
122	653	1.0665	662	1.0812	661	1.0796	628	1.0257	6866482488	1.0813
123	597	0.9750	599	0.9783	614	1.0028	566	0.9244	6020098480	0.9480
124	500	0.8166	486	0.7938	491	0.8019	520	0.8493	5237248656	0.8247
125	427	0.6974	416	0.6794	451	0.7366	420	0.6860	4520438996	0.7119
126	397	0.6484	367	0.5994	374	0.6108	378	0.6174	3870662368	0.6095
127	307	0.5014	301	0.4916	312	0.5096	325	0.5308	3287427876	0.5177
128	262	0.4279	272	0.4442	267	0.4361	287	0.4687	2769074104	0.4361
129	220	0.3593	220	0.3593	221	0.3609	207	0.3381	2312858508	0.3642
130	170	0.2777	198	0.3234	191	0.3119	173	0.2826	1915276928	0.3016
131	140	0.2287	120	0.1960	167	0.2728	158	0.2581	1572168200	0.2476
132	141	0.2303	145	0.2368	147	0.2401	125	0.2042	1279004300	0.2014
133	91	0.1486	107	0.1748	110	0.1797	97	0.1584	1030988200	0.1624
134	69	0.1127	79	0.1290	93	0.1519	81	0.1323	823287808	0.1296
135	58	0.0947	55	0.0898	51	0.0833	62	0.1013	651106144	0.1025
136	42	0.0686	41	0.0670	47	0.0768	50	0.0817	509855124	0.0803
137	46	0.0751	32	0.0523	49	0.0800	40	0.0653	395185876	0.0622
138	26	0.0425	16	0.0261	27	0.0441	25	0.0408	303102568	0.0477
139	24	0.0392	24	0.0392	18	0.0294	21	0.0343	229959256	0.0362
140	27	0.0441	11	0.0180	19	0.0310	25	0.0408	172518652	0.0272
141	11	0.0180	10	0.0163	13	0.0212	11	0.0180	127923728	0.0201
142	6	0.0098	10	0.0163	14	0.0229	13	0.0212	93717520	0.0148
143	4	0.0065	10	0.0163	6	0.0098	9	0.0147	67796512	0.0107
144	2	0.0033	7	0.0114	3	0.0049	1	0.0016	48406056	0.0076
145	7	0.0114	2	0.0033	2	0.0033	6	0.0098	34088292	0.0054
146	1	0.0016	4	0.0065	2	0.0033	4	0.0065	23662872	0.0037
147	0	0	1	0.0016	1	0.0016	1	0.0016	16177656	0.0025
148	1	0.0016	1	0.0016	2	0.0033	1	0.0016	10885276	0.0017
149	0	0	1	0.0016	0	0	1	0.0016	7200352	0.0011
150	0	0	1	0.0016	1	0.0016	0	0	4678132	0.0007
151	0	0	0	0	0	0	0	0	2980992	0.0005
152	0	0	0	0	0	0	0	0	1860884	0.0003
153	0	0	0	0	1	0.0016	0	0	1135720	0.0002
154	0	0	0	0	0	0	0	0	676704	0.0001
155	0	0	0	0	0	0	0	0	392460	0.0001
156	0	0	0	0	0	0	0	0	221128	0.0000
157	0	0	0	0	0	0	0	0	120504	0.0000
158	0	0	0	0	0	0	0	0	63344	0.0000
159	0	0	0	0	0	0	0	0	31884	0.0000
160	0	0	0	0	0	0	0	0	15308	0.0000
161	0	0	0	0	0	0	0	0	6916	0.0000
162	0	0	0	0	0	0	0	0	2928	0.0000
163	0	0	0	0	0	0	0	0	1132	0.0000
164	0	0	0	0	0	0	0	0	392	0.0000
165	0	0	0	0	0	0	0	0	116	0.0000
166	0	0	0	0	0	0	0	0	28	0.0000
167	0	0	0	0	0	0	0	0	4	0.0000
127	61228	103.9801	61228	103.8889	61228	104.1532	61228	103.9779	635013559600	104.0000

Stats 8H29 Main

Top RP BBO Matches

Spades

Number of spades in hand

Spades	North		South		West		East		Theoretical
0	758	1.2380	721	1.1776	801	1.3082	703	1.1482	8122425444	1.2791
1	4846	7.9147	4818	7.8689	5024	8.2054	5033	8.2201	50840366668	8.0062
2	12486	20.3926	12732	20.7944	12437	20.3126	12618	20.6082	130732371432	20.5873
3	17649	28.8250	17796	29.0651	17379	28.3841	17557	28.6748	181823183256	28.6330
4	14824	24.2111	14433	23.5725	14733	24.0625	14594	23.8355	151519319380	23.8608
5	7536	12.3081	7570	12.3636	7658	12.5073	7611	12.4306	79181063676	12.4692
6	2533	4.1370	2551	4.1664	2573	4.2023	2505	4.0913	26393687892	4.1564
7	522	0.8526	535	0.8738	526	0.8591	537	0.8770	5598661068	0.8817
8	66	0.1078	69	0.1127	87	0.1421	64	0.1045	740999259	0.1167
9	8	0.0131	3	0.0049	10	0.0163	6	0.0098	58809465	0.0093
10	0	0	0	0	0	0	0	0	2613754	0.0004
11	0	0	0	0	0	0	0	0	57798	0.0000
12	0	0	0	0	0	0	0	0	507	0.0000
13	0	0	0	0	0	0	0	0	1	0.0000
14	61228	3.2533	61228	3.2482	61228	3.2528	61228	3.2457	635013559600	3.2500

Stats 8H29 Main

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Hearts

Number of hearts in hand

Hearts	North		South		West		East		Theoretical
0	761	1.2429	729	1.1906	794	1.2968	821	1.3409	8122425444	1.2791
1	4873	7.9588	4849	7.9196	4919	8.0339	4871	7.9555	50840366668	8.0062
2	12853	20.9920	12625	20.6197	12503	20.4204	12734	20.7977	130732371432	20.5873
3	17520	28.6144	17554	28.6699	17495	28.5735	17444	28.4902	181823183256	28.6330
4	14606	23.8551	14446	23.5938	14649	23.9253	14660	23.9433	151519319380	23.8608
5	7515	12.2738	7817	12.7670	7673	12.5318	7513	12.2705	79181063676	12.4692
6	2492	4.0700	2597	4.2415	2590	4.2301	2546	4.1582	26393687892	4.1564
7	534	0.8721	524	0.8558	520	0.8493	561	0.9162	5598661068	0.8817
8	68	0.1111	79	0.1290	77	0.1258	69	0.1127	740999259	0.1167
9	5	0.0082	7	0.0114	8	0.0131	8	0.0131	58809465	0.0093
10	1	0.0016	1	0.0016	0	0	1	0.0016	2613754	0.0004
11	0	0	0	0	0	0	0	0	57798	0.0000
12	0	0	0	0	0	0	0	0	507	0.0000
13	0	0	0	0	0	0	0	0	1	0.0000
14	61228	3.2408	61228	3.2597	61228	3.2541	61228	3.2455	635013559600	3.2500

Stats 8H29 Main

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Diamonds

Number of diamonds in hand

Diamonds	North		South		West		East		Theoretical
0	791	1.2919	774	1.2641	723	1.1808	748	1.2217	8122425444	1.2791
1	4840	7.9049	4895	7.9947	4886	7.9800	4773	7.7955	50840366668	8.0062
2	12683	20.7144	12692	20.7291	12529	20.4629	12761	20.8418	130732371432	20.5873
3	17567	28.6911	17606	28.7548	17600	28.7450	17680	28.8757	181823183256	28.6330
4	14533	23.7359	14565	23.7881	14691	23.9939	14400	23.5187	151519319380	23.8608
5	7746	12.6511	7518	12.2787	7711	12.5939	7675	12.5351	79181063676	12.4692
6	2491	4.0684	2589	4.2285	2512	4.1027	2554	4.1713	26393687892	4.1564
7	513	0.8379	519	0.8477	497	0.8117	540	0.8819	5598661068	0.8817
8	54	0.0882	63	0.1029	73	0.1192	84	0.1372	740999259	0.1167
9	10	0.0163	7	0.0114	6	0.0098	13	0.0212	58809465	0.0093
10	0	0	0	0	0	0	0	0	2613754	0.0004
11	0	0	0	0	0	0	0	0	57798	0.0000
12	0	0	0	0	0	0	0	0	507	0.0000
13	0	0	0	0	0	0	0	0	1	0.0000
14	61228	3.2473	61228	3.2449	61228	3.2543	61228	3.2535	635013559600	3.2500

Stats 8H29 Main

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Clubs

Number of clubs in hand

Clubs	North		South		West		East		Theoretical
0	826	1.3491	753	1.2298	785	1.2821	808	1.3197	8122425444	1.2791
1	4809	7.8542	4909	8.0176	5033	8.2201	4906	8.0127	50840366668	8.0062
2	12471	20.3681	12633	20.6327	12570	20.5298	12605	20.5870	130732371432	20.5873
3	17537	28.6421	17648	28.8234	17609	28.7597	17426	28.4608	181823183256	28.6330
4	14716	24.0348	14528	23.7277	14636	23.9041	14531	23.7326	151519319380	23.8608
5	7624	12.4518	7651	12.4959	7488	12.2297	7661	12.5122	79181063676	12.4692
6	2637	4.3069	2504	4.0896	2500	4.0831	2635	4.3036	26393687892	4.1564
7	524	0.8558	517	0.8444	536	0.8754	570	0.9309	5598661068	0.8817
8	76	0.1241	79	0.1290	67	0.1094	76	0.1241	740999259	0.1167
9	8	0.0131	5	0.0082	2	0.0033	9	0.0147	58809465	0.0093
10	0	0	1	0.0016	2	0.0033	1	0.0016	2613754	0.0004
11	0	0	0	0	0	0	0	0	57798	0.0000
12	0	0	0	0	0	0	0	0	507	0.0000
13	0	0	0	0	0	0	0	0	1	0.0000
14	61228	3.2586	61228	3.2471	61228	3.2389	61228	3.2554	635013559600	3.2500

Stats 8H29 Main

Top RP BBO Matches

Spade tricks

Evaluated in half-tricks (refinements)

K Qx Kx JTx Qxx = 1 A KJ KQ Ax QJx Kxx Axx = 2
AJ AQ KJT KQx AJx AQx = 3 AK KQJ AQT AKx = 4
AQJ AKJ = 5 AKQ = 6 Each spade over three = 2

Half-tricks	North		South		West		East		Theoretical
0	19111	31.2128	19323	31.5591	18841	30.7719	19249	31.4382	197767203572	31.1438
1	6096	9.9562	6232	10.1783	6060	9.8974	6061	9.8991	63728659696	10.0358
2	11177	18.2547	11258	18.3870	11297	18.4507	11280	18.4229	117497308188	18.5031
3	4361	7.1226	4282	6.9935	4334	7.0785	4172	6.8139	44251732564	6.9686
4	6895	11.2612	6624	10.8186	6797	11.1011	6853	11.1926	69892220632	11.0064
5	3410	5.5693	3331	5.4403	3517	5.7441	3453	5.6396	35355647184	5.5677
6	3626	5.9221	3633	5.9336	3751	6.1263	3529	5.7637	38137887788	6.0058
7	2118	3.4592	2111	3.4478	2132	3.4821	2267	3.7026	22333120524	3.5170
8	1767	2.8859	1793	2.9284	1724	2.8157	1764	2.8810	18324133672	2.8856
9	1029	1.6806	1017	1.6610	1085	1.7721	1012	1.6528	10700471262	1.6851
10	806	1.3164	777	1.2690	804	1.3131	727	1.1874	8001815952	1.2601
11	350	0.5716	373	0.6092	351	0.5733	372	0.6076	3827056779	0.6027
12	283	0.4622	259	0.4230	299	0.4883	287	0.4687	2981489082	0.4695
13	80	0.1307	89	0.1454	90	0.1470	88	0.1437	911999088	0.1436
14	87	0.1421	90	0.1470	101	0.1650	79	0.1290	907310781	0.1429
15	14	0.0229	16	0.0261	18	0.0294	17	0.0278	194194611	0.0306
16	12	0.0196	17	0.0278	19	0.0310	13	0.0212	158762708	0.0250
17	3	0.0049	1	0.0016	2	0.0033	2	0.0033	12840295	0.0020
18	3	0.0049	2	0.0033	6	0.0098	3	0.0049	27645475	0.0044
19	0	0	0	0	0	0	0	0	493506	0.0001
20	0	0	0	0	0	0	0	0	1516827	0.0002
22	0	0	0	0	0	0	0	0	48945	0.0000
24	0	0	0	0	0	0	0	0	468	0.0000
26	0	0	0	0	0	0	0	0	1	0.0000
24	61228	2.6820	61228	2.6586	61228	2.7145	61228	2.6734	635013559600	2.6843

Stats 8H29 Main

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Heart tricks

Evaluated in half-tricks (refinements)

K Qx Kx JTx Qxx = 1 A KJ KQ Ax QJx Kxx Axx = 2
AJ AQ KJT KQx AJx AQx = 3 AK KQJ AQT AKx = 4
AQJ AKJ = 5 AKQ = 6 Each heart over three = 2

Half-tricks	North		South		West		East		Theoretical
0	19091	31.1802	18985	31.0071	19017	31.0593	19290	31.5052	197767203572	31.1438
1	6132	10.0150	6204	10.1326	6029	9.8468	6066	9.9072	63728659696	10.0358
2	11373	18.5748	11191	18.2776	11378	18.5830	11340	18.5209	117497308188	18.5031
3	4471	7.3022	4359	7.1193	4261	6.9592	4211	6.8776	44251732564	6.9686
4	6782	11.0766	6790	11.0897	6735	10.9999	6678	10.9068	69892220632	11.0064
5	3333	5.4436	3305	5.3979	3457	5.6461	3337	5.4501	35355647184	5.5677
6	3623	5.9172	3673	5.9989	3719	6.0740	3623	5.9172	38137887788	6.0058
7	2113	3.4510	2253	3.6797	2132	3.4821	2227	3.6372	22333120524	3.5170
8	1724	2.8157	1766	2.8843	1768	2.8876	1752	2.8614	18324133672	2.8856
9	1001	1.6349	1068	1.7443	1054	1.7214	1047	1.7100	10700471262	1.6851
10	742	1.2119	767	1.2527	792	1.2935	746	1.2184	8001815952	1.2601
11	341	0.5569	352	0.5749	373	0.6092	405	0.6615	3827056779	0.6027
12	288	0.4704	283	0.4622	286	0.4671	284	0.4638	2981489082	0.4695
13	92	0.1503	98	0.1601	103	0.1682	94	0.1535	911999088	0.1436
14	90	0.1470	91	0.1486	83	0.1356	90	0.1470	907310781	0.1429
15	14	0.0229	20	0.0327	20	0.0327	17	0.0278	194194611	0.0306
16	15	0.0245	16	0.0261	16	0.0261	14	0.0229	158762708	0.0250
17	1	0.0016	3	0.0049	1	0.0016	1	0.0016	12840295	0.0020
18	1	0.0016	3	0.0049	4	0.0065	5	0.0082	27645475	0.0044
19	0	0	0	0	0	0	0	0	493506	0.0001
20	1	0.0016	1	0.0016	0	0	1	0.0016	1516827	0.0002
22	0	0	0	0	0	0	0	0	48945	0.0000
24	0	0	0	0	0	0	0	0	468	0.0000
26	0	0	0	0	0	0	0	0	1	0.0000
24	61228	2.6622	61228	2.6959	61228	2.6991	61228	2.6777	635013559600	2.6843

Stats 8H29 Main

Top RP BBO Matches

Diamond tricks

Evaluated in half-tricks (refinements)

K Qx Kx JTx Qxx = 1 A KJ KQ Ax QJx Kxx Axx = 2
AJ AQ KJT KQx AJx AQx = 3 AK KQJ AQT AKx = 4
AQJ AKJ = 5 AKQ = 6 Each diamond over three = 2

Half-tricks	North		South		West		East		Theoretical
0	19062	31.1328	19123	31.2324	18887	30.8470	19042	31.1002	197767203572	31.1438
1	6256	10.2175	6260	10.2241	6124	10.0020	6195	10.1179	63728659696	10.0358
2	11339	18.5193	11425	18.6598	11406	18.6287	11398	18.6157	117497308188	18.5031
3	4243	6.9298	4197	6.8547	4282	6.9935	4257	6.9527	44251732564	6.9686
4	6650	10.8610	6747	11.0195	6807	11.1175	6667	10.8888	69892220632	11.0064
5	3359	5.4861	3307	5.4011	3412	5.5726	3364	5.4942	35355647184	5.5677
6	3781	6.1753	3636	5.9385	3682	6.0136	3707	6.0544	38137887788	6.0058
7	2226	3.6356	2157	3.5229	2207	3.6046	2104	3.4363	22333120524	3.5170
8	1708	2.7896	1710	2.7928	1789	2.9219	1832	2.9921	18324133672	2.8856
9	1024	1.6724	1008	1.6463	1013	1.6545	988	1.6136	10700471262	1.6851
10	747	1.2200	785	1.2821	758	1.2380	811	1.3246	8001815952	1.2601
11	373	0.6092	382	0.6239	381	0.6223	362	0.5912	3827056779	0.6027
12	254	0.4148	284	0.4638	280	0.4573	266	0.4344	2981489082	0.4695
13	82	0.1339	99	0.1617	75	0.1225	83	0.1356	911999088	0.1436
14	95	0.1552	74	0.1209	83	0.1356	103	0.1682	907310781	0.1429
15	12	0.0196	14	0.0229	24	0.0392	19	0.0310	194194611	0.0306
16	10	0.0163	15	0.0245	13	0.0212	18	0.0294	158762708	0.0250
17	1	0.0016	2	0.0033	1	0.0016	4	0.0065	12840295	0.0020
18	6	0.0098	3	0.0049	4	0.0065	8	0.0131	27645475	0.0044
19	0	0	0	0	0	0	0	0	493506	0.0001
20	0	0	0	0	0	0	0	0	1516827	0.0002
22	0	0	0	0	0	0	0	0	48945	0.0000
24	0	0	0	0	0	0	0	0	468	0.0000
26	0	0	0	0	0	0	0	0	1	0.0000
24	61228	2.6734	61228	2.6656	61228	2.6943	61228	2.6844	635013559600	2.6843

Stats 8H29 Main

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Club tricks

Evaluated in half-tricks (refinements)

K Qx Kx JTx Qxx = 1 A KJ KQ Ax QJx Kxx Axx = 2
AJ AQ KJT KQx AJx AQx = 3 AK KQJ AQT AKx = 4
AQJ AKJ = 5 AKQ = 6 Each club over three = 2

Half-tricks	North		South		West		East		Theoretical
0	19022	31.0675	19074	31.1524	19247	31.4350	19100	31.1949	197767203572	31.1438
1	6028	9.8452	6213	10.1473	5979	9.7651	6076	9.9236	63728659696	10.0358
2	11359	18.5520	11447	18.6957	11310	18.4719	11359	18.5520	117497308188	18.5031
3	4212	6.8792	4205	6.8678	4432	7.2385	4167	6.8057	44251732564	6.9686
4	6789	11.0881	6723	10.9803	6694	10.9329	6710	10.9590	69892220632	11.0064
5	3410	5.5693	3386	5.5301	3451	5.6363	3442	5.6216	35355647184	5.5677
6	3659	5.9760	3677	6.0054	3617	5.9074	3653	5.9662	38137887788	6.0058
7	2205	3.6013	2147	3.5066	2125	3.4706	2087	3.4086	22333120524	3.5170
8	1846	3.0150	1779	2.9055	1731	2.8271	1786	2.9170	18324133672	2.8856
9	1048	1.7116	980	1.6006	1014	1.6561	1145	1.8701	10700471262	1.6851
10	754	1.2315	768	1.2543	784	1.2805	781	1.2756	8001815952	1.2601
11	400	0.6533	340	0.5553	384	0.6272	359	0.5863	3827056779	0.6027
12	276	0.4508	278	0.4540	249	0.4067	330	0.5390	2981489082	0.4695
13	83	0.1356	87	0.1421	94	0.1535	84	0.1372	911999088	0.1436
14	92	0.1503	77	0.1258	79	0.1290	108	0.1764	907310781	0.1429
15	24	0.0392	20	0.0327	17	0.0278	19	0.0310	194194611	0.0306
16	18	0.0294	22	0.0359	17	0.0278	16	0.0261	158762708	0.0250
17	0	0	1	0.0016	1	0.0016	4	0.0065	12840295	0.0020
18	3	0.0049	4	0.0065	2	0.0033	2	0.0033	27645475	0.0044
19	0	0	0	0	0	0	0	0	493506	0.0001
20	0	0	0	0	1	0.0016	0	0	1516827	0.0002
22	0	0	0	0	0	0	0	0	48945	0.0000
24	0	0	0	0	0	0	0	0	468	0.0000
26	0	0	0	0	0	0	0	0	1	0.0000
24	61228	2.7030	61228	2.6686	61228	2.6696	61228	2.7019	635013559600	2.6843

Stats 8H29 Main

Top RP BBO Matches

Spade control

Spade stop = 16 Half-stop = 8 1st rd control = 4 2nd rd = 2 3rd rd = 1

Bitmap	North		South		West		East		Theoretical
00000	6787	11.0848	6738	11.0048	6406	10.4625	6647	10.8561	68236672504	10.7457
00001	7247	11.8361	7346	11.9978	7091	11.5813	7365	12.0288	75422521980	11.8773
00011	4140	6.7616	4108	6.7093	4225	6.9004	4278	6.9870	43018771796	6.7745
00111	758	1.2380	721	1.1776	801	1.3082	703	1.1482	8122425444	1.2791
01000	3572	5.8339	3802	6.2096	3696	6.0365	3712	6.0626	38199411536	6.0155
01001	1622	2.6491	1662	2.7144	1614	2.6360	1550	2.5315	16760560440	2.6394
01011	348	0.5684	347	0.5667	394	0.6435	374	0.6108	3910797436	0.6159
10000	3180	5.1937	3279	5.3554	3215	5.2509	3195	5.2182	33507777940	5.2767
10001	6910	11.2857	6992	11.4196	6774	11.0636	6776	11.0668	71592376960	11.2741
10010	6938	11.3314	6697	10.9378	6979	11.3984	6823	11.1436	71592376960	11.2741
10011	4406	7.1961	4522	7.3855	4490	7.3332	4454	7.2744	45896476704	7.2276
10100	6896	11.2628	6773	11.0619	6950	11.3510	6981	11.4016	71592376960	11.2741
10101	4373	7.1422	4395	7.1781	4484	7.3234	4413	7.2075	45896476704	7.2276
10110	2758	4.5045	2559	4.1795	2698	4.4065	2651	4.3297	27459860220	4.3243
10111	1293	2.1118	1287	2.1020	1411	2.3045	1306	2.1330	13804676016	2.1739
15	61228	12.5611	61228	12.5001	61228	12.6789	61228	12.5316	635013559600	12.5855

Stats 8H29 Main

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Heart control

Heart stop = 16 Half-stop = 8 1st rd control = 4 2nd rd = 2 3rd rd = 1

Bitmap	North		South		West		East		Theoretical
00000	6502	10.6193	6526	10.6585	6512	10.6357	6684	10.9166	68236672504	10.7457
00001	7420	12.1186	7232	11.8116	7249	11.8394	7442	12.1546	75422521980	11.8773
00011	4108	6.7093	4062	6.6342	4126	6.7387	4111	6.7142	43018771796	6.7745
00111	761	1.2429	729	1.1906	794	1.2968	821	1.3409	8122425444	1.2791
01000	3713	6.0642	3765	6.1491	3763	6.1459	3615	5.9042	38199411536	6.0155
01001	1633	2.6671	1587	2.5920	1519	2.4809	1610	2.6295	16760560440	2.6394
01011	378	0.6174	407	0.6647	427	0.6974	359	0.5863	3910797436	0.6159
10000	3241	5.2933	3240	5.2917	3164	5.1676	3199	5.2247	33507777940	5.2767
10001	7060	11.5307	6967	11.3788	6836	11.1648	6864	11.2106	71592376960	11.2741
10010	6728	10.9884	6979	11.3984	6997	11.4278	6823	11.1436	71592376960	11.2741
10011	4396	7.1797	4500	7.3496	4410	7.2026	4425	7.2271	45896476704	7.2276
10100	6828	11.1518	6870	11.2204	6858	11.2008	6768	11.0538	71592376960	11.2741
10101	4530	7.3986	4457	7.2793	4521	7.3839	4463	7.2891	45896476704	7.2276
10110	2631	4.2971	2604	4.2530	2753	4.4963	2678	4.3738	27459860220	4.3243
10111	1299	2.1216	1303	2.1281	1299	2.1216	1366	2.2310	13804676016	2.1739
15	61228	12.5691	61228	12.6259	61228	12.6212	61228	12.5279	635013559600	12.5855

Stats 8H29 Main

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Diamond control

Diamond stop = 16 Half-stop = 8 1st rd control = 4 2nd rd = 2 3rd rd = 1

Bitmap	North		South		West		East		Theoretical
00000	6521	10.6504	6667	10.8888	6525	10.6569	6715	10.9672	68236672504	10.7457
00001	7253	11.8459	7268	11.8704	7231	11.8100	7248	11.8377	75422521980	11.8773
00011	4131	6.7469	4137	6.7567	4092	6.6832	4093	6.6849	43018771796	6.7745
00111	791	1.2919	774	1.2641	723	1.1808	748	1.2217	8122425444	1.2791
01000	3738	6.1050	3802	6.2096	3767	6.1524	3648	5.9581	38199411536	6.0155
01001	1664	2.7177	1686	2.7536	1641	2.6801	1677	2.7389	16760560440	2.6394
01011	357	0.5831	385	0.6288	407	0.6647	357	0.5831	3910797436	0.6159
10000	3280	5.3570	3219	5.2574	3171	5.1790	3204	5.2329	33507777940	5.2767
10001	6908	11.2824	6951	11.3526	6932	11.3216	6798	11.1028	71592376960	11.2741
10010	6886	11.2465	6838	11.1681	6806	11.1158	6937	11.3298	71592376960	11.2741
10011	4402	7.1895	4423	7.2238	4325	7.0638	4558	7.4443	45896476704	7.2276
10100	6828	11.1518	6705	10.9509	7009	11.4474	6847	11.1828	71592376960	11.2741
10101	4539	7.4133	4385	7.1618	4512	7.3692	4421	7.2206	45896476704	7.2276
10110	2662	4.3477	2680	4.3771	2736	4.4685	2718	4.4391	27459860220	4.3243
10111	1268	2.0709	1308	2.1363	1351	2.2065	1259	2.0562	13804676016	2.1739
15	61228	12.5939	61228	12.5260	61228	12.6316	61228	12.5727	635013559600	12.5855

Stats 8H29 Main

Top RP BBO Matches

Club control

Club stop = 16 Half-stop = 8 1st rd control = 4 2nd rd = 2 3rd rd = 1

Bitmap	North		South		West		East		Theoretical
00000	6549	10.6961	6655	10.8692	6598	10.7761	6632	10.8316	68236672504	10.7457
00001	7204	11.7659	7298	11.9194	7282	11.8933	7270	11.8737	75422521980	11.8773
00011	4105	6.7044	4125	6.7371	4270	6.9739	4143	6.7665	43018771796	6.7745
00111	826	1.3491	753	1.2298	785	1.2821	808	1.3197	8122425444	1.2791
01000	3680	6.0103	3654	5.9679	3711	6.0610	3625	5.9205	38199411536	6.0155
01001	1559	2.5462	1595	2.6050	1641	2.6801	1648	2.6916	16760560440	2.6394
01011	355	0.5798	400	0.6533	349	0.5700	352	0.5749	3910797436	0.6159
10000	3269	5.3391	3255	5.3162	3190	5.2100	3232	5.2786	33507777940	5.2767
10001	6853	11.1926	6992	11.4196	6891	11.2547	6823	11.1436	71592376960	11.2741
10010	6977	11.3951	6905	11.2775	6867	11.2155	6848	11.1844	71592376960	11.2741
10011	4411	7.2042	4461	7.2859	4474	7.3071	4364	7.1275	45896476704	7.2276
10100	6962	11.3706	6851	11.1893	6747	11.0195	7027	11.4768	71592376960	11.2741
10101	4458	7.2810	4359	7.1193	4438	7.2483	4363	7.1258	45896476704	7.2276
10110	2724	4.4489	2636	4.3052	2609	4.2611	2658	4.3412	27459860220	4.3243
10111	1296	2.1167	1289	2.1052	1376	2.2473	1435	2.3437	13804676016	2.1739
15	61228	12.6326	61228	12.5616	61228	12.5411	61228	12.5855	635013559600	12.5855

Stats 8H29 Main

Top RP BBO Matches

Spade quality

A = 64  K = 32  Q = 16  J = 8  10 = 4  9 = 2  8 = 1

Bitmap	North		South		West		East		Theoretical
0000000	7078	11.5601	6961	11.3690	7043	11.5029	7085	11.5715	73006209045	11.4968
0000001	2852	4.6580	2837	4.6335	2686	4.3869	2772	4.5273	28760021745	4.5290
0000010	2856	4.6645	2777	4.5355	2690	4.3934	2887	4.7152	28760021745	4.5290
0000011	981	1.6022	1012	1.6528	930	1.5189	944	1.5418	10150595910	1.5985
0000100	2740	4.4751	2814	4.5959	2759	4.5061	2842	4.6417	28760021745	4.5290
0000101	900	1.4699	965	1.5761	939	1.5336	986	1.6104	10150595910	1.5985
0000110	970	1.5842	970	1.5842	964	1.5744	1045	1.7067	10150595910	1.5985
0000111	321	0.5243	291	0.4753	336	0.5488	303	0.4949	3190187286	0.5024
0001000	2769	4.5224	2956	4.8279	2751	4.4930	2714	4.4326	28760021745	4.5290
0001001	955	1.5597	1058	1.7280	993	1.6218	1024	1.6724	10150595910	1.5985
0001010	978	1.5973	943	1.5401	984	1.6071	955	1.5597	10150595910	1.5985
0001011	281	0.4589	323	0.5275	295	0.4818	298	0.4867	3190187286	0.5024
0001100	949	1.5499	990	1.6169	989	1.6153	968	1.5810	10150595910	1.5985
0001101	298	0.4867	285	0.4655	331	0.5406	311	0.5079	3190187286	0.5024
0001110	331	0.5406	339	0.5537	276	0.4508	298	0.4867	3190187286	0.5024
0001111	76	0.1241	82	0.1339	77	0.1258	92	0.1503	886163135	0.1396
0010000	2779	4.5388	2882	4.7070	2786	4.5502	2727	4.4538	28760021745	4.5290
0010001	981	1.6022	938	1.5320	940	1.5352	922	1.5058	10150595910	1.5985
0010010	1015	1.6577	922	1.5058	979	1.5989	948	1.5483	10150595910	1.5985
0010011	320	0.5226	332	0.5422	292	0.4769	298	0.4867	3190187286	0.5024
0010100	996	1.6267	974	1.5908	928	1.5156	939	1.5336	10150595910	1.5985
0010101	294	0.4802	344	0.5618	304	0.4965	311	0.5079	3190187286	0.5024
0010110	323	0.5275	281	0.4589	311	0.5079	348	0.5684	3190187286	0.5024
0010111	82	0.1339	86	0.1405	97	0.1584	92	0.1503	886163135	0.1396
0011000	984	1.6071	1050	1.7149	964	1.5744	951	1.5532	10150595910	1.5985
0011001	286	0.4671	334	0.5455	305	0.4981	308	0.5030	3190187286	0.5024
0011010	280	0.4573	287	0.4687	296	0.4834	305	0.4981	3190187286	0.5024
0011011	73	0.1192	80	0.1307	81	0.1323	81	0.1323	886163135	0.1396
0011100	296	0.4834	327	0.5341	310	0.5063	306	0.4998	3190187286	0.5024
0011101	77	0.1258	99	0.1617	82	0.1339	70	0.1143	886163135	0.1396
0011110	84	0.1372	96	0.1568	83	0.1356	79	0.1290	886163135	0.1396
0011111	11	0.0180	13	0.0212	21	0.0343	17	0.0278	215553195	0.0339
0100000	2736	4.4685	2703	4.4146	2775	4.5322	2705	4.4179	28760021745	4.5290
0100001	977	1.5957	980	1.6006	1042	1.7018	1007	1.6447	10150595910	1.5985
0100010	1008	1.6463	916	1.4960	1007	1.6447	975	1.5924	10150595910	1.5985
0100011	327	0.5341	281	0.4589	266	0.4344	315	0.5145	3190187286	0.5024
0100100	949	1.5499	1036	1.6920	948	1.5483	973	1.5891	10150595910	1.5985
0100101	323	0.5275	320	0.5226	292	0.4769	297	0.4851	3190187286	0.5024
0100110	298	0.4867	323	0.5275	313	0.5112	288	0.4704	3190187286	0.5024
0100111	88	0.1437	93	0.1519	74	0.1209	83	0.1356	886163135	0.1396
0101000	953	1.5565	923	1.5075	983	1.6055	927	1.5140	10150595910	1.5985
0101001	300	0.4900	276	0.4508	333	0.5439	304	0.4965	3190187286	0.5024
0101010	329	0.5373	263	0.4295	298	0.4867	301	0.4916	3190187286	0.5024
0101011	75	0.1225	90	0.1470	92	0.1503	71	0.1160	886163135	0.1396
0101100	317	0.5177	314	0.5128	341	0.5569	327	0.5341	3190187286	0.5024
0101101	84	0.1372	84	0.1372	86	0.1405	100	0.1633	886163135	0.1396
0101110	72	0.1176	64	0.1045	85	0.1388	87	0.1421	886163135	0.1396
0101111	17	0.0278	18	0.0294	22	0.0359	21	0.0343	215553195	0.0339
0110000	963	1.5728	1017	1.6610	1019	1.6643	990	1.6169	10150595910	1.5985
0110001	311	0.5079	327	0.5341	317	0.5177	301	0.4916	3190187286	0.5024
0110010	324	0.5292	318	0.5194	309	0.5047	337	0.5504	3190187286	0.5024
0110011	84	0.1372	78	0.1274	79	0.1290	95	0.1552	886163135	0.1396
0110100	285	0.4655	303	0.4949	309	0.5047	297	0.4851	3190187286	0.5024
0110101	81	0.1323	80	0.1307	87	0.1421	97	0.1584	886163135	0.1396
0110110	98	0.1601	106	0.1731	116	0.1895	76	0.1241	886163135	0.1396
0110111	34	0.0555	21	0.0343	17	0.0278	24	0.0392	215553195	0.0339
0111000	325	0.5308	307	0.5014	289	0.4720	307	0.5014	3190187286	0.5024
0111001	89	0.1454	97	0.1584	89	0.1454	85	0.1388	886163135	0.1396
0111010	90	0.1470	78	0.1274	98	0.1601	91	0.1486	886163135	0.1396
0111011	23	0.0376	15	0.0245	29	0.0474	24	0.0392	215553195	0.0339
0111100	89	0.1454	87	0.1421	100	0.1633	90	0.1470	886163135	0.1396
0111101	19	0.0310	23	0.0376	27	0.0441	27	0.0441	215553195	0.0339
0111110	19	0.0310	23	0.0376	19	0.0310	25	0.0408	215553195	0.0339
0111111	5	0.0082	2	0.0033	2	0.0033	4	0.0065	45379620	0.0071
1000000	2706	4.4195	2790	4.5567	2738	4.4718	2783	4.5453	28760021745	4.5290
1000001	952	1.5548	983	1.6055	1055	1.7231	1004	1.6398	10150595910	1.5985
1000010	1049	1.7133	910	1.4862	967	1.5793	954	1.5581	10150595910	1.5985
1000011	346	0.5651	301	0.4916	334	0.5455	323	0.5275	3190187286	0.5024
1000100	934	1.5254	980	1.6006	964	1.5744	965	1.5761	10150595910	1.5985
1000101	311	0.5079	326	0.5324	315	0.5145	316	0.5161	3190187286	0.5024
1000110	309	0.5047	256	0.4181	307	0.5014	339	0.5537	3190187286	0.5024
1000111	78	0.1274	89	0.1454	89	0.1454	80	0.1307	886163135	0.1396
1001000	998	1.6300	951	1.5532	1015	1.6577	1011	1.6512	10150595910	1.5985
1001001	288	0.4704	302	0.4932	323	0.5275	306	0.4998	3190187286	0.5024
1001010	294	0.4802	313	0.5112	281	0.4589	327	0.5341	3190187286	0.5024
1001011	79	0.1290	85	0.1388	84	0.1372	83	0.1356	886163135	0.1396
1001100	316	0.5161	272	0.4442	318	0.5194	338	0.5520	3190187286	0.5024
1001101	84	0.1372	92	0.1503	81	0.1323	96	0.1568	886163135	0.1396
1001110	79	0.1290	97	0.1584	92	0.1503	99	0.1617	886163135	0.1396
1001111	18	0.0294	22	0.0359	20	0.0327	16	0.0261	215553195	0.0339
1010000	1006	1.6430	938	1.5320	986	1.6104	944	1.5418	10150595910	1.5985
1010001	301	0.4916	257	0.4197	297	0.4851	315	0.5145	3190187286	0.5024
1010010	299	0.4883	314	0.5128	317	0.5177	294	0.4802	3190187286	0.5024
1010011	80	0.1307	93	0.1519	89	0.1454	81	0.1323	886163135	0.1396
1010100	303	0.4949	336	0.5488	306	0.4998	303	0.4949	3190187286	0.5024
1010101	84	0.1372	95	0.1552	78	0.1274	71	0.1160	886163135	0.1396
1010110	90	0.1470	80	0.1307	88	0.1437	88	0.1437	886163135	0.1396
1010111	20	0.0327	16	0.0261	28	0.0457	17	0.0278	215553195	0.0339
1011000	286	0.4671	304	0.4965	338	0.5520	303	0.4949	3190187286	0.5024
1011001	79	0.1290	87	0.1421	87	0.1421	81	0.1323	886163135	0.1396
1011010	92	0.1503	84	0.1372	94	0.1535	92	0.1503	886163135	0.1396
1011011	18	0.0294	26	0.0425	13	0.0212	23	0.0376	215553195	0.0339
1011100	86	0.1405	82	0.1339	97	0.1584	69	0.1127	886163135	0.1396
1011101	21	0.0343	20	0.0327	14	0.0229	15	0.0245	215553195	0.0339
1011110	17	0.0278	24	0.0392	23	0.0376	32	0.0523	215553195	0.0339
1011111	4	0.0065	6	0.0098	1	0.0016	7	0.0114	45379620	0.0071
1100000	1013	1.6545	908	1.4830	1022	1.6692	978	1.5973	10150595910	1.5985
1100001	315	0.5145	297	0.4851	311	0.5079	308	0.5030	3190187286	0.5024
1100010	322	0.5259	289	0.4720	332	0.5422	278	0.4540	3190187286	0.5024
1100011	105	0.1715	86	0.1405	93	0.1519	96	0.1568	886163135	0.1396
1100100	303	0.4949	304	0.4965	282	0.4606	315	0.5145	3190187286	0.5024
1100101	71	0.1160	88	0.1437	76	0.1241	76	0.1241	886163135	0.1396
1100110	109	0.1780	84	0.1372	93	0.1519	87	0.1421	886163135	0.1396
1100111	21	0.0343	25	0.0408	19	0.0310	30	0.0490	215553195	0.0339
1101000	330	0.5390	285	0.4655	326	0.5324	316	0.5161	3190187286	0.5024
1101001	87	0.1421	96	0.1568	82	0.1339	82	0.1339	886163135	0.1396
1101010	82	0.1339	82	0.1339	90	0.1470	76	0.1241	886163135	0.1396
1101011	18	0.0294	20	0.0327	10	0.0163	26	0.0425	215553195	0.0339
1101100	81	0.1323	84	0.1372	88	0.1437	80	0.1307	886163135	0.1396
1101101	18	0.0294	14	0.0229	16	0.0261	22	0.0359	215553195	0.0339
1101110	29	0.0474	29	0.0474	22	0.0359	22	0.0359	215553195	0.0339
1101111	3	0.0049	4	0.0065	11	0.0180	4	0.0065	45379620	0.0071
1110000	301	0.4916	303	0.4949	345	0.5635	323	0.5275	3190187286	0.5024
1110001	90	0.1470	95	0.1552	77	0.1258	89	0.1454	886163135	0.1396
1110010	88	0.1437	67	0.1094	86	0.1405	78	0.1274	886163135	0.1396
1110011	28	0.0457	20	0.0327	29	0.0474	14	0.0229	215553195	0.0339
1110100	85	0.1388	90	0.1470	88	0.1437	92	0.1503	886163135	0.1396
1110101	18	0.0294	25	0.0408	26	0.0425	18	0.0294	215553195	0.0339
1110110	18	0.0294	15	0.0245	25	0.0408	12	0.0196	215553195	0.0339
1110111	5	0.0082	4	0.0065	2	0.0033	0	0	45379620	0.0071
1111000	76	0.1241	91	0.1486	80	0.1307	75	0.1225	886163135	0.1396
1111001	22	0.0359	19	0.0310	15	0.0245	20	0.0327	215553195	0.0339
1111010	19	0.0310	20	0.0327	21	0.0343	22	0.0359	215553195	0.0339
1111011	4	0.0065	3	0.0049	10	0.0163	3	0.0049	45379620	0.0071
1111100	22	0.0359	28	0.0457	19	0.0310	15	0.0245	215553195	0.0339
1111101	4	0.0065	4	0.0065	2	0.0033	8	0.0131	45379620	0.0071
1111110	6	0.0098	4	0.0065	5	0.0082	9	0.0147	45379620	0.0071
1111111	0	0	0	0	1	0.0016	2	0.0033	8145060	0.0013
128	61228	31.7652	61228	31.3769	61228	32.1547	61228	31.7032	635013559600	31.7500