Study 7Z76   Main

High Card Expectancy

by Richard Pavlicek

When you pick up a bridge hand, what is the chance that it will have a specific number of high-card points (HCP)? It should be no surprise that 10 is the average HCP, but how often will you have exactly 10? Also, if you’re developing a bridge system, it is useful to know which HCP ranges are more common. For example, in deciding your opening notrump range, what is the chance of 12-14 versus 15-17? And how does HCP expectancy vary with different hand patterns? The answers to these and other questions can be found in the following tables.

Basic HCP Table

HCP by Range 2-point 3-point 4-point 5-point

HCP by Pattern

Basic HCP Table

This table shows, for each HCP total, the number of ways* and specific ways it can be achieved, the number of hands containing that number of HCP, and the percent chance of its occurrence. Observe that the total of the “Hands” column agrees with 52c13 (combinations of 52 items taken 13 at a time), which is indisputably the total number of bridge hands.

*For example, there are five ways to obtain 5 HCP: (1) ace plus jack, (2) king plus queen, (3) king plus two jacks, (4) two queens plus jack, or (5) queen plus three jacks. If specific suits are considered — A plus J, A plus J, etc. (I’ll spare you the list) — there are 96 specific ways to obtain 5 HCP.

Percentages are not exact but accurate to 12 decimal places, with proper rounding from the 13th place.

The “Ways” and “Specific” columns have an interesting characteristic. Note that 20 HCP can be obtained in the most ways (31 or 4658 specific). If you move sequentially backward or forward from 20 HCP, the number of ways is an exact mirror until you reach 8 HCP and 32 HCP. This is obvious if you think about it. Selecting, say, 21 HCP is the same as selecting 19 HCP not to be held; so the combinations must be identical. The reason for the mismatch at 8 and 32 is that one of the ways to make 8 HCP is two aces; if you try to make 32 HCP with “all but two aces” you need 14 cards — hence that combination is impossible.

HCP	Ways	Specific	Hands	Percent
0	1	1	2310789600	0.363896103487
1	1	4	5006710800	0.788441557556
2	2	10	8611542576	1.356119478996
3	3	24	15636342960	2.462363633597
4	5	51	24419055136	3.845438379518
5	5	96	32933031040	5.186193356366
6	8	170	41619399184	6.554096137761
7	9	284	50979441968	8.028087148267
8	12	445	56466608128	8.892189351605
9	13	664	59413313872	9.356227591333
10	16	952	59723754816	9.405114885046
11	17	1304	56799933520	8.944680418443
12	21	1716	50971682080	8.026865144755
13	21	2184	43906944752	6.914331841931
14	24	2680	36153374224	5.693323186165
15	25	3176	28090962724	4.423679195401
16	28	3650	21024781756	3.310918552550
17	27	4064	14997082848	2.361694899468
18	30	4380	10192504020	1.605084468814
19	29	4584	6579838440	1.036172903795
20	31	4658	4086538404	0.643535613094
21	29	4584	2399507844	0.377867182161
22	30	4380	1333800036	0.210042764574
23	27	4064	710603628	0.111903693592
24	28	3650	354993864	0.055903351769
25	25	3176	167819892	0.026427765118
26	24	2680	74095248	0.011668293831
27	21	2184	31157940	0.004906657430
28	21	1716	11790760	0.001856772950
29	17	1304	4236588	0.000667164966
30	16	952	1396068	0.000219848534
31	13	664	388196	0.000061131923
32	11	439	109156	0.000017189554
33	8	268	22360	0.000003521185
34	6	148	4484	0.000000706127
35	3	64	624	0.000000098266
36	2	25	60	0.000000009449
37	1	4	4	0.000000000630
Totals	610	65399	635013559600	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

HCP by Range

The next four tables are derived from the basic table but show HCP expectancy for ranges of 2 to 5 points.

2-Point Ranges

Range	Ways	Specific	Hands	Percent
0-1	2	5	7317500400	1.152337661043
1-2	3	14	13618253376	2.144561036551
2-3	5	34	24247885536	3.818483112593
3-4	8	75	40055398096	6.307802013115
4-5	10	147	57352086176	9.031631735884
5-6	13	266	74552430224	11.740289494127
6-7	17	454	92598841152	14.582183286028
7-8	21	729	107446050096	16.920276499872
8-9	25	1109	115879922000	18.248416942938
9-10	29	1616	119137068688	18.761342476379
10-11	33	2256	116523688336	18.349795303489
11-12	38	3020	107771615600	16.971545563198
12-13	42	3900	94878626832	14.941196986686
13-14	45	4864	80060318976	12.607655028096
14-15	49	5856	64244336948	10.117002381566
15-16	53	6826	49115744480	7.734597747950
16-17	55	7714	36021864604	5.672613452017
17-18	57	8444	25189586868	3.966779368281
18-19	59	8964	16772342460	2.641257372609
19-20	60	9242	10666376844	1.679708516889
20-21	60	9242	6486046248	1.021402795255
21-22	59	8964	3733307880	0.587909946734
22-23	57	8444	2044403664	0.321946458165
23-24	55	7714	1065597492	0.167807045360
24-25	53	6826	522813756	0.082331116887
25-26	49	5856	241915140	0.038096058949
26-27	45	4864	105253188	0.016574951260
27-28	42	3900	42948700	0.006763430379
28-29	38	3020	16027348	0.002523937916
29-30	33	2256	5632656	0.000887013500
30-31	29	1616	1784264	0.000280980457
31-32	24	1103	497352	0.000078321477
32-33	19	707	131516	0.000020710739
33-34	14	416	26844	0.000004227311
34-35	9	212	5108	0.000000804392
35-36	5	89	684	0.000000107714
36-37	3	29	64	0.000000010079

3-Point Ranges

Range	Ways	Specific	Hands	Percent
0-2	4	15	15929042976	2.508457140039
1-3	6	38	29254596336	4.606924670148
2-4	10	85	48666940672	7.663921492110
3-5	13	171	72988429136	11.493995369481
4-6	18	317	98971485360	15.585727873645
5-7	22	550	125531872192	19.768376642394
6-8	29	899	149065449280	23.474372637633
7-9	34	1393	166859363968	26.276504091205
8-10	41	2061	175603676816	27.653531827984
9-11	46	2920	175937002208	27.706022894822
10-12	54	3972	167495370416	26.376660448244
11-13	59	5204	151678560352	23.885877405129
12-14	66	6580	131032001056	20.634520172851
13-15	70	8040	108151281700	17.031334223497
14-16	77	9506	85269118704	13.427920934115
15-17	80	10890	64112827328	10.096292647418
16-18	85	12094	46214368624	7.277697920830
17-19	86	13028	31769425308	5.002952272076
18-20	90	13622	20858880864	3.284792985702
19-21	89	13826	13065884688	2.057575699050
20-22	90	13622	7819846284	1.231445559828
21-23	86	13028	4443911508	0.699813640326
22-24	85	12094	2399397528	0.377849809933
23-25	80	10890	1233417384	0.194234810478
24-26	77	9506	596909004	0.093999410717
25-27	70	8040	273073080	0.043002716379
26-28	66	6580	117043948	0.018431724210
27-29	59	5204	47185288	0.007430595345
28-30	54	3972	17423416	0.002743786449
29-31	46	2920	6020852	0.000948145423
30-32	40	2055	1893420	0.000298170011
31-33	32	1371	519712	0.000081842662
32-34	25	855	136000	0.000021416866
33-35	17	480	27468	0.000004325577
34-36	11	237	5168	0.000000813841
35-37	6	93	688	0.000000108344

4-Point Ranges

Range	Ways	Specific	Hands	Percent
0-3	7	39	31565385936	4.970820773636
1-4	11	89	53673651472	8.452363049666
2-5	15	181	81599971712	12.850114848477
3-6	21	341	114607828320	18.048091507242
4-7	27	601	149950927328	23.613815021912
5-8	34	995	181998480320	28.660565993999
6-9	42	1563	208478763152	32.830600228966
7-10	50	2345	226583118784	35.681618976251
8-11	58	3365	232403610336	36.598212246427
9-12	67	4636	226908684288	35.732888039577
10-13	75	6156	211402315168	33.290992290175
11-14	83	7884	187831934576	29.579200591294
12-15	91	9756	159122963780	25.058199368252
13-16	98	11690	129176063456	20.342252776046
14-17	104	13570	100266201552	15.789615833583
15-18	110	15270	74305331348	11.701377116231
16-19	114	16678	52794207064	8.313870824625
17-20	117	17686	35855963712	5.646487885170
18-21	119	18206	23258388708	3.662660167863
19-22	119	18206	14399684724	2.267618463623
20-23	117	17686	8530449912	1.343349253420
21-24	114	16678	4798905372	0.755716992094
22-25	110	15270	2567217420	0.404277575052
23-26	104	13570	1307512632	0.205903104309
24-27	98	11690	628066944	0.098906068147
25-28	91	9756	284863840	0.044859489328
26-29	83	7884	121280536	0.019098889176
27-30	75	6156	48581356	0.007650443879
28-31	67	4636	17811612	0.002804918372
29-32	57	3359	6130008	0.000965334977
30-33	48	2323	1915780	0.000301691196
31-34	38	1519	524196	0.000082548788
32-35	28	919	136624	0.000021515131
33-36	19	505	27528	0.000004335026
34-37	12	241	5172	0.000000814471

5-Point Ranges

Range	Ways	Specific	Hands	Percent
0-4	12	90	55984441072	8.816259153153
1-5	16	185	86606682512	13.638556406032
2-6	23	351	123219370896	19.404210986237
3-7	30	625	165587270288	26.076178655509
4-8	39	1046	206417535456	32.506004373517
5-9	47	1659	241411794192	38.016793585332
6-10	58	2515	268202517968	42.235715114012
7-11	67	3649	283383052304	44.626299394694
8-12	79	5081	283375292416	44.625077391182
9-13	88	6820	270815629040	42.647219881508
10-14	99	8836	247555689392	38.984315476340
11-15	108	11060	215922897300	34.002879786695
12-16	119	13406	180147745536	28.369117920801
13-17	125	15754	144173146304	22.703947675514
14-18	134	17950	110458705572	17.394700302397
15-19	139	19854	80885169788	12.737550020026
16-20	145	21336	56880745468	8.957406437719
17-21	146	22270	38255471556	6.024355067331
18-22	149	22586	24592188744	3.872702932437
19-23	146	22270	15110288352	2.379522157215
20-24	145	21336	8885443776	1.399252605188
21-25	139	19854	4966725264	0.782144757213
22-26	134	17950	2641312668	0.415945868883
23-27	125	15754	1338670572	0.210809761739
24-28	119	13406	639857704	0.100762841096
25-29	108	11060	289100428	0.045526654294
26-30	99	8836	122676604	0.019318737710
27-31	88	6820	48969552	0.007711575802
28-32	78	5075	17920768	0.002822107927
29-33	65	3627	6152368	0.000968856162
30-34	54	2471	1920264	0.000302397322
31-35	41	1583	524820	0.000082647054
32-36	30	944	136684	0.000021524580
33-37	20	509	27532	0.000004335655

Study 7Z76   Main

Top   High Card Expectancy

HCP by Pattern

The following 39 tables show the HCP expectancy for each of the 39 generic hand patterns. If a HCP total is not listed, it is impossible. For example, with 5-4-3-1 shape the most you can have is 33 HCP. The HCP window is always contiguous but narrows as shapes become extreme, down to the ultimate 13-0-0-0 forced at 10 HCP.

4-3-3-3	4-4-3-2	4-4-4-1	5-3-3-2	5-4-2-2	5-4-3-1	5-4-4-0	5-5-2-1	5-5-3-0	6-3-2-2	6-3-3-1	6-4-2-1	6-4-3-0
6-5-1-1	6-5-2-0	6-6-1-0	7-2-2-2	7-3-2-1	7-3-3-0	7-4-1-1	7-4-2-0	7-5-1-0	7-6-0-0	8-2-2-1	8-3-1-1	8-3-2-0
8-4-1-0	8-5-0-0	9-2-1-1	9-2-2-0	9-3-1-0	9-4-0-0	10-1-1-1	10-2-1-0	10-3-0-0	11-1-1-0	11-2-0-0	12-1-0-0	13-0-0-0

The “Ways” and “Specific” columns have a different connotation than before. To illustrate, consider the trivial case of 1 HCP; the jack can be in any suit, so there are four ways to assign the card, assuming no void. (If the pattern contained a void, there would be only three ways.) Further, each generic pattern can be permuted into 4, 12 or 24 specific patterns (depending on the number of like digits) so the “Ways” are multiplied by this factor to get the “Specific” number.

The “Percent” column shows the overall percentage (based on all bridge hands), and the “Relative” column shows the percentage relative to the current table. Note that the total of the “Percent” column shows the chance of any bridge hand with that pattern.

4-3-3-3 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	4	298722816	0.047041958630	0.446482315816
1	4	16	583220736	0.091843823991	0.871703568975
2	10	40	1003871232	0.158086582062	1.500423564717
3	24	96	1739138688	0.273874260117	2.599381859551
4	51	204	2698012800	0.424874832862	4.032551042390
5	96	384	3539168640	0.557337490908	5.289774084254
6	170	680	4403572128	0.693461117708	6.581743932055
7	284	1136	5311985184	0.836515237146	7.939492129503
8	445	1780	5863612032	0.923383751946	8.763974289452
9	664	2656	6098710968	0.960406415863	9.115361969833
10	949	3796	6094244088	0.959702985215	9.108685603583
11	1295	5180	5820897816	0.916657247393	8.700132021448
12	1698	6792	5236272216	0.824592189700	7.826328690089
13	2145	8580	4525112736	0.712600962230	6.763403079662
14	2608	10432	3762309384	0.592477015195	5.623288602724
15	3059	12236	2976568236	0.468740893954	4.448890436260
16	3467	13868	2254937832	0.355100737285	3.370314590411
17	3794	15176	1641613500	0.258516290744	2.453617058683
18	4011	16044	1145716128	0.180423883975	1.712430262099
19	4101	16404	761091672	0.119854396886	1.137556135863
20	4049	16196	486317352	0.076583774417	0.726868139669
21	3861	15444	296791896	0.046737883233	0.443596290421
22	3555	14220	172256424	0.027126416656	0.257460906842
23	3155	12620	95566800	0.015049568400	0.142837720769
24	2696	10784	50363112	0.007931029383	0.075274594618
25	2216	8864	25179360	0.003965168872	0.037634015085
26	1747	6988	11820648	0.001861479621	0.017667583495
27	1317	5268	5307456	0.000835801995	0.007932722641
28	948	3792	2183392	0.000343833918	0.003263379509
29	647	2588	846960	0.000133376679	0.001265898157
30	417	1668	308448	0.000048573451	0.000461017940
31	252	1008	95632	0.000015059836	0.000142935171
32	141	564	30720	0.000004837692	0.000045915263
33	72	288	6960	0.000001096040	0.000010402677
34	33	132	1840	0.000000289758	0.000002750133
35	13	52	276	0.000000043464	0.000000412520
36	4	16	48	0.000000007559	0.000000071743
37	1	4	4	0.000000000630	0.000000005979
Totals	54000	216000	66905856160	10.536130315413	100.000000000000

4-4-3-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	576108288	0.090723777357	0.420969040627
1	4	48	1159075008	0.182527599683	0.846949617452
2	10	120	1998089856	0.314653100834	1.460027545666
3	24	288	3500086464	0.551182948944	2.557553973015
4	51	612	5447418480	0.857842859833	3.980492173407
5	96	1152	7201988640	1.134147221130	5.262577038966
6	169	2028	8995078512	1.416517549273	6.572808707034
7	280	3360	10896685056	1.715976752192	7.962334772102
8	435	5220	12048600960	1.897376957996	8.804053148821
9	641	7692	12566324448	1.978906474992	9.182359735609
10	904	10848	12574353168	1.980170813348	9.188226414888
11	1216	14592	12003625008	1.890294282151	8.771188696496
12	1567	18804	10792467648	1.699564912409	7.886181897414
13	1944	23328	9314807760	1.466867536792	6.806438595016
14	2319	27828	7725746736	1.216627049801	5.645293184153
15	2663	31956	6084044784	0.958096829906	4.445682433668
16	2951	35412	4593528252	0.723374829176	3.356544631653
17	3156	37872	3323621808	0.523393832739	2.428609192167
18	3254	39048	2303233056	0.362706121969	1.682999238373
19	3240	38880	1517291568	0.238938451796	1.108702632885
20	3114	37368	961283664	0.151380021650	0.702421177118
21	2884	34608	579570336	0.091268970125	0.423498799451
22	2575	30900	331988400	0.052280521413	0.242587793230
23	2214	26568	181741248	0.028620057832	0.132800448121
24	1829	21948	93978144	0.014799391695	0.068670925143
25	1449	17388	46084320	0.007257218260	0.033674349740
26	1100	13200	21121560	0.003326158895	0.015433770065
27	796	9552	9244080	0.001455729545	0.006754756996
28	547	6564	3659760	0.000576327851	0.002674229287
29	356	4272	1376688	0.000216796630	0.001005961967
30	217	2604	473136	0.000074508015	0.000345725990
31	123	1476	139152	0.000021913233	0.000101679988
32	64	768	40992	0.000006455295	0.000029953332
33	30	360	8592	0.000001353042	0.000006278275
34	12	144	1776	0.000000279679	0.000001297744
35	4	48	240	0.000000037794	0.000000175371
36	1	12	12	0.000000001890	0.000000008769
Totals	42240	506880	136852887600	21.551175645163	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

4-4-4-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	4	72013536	0.011340472170	0.378872136564
1	4	16	152028576	0.023940996803	0.799841177191
2	10	40	264049632	0.041581731289	1.389197834069
3	23	92	469802592	0.073983080345	2.471689652824
4	47	188	737366112	0.116118168006	3.879374487090
5	85	340	987952896	0.155579811024	5.197742609561
6	143	572	1244046384	0.195908633004	6.545082184148
7	227	908	1518005664	0.239050905457	7.986415904314
8	337	1348	1687649040	0.265765827278	8.878930727071
9	474	1896	1768663296	0.278523705402	9.305156766893
10	639	2556	1776222000	0.279714027070	9.344924045286
11	821	3284	1695428928	0.266990980329	8.919861681896
12	1009	4036	1524045240	0.240001999479	8.018190862054
13	1195	4780	1312019208	0.206612786163	6.902695634169
14	1361	5444	1083496608	0.170625743596	5.700409917839
15	1489	5956	845748000	0.133185817407	4.449585030166
16	1573	6292	633339864	0.099736431518	3.332079505789
17	1604	6416	452355840	0.071235619013	2.379900128611
18	1573	6292	308297340	0.048549725488	1.621990508880
19	1489	5956	199296720	0.031384640058	1.048524740080
20	1361	5444	123431040	0.019437543992	0.649385996587
21	1195	4780	72363024	0.011395508475	0.380710836240
22	1009	4036	39978396	0.006295675958	0.210331295341
23	821	3284	21212568	0.003340490558	0.111601948836
24	639	2556	10350936	0.001630033854	0.054457556948
25	474	1896	4855824	0.000764680364	0.025547091781
26	337	1348	2060532	0.000324486299	0.010840714186
27	227	908	837936	0.000131955607	0.004408485130
28	143	572	293040	0.000046147046	0.001541719753
29	85	340	100224	0.000015782970	0.000527290883
30	47	188	26604	0.000004189517	0.000139966941
31	23	92	6592	0.000001038088	0.000034681329
32	10	40	1192	0.000000187713	0.000006271260
33	4	16	112	0.000000017637	0.000000589246
34	1	4	4	0.000000000630	0.000000021044
Totals	20480	81920	19007345500	2.993218839606	100.000000000000

5-3-3-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	384072192	0.060482518238	0.389786148729
1	4	48	809294976	0.127445306288	0.821335099107
2	10	120	1387362816	0.218477667922	1.408003027040
3	24	288	2484929664	0.391319150030	2.521898704898
4	51	612	3863039040	0.608339614422	3.920510625747
5	96	1152	5164290432	0.813256717739	5.241121123410
6	169	2028	6473253024	1.019388157330	6.569557542898
7	280	3360	7889841288	1.242468159730	8.007220813659
8	435	5220	8710024608	1.371628129246	8.839606245912
9	641	7692	9129408264	1.437671389214	9.265229197838
10	903	10836	9137498544	1.438945421851	9.273439839351
11	1213	14556	8712017856	1.371942019866	8.841629148058
12	1561	18732	7818628896	1.231253849276	7.934948973631
13	1931	23172	6747673248	1.062603017840	6.848060398544
14	2295	27540	5574925872	0.877922335314	5.657865709514
15	2624	31488	4369007808	0.688018033938	4.434006842249
16	2891	34692	3286951056	0.517619034477	3.335852008723
17	3069	36828	2366938908	0.372738325382	2.402152565175
18	3137	37644	1627474068	0.256289656086	1.651686485861
19	3091	37092	1064030076	0.167560213465	1.079859969283
20	2932	35184	669602052	0.105446890366	0.679563921748
21	2675	32100	399634416	0.062933209844	0.405579896584
22	2346	28152	226171692	0.035616828740	0.229536515823
23	1974	23688	122438916	0.019281307328	0.124260476328
24	1590	19080	62578476	0.009854667677	0.063509474681
25	1223	14676	30116196	0.004742606759	0.030564243644
26	896	10752	13574448	0.002137662699	0.013776399118
27	621	7452	5838444	0.000919420367	0.005925304275
28	406	4872	2258748	0.000355700751	0.002292352069
29	248	2976	821196	0.000129319443	0.000833413178
30	140	1680	277020	0.000043624265	0.000281141309
31	72	864	77904	0.000012268084	0.000079063001
32	33	396	21636	0.000003407171	0.000021957885
33	13	156	4428	0.000000697308	0.000004493877
34	4	48	756	0.000000119053	0.000000767247
35	1	12	108	0.000000017008	0.000000109607
Totals	39600	475200	98534079072	15.516846464518	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

5-4-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	246903552	0.038881618867	0.367512654516
1	4	48	534957696	0.084243507546	0.796277418117
2	10	120	920744496	0.144996037026	1.370515940798
3	24	288	1663414704	0.261949477905	2.475970671444
4	51	612	2599672320	0.409388473789	3.869577685111
5	96	1152	3498126912	0.550874364668	5.206915400154
6	168	2016	4406978016	0.693997466570	6.559728185085
7	276	3312	5389847568	0.848776768073	8.022716445773
8	425	5100	5968963224	0.939974136577	8.884722400260
9	618	7416	6267660768	0.987012115450	9.329329723255
10	858	10296	6288743232	0.990332117626	9.360710690623
11	1134	13608	5988505392	0.943051577634	8.913810657511
12	1431	17172	5376127896	0.846616235941	8.002294896407
13	1734	20808	4629605760	0.729056205180	6.891106622145
14	2016	24192	3817654200	0.601192548141	5.682527520157
15	2250	27000	2974849200	0.468470185404	4.428023482933
16	2415	28980	2231960400	0.351482321323	3.322243381001
17	2496	29952	1594443744	0.251088141331	2.373308314468
18	2479	29748	1088865180	0.171471169952	1.620761343731
19	2368	28416	705038724	0.111027349470	1.049440767031
20	2177	26124	439647696	0.069234379228	0.654409750284
21	1920	23040	258562800	0.040717681708	0.384867290151
22	1624	19488	144483192	0.022752772727	0.215061310357
23	1316	15792	76884012	0.012107459886	0.114440829672
24	1019	12228	38504268	0.006063534773	0.057313090995
25	750	9000	18089424	0.002848667359	0.026925867121
26	524	6288	7959168	0.001253385519	0.011847115749
27	346	4152	3302208	0.000520021652	0.004915292704
28	213	2556	1223244	0.000192632737	0.001820782431
29	122	1464	427356	0.000067298720	0.000636113724
30	64	768	135648	0.000021361434	0.000201910245
31	30	360	34272	0.000005397050	0.000051013416
32	12	144	8640	0.000001360601	0.000012860525
33	4	48	1620	0.000000255113	0.000002411348
34	1	12	108	0.000000017008	0.000000160757
Totals	30976	371712	67182326640	10.579668043989	100.000000000000

5-4-3-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	288054144	0.045361888679	0.350807533856
1	4	96	635548032	0.100084167085	0.774003923904
2	10	240	1100397312	0.173287214952	1.340121901819
3	23	552	1996946784	0.314473093340	2.431987149389
4	47	1128	3137188320	0.494034855252	3.820633449316
5	85	2040	4244734368	0.668447831362	5.169461458992
6	143	3432	5370642144	0.845752356435	6.540651349764
7	227	5448	6588576288	1.037548913467	8.023915806655
8	337	8088	7323861888	1.153339448785	8.919385402870
9	474	11376	7706183184	1.213546241257	9.384996447821
10	638	15312	7749400896	1.220352034826	9.437629257594
11	818	19632	7383262320	1.162693647778	8.991726382834
12	1003	24072	6630108768	1.044089321837	8.074496251988
13	1183	28392	5702287680	0.897978884670	6.944546780612
14	1340	32160	4693321440	0.739089956277	5.715774462036
15	1457	34968	3641808816	0.573500953002	4.435186912344
16	1527	36648	2719135008	0.428201093802	3.311506070114
17	1541	36984	1929268368	0.303815302655	2.349564803775
18	1494	35856	1304790336	0.205474405432	1.589042509908
19	1395	33480	835879176	0.131631705081	1.017977760230
20	1253	30072	513892584	0.080926237910	0.625845500976
21	1079	25896	297351000	0.046825929227	0.362129735580
22	891	21384	162337464	0.025564409066	0.197703128334
23	705	16920	84834648	0.013359501812	0.103316110080
24	531	12744	40853664	0.006433510495	0.049753747396
25	380	9120	18688320	0.002942979676	0.022759622063
26	258	6192	7809120	0.001229756417	0.009510358333
27	164	3936	3074976	0.000484237849	0.003744868004
28	97	2328	1044864	0.000164541998	0.001272490505
29	53	1272	340632	0.000053641689	0.000414839621
30	26	624	87768	0.000013821437	0.000106888501
31	11	264	18792	0.000002959307	0.000022885889
32	4	96	3240	0.000000510225	0.000003945843
33	1	24	216	0.000000034015	0.000000263056
Totals	19200	460800	82111732560	12.930705387098	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

5-4-4-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	24004512	0.003780157390	0.304033196008
1	3	36	56010528	0.008820367243	0.709410790686
2	6	72	98685216	0.015540647047	1.249914250257
3	13	156	181748448	0.028621191666	2.301965626920
4	24	288	289959264	0.045661901170	3.672527970831
5	39	468	398805120	0.062802614837	5.051133520985
6	61	732	511388640	0.080531924440	6.477079085031
7	90	1080	633298176	0.099729866619	8.021144877910
8	123	1476	711807264	0.112093238521	9.015514975513
9	161	1932	754028352	0.118742086779	9.550273287767
10	204	2448	763599312	0.120249292390	9.671495896152
11	243	2916	728808192	0.114770492847	9.230843096949
12	278	3336	655299720	0.103194602713	8.299809144838
13	309	3708	561789432	0.088468887555	7.115438818114
14	327	3924	459690768	0.072390701120	5.822290966406
15	332	3984	352176768	0.055459724076	4.460554263087
16	327	3924	258943608	0.040777650191	3.279693947795
17	309	3708	179644176	0.028289817325	2.275313614939
18	278	3336	117527544	0.018507879434	1.488564934015
19	243	2916	72518544	0.011419999290	0.918495852038
20	204	2448	42273576	0.006657113909	0.535423107872
21	161	1932	22965552	0.003616545136	0.290874072868
22	123	1476	11394972	0.001794445461	0.144324940061
23	90	1080	5509872	0.000867677850	0.069786213265
24	61	732	2202156	0.000346788815	0.027891778295
25	39	468	893664	0.000140731483	0.011318852142
26	24	288	284940	0.000044871483	0.003608955636
27	13	156	79200	0.000012472175	0.001003120960
28	6	72	18900	0.000002976314	0.000239381138
29	3	36	2376	0.000000374165	0.000030093629
30	1	12	108	0.000000017008	0.000001367892
Totals	4096	49152	7895358900	1.243337056452	100.000000000000

5-5-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	61725888	0.009720404717	0.306260545430
1	4	48	145741680	0.022950955581	0.723115176709
2	10	120	253761984	0.039961663836	1.259071131211
3	23	276	471517200	0.074253091587	2.339490277588
4	47	564	748331136	0.117844906567	3.712936489036
5	85	1020	1026669168	0.161676731540	5.093944689261
6	142	1704	1314750528	0.207042906112	6.523295603446
7	223	2676	1624967568	0.255894940105	8.062475402236
8	327	3924	1816432128	0.286046195477	9.012450242226
9	452	5424	1919571696	0.302288300302	9.524189827910
10	596	7152	1941202368	0.305694632603	9.631513053535
11	747	8964	1842063552	0.290082554010	9.139623688389
12	892	10704	1655365680	0.260681942137	8.213299354111
13	1021	12252	1417246848	0.223183714202	7.031843635477
14	1120	13440	1160905392	0.182815842977	5.759974138341
15	1175	14100	888961824	0.139990998706	4.410692853611
16	1183	14196	660369024	0.103992901256	3.276501708247
17	1144	13728	460066608	0.072449887257	2.282676764408
18	1058	12696	306517824	0.048269492732	1.520825686010
19	937	11244	192340656	0.030289220300	0.954321697484
20	795	9540	115912080	0.018253481087	0.575111966679
21	643	7716	64890828	0.010218809822	0.321963782468
22	494	5928	34538616	0.005439035982	0.171367569059
23	361	4332	17330544	0.002729161250	0.085987614435
24	249	2988	8001288	0.001260018448	0.039699369364
25	160	1920	3445200	0.000542539596	0.017093781318
26	96	1152	1376352	0.000216743718	0.006828938844
27	53	636	492480	0.000077554249	0.002443499775
28	26	312	148392	0.000023368320	0.000736265064
29	11	132	42768	0.000006734974	0.000212198665
30	4	48	9720	0.000001530676	0.000048226969
31	1	12	972	0.000000153068	0.000004822697
Totals	14080	168960	20154697992	3.173900413197	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

5-5-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	16003008	0.002520104927	0.281512218526
1	3	36	38864448	0.006120254822	0.683672530707
2	6	72	68584320	0.010800449685	1.206480936541
3	13	156	128214576	0.020190840662	2.255449084145
4	24	288	205562448	0.032371347807	3.616091473688
5	39	468	284815440	0.044851867443	5.010247222580
6	61	732	367751664	0.057912411230	6.469195466212
7	90	1080	457274160	0.072010141057	8.044004180735
8	123	1476	515217024	0.081134806684	9.063289067201
9	161	1932	547132320	0.086160730228	9.624717629999
10	203	2436	555823296	0.087529358641	9.777602383598
11	241	2892	529060896	0.083314897454	9.306819478466
12	275	3300	475892928	0.074942167896	8.371530773604
13	303	3636	407021760	0.064096546262	7.160003834658
14	318	3816	332133264	0.052303334154	5.842624836219
15	320	3840	252522576	0.039766485642	4.442176783123
16	311	3732	185235984	0.029170398206	3.258524447825
17	289	3468	127169136	0.020026207957	2.237058533210
18	256	3072	82486944	0.012989792541	1.451044866371
19	219	2628	50289984	0.007919513409	0.884661493982
20	178	2136	28983312	0.004564203640	0.509851426767
21	137	1644	15414192	0.002427379977	0.271154234673
22	101	1212	7533648	0.001186375926	0.132525957750
23	70	840	3545964	0.000558407603	0.062377785005
24	45	540	1376028	0.000216692696	0.024205992713
25	27	324	530712	0.000083574908	0.009335864390
26	15	180	167832	0.000026429672	0.002952367371
27	7	84	40824	0.000006428839	0.000718143415
28	3	36	8748	0.000001377608	0.000153887875
29	1	12	972	0.000000153068	0.000017098653
Totals	3840	46080	5684658408	0.895202680645	100.000000000000

6-3-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	109734912	0.017280719497	0.306260545430
1	4	48	266499072	0.041967461635	0.743775610329
2	10	120	449717184	0.070820091508	1.255121342430
3	24	288	863890272	0.136042807109	2.411042220493
4	51	612	1338156288	0.210728773862	3.734677206767
5	96	1152	1847667024	0.290964971703	5.156677125167
6	168	2016	2350716984	0.370183746231	6.560645582607
7	276	3312	2913941520	0.458878629590	8.132556020689
8	425	5100	3205597248	0.504807684740	8.946541658504
9	618	7416	3408949152	0.536830922815	9.514079043810
10	857	10284	3424218840	0.539235546743	9.556695408011
11	1131	13572	3244906656	0.510998010506	9.056250779468
12	1425	17100	2898328752	0.456419978469	8.088982150202
13	1721	20652	2499992640	0.393691221582	6.977260887552
14	1992	23904	2042896320	0.321709086226	5.701545021692
15	2211	26532	1573412976	0.247776280083	4.391258054828
16	2356	28272	1170675936	0.184354478468	3.267254186897
17	2412	28944	830508048	0.130785876214	2.317875351868
18	2368	28416	556662096	0.087661450308	1.553595241786
19	2231	26772	354639744	0.055847586030	0.989768519872
20	2015	24180	218278656	0.034373857487	0.609196645113
21	1741	20892	126158832	0.019867108362	0.352098270230
22	1437	17244	68465232	0.010781696070	0.191080476697
23	1130	13560	35695728	0.005621254454	0.099623656023
24	844	10128	17525952	0.002759933506	0.048913399764
25	595	7140	7927488	0.001248396649	0.022124925919
26	395	4740	3352680	0.000527969828	0.009357036760
27	244	2928	1358496	0.000213931810	0.003791443565
28	139	1668	483120	0.000076080265	0.001348345682
29	72	864	154080	0.000024264049	0.000430023809
30	33	396	48168	0.000007585350	0.000134432677
31	13	156	11376	0.000001791458	0.000031749421
32	4	48	2304	0.000000362827	0.000006430263
33	1	12	432	0.000000068030	0.000001205674
Totals	29040	348480	35830574208	5.642489623461	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

6-3-3-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	64012032	0.010080419706	0.292339611546
1	4	48	157997952	0.024881035942	0.721568406277
2	10	120	268821504	0.042333191148	1.227693788173
3	23	276	517466880	0.081489107150	2.363244252071
4	47	564	807371712	0.127142436535	3.687224499602
5	85	1020	1119557376	0.176304483436	5.112960144803
6	143	1716	1431860976	0.225485102539	6.539234397565
7	227	2724	1779410808	0.280216190835	8.126476353576
8	337	4044	1967529312	0.309840519506	8.985603749877
9	474	5688	2094792840	0.329881592028	9.566809644724
10	637	7644	2110824576	0.332406220952	9.640025746888
11	815	9780	2000693520	0.315063117906	9.137062958107
12	997	11964	1788624288	0.281667101585	8.168553836200
13	1171	14052	1539727200	0.242471546745	7.031853816726
14	1319	15828	1256282784	0.197835583982	5.737377952119
15	1425	17100	962553888	0.151580052654	4.395933403746
16	1481	17772	712974672	0.112277078374	3.256118141273
17	1478	17736	501522624	0.078978254309	2.290427666504
18	1415	16980	332747136	0.052400004846	1.519638815425
19	1301	15612	209448144	0.032983255370	0.956538749717
20	1146	13752	126998208	0.019999290736	0.579994192245
21	965	11580	71982576	0.011335596683	0.328740670285
22	776	9312	38137392	0.006005760259	0.174171480179
23	594	7128	19456992	0.003064027800	0.088859067669
24	430	5160	9171936	0.001444368527	0.041887753343
25	294	3528	4002336	0.000630275675	0.018278459767
26	188	2256	1612800	0.000253978829	0.007365573483
27	111	1332	607752	0.000095706933	0.002775571686
28	60	720	197280	0.000031067053	0.000900967471
29	29	348	57384	0.000009036657	0.000262069735
30	12	144	14400	0.000002267668	0.000065764049
31	4	48	2304	0.000000362827	0.000010522248
32	1	12	432	0.000000068030	0.000001972921
Totals	18000	216000	21896462016	3.448188103226	100.000000000000

6-4-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	82301184	0.012960539622	0.275634490887
1	4	96	208039104	0.032761364046	0.696742740852
2	10	240	357019488	0.056222340862	1.195692212782
3	23	552	689925600	0.108647380764	2.310626436501
4	47	1128	1086390144	0.171081408826	3.638423892489
5	85	2040	1512689472	0.238213727744	5.066140876957
6	142	3408	1948375296	0.306824203443	6.525294129051
7	223	5352	2426856768	0.382174007360	8.127774075554
8	327	7848	2698584336	0.424964836609	9.037815538209
9	452	10848	2874342240	0.452642655664	9.626445470779
10	596	14304	2908319904	0.457993354635	9.740239898307
11	747	17928	2751350112	0.433274230196	9.214533139307
12	892	21408	2463525792	0.387948533501	8.250582123632
13	1021	24504	2113475328	0.332823653298	7.078229834881
14	1120	26880	1721571264	0.271107795727	5.765705860049
15	1175	28200	1309621536	0.206235208084	4.386047050424
16	1183	28392	967753728	0.152398907609	3.241099254671
17	1144	27456	673095456	0.105997020981	2.254260683938
18	1058	25392	443031264	0.069767213204	1.483753829101
19	937	22488	275793408	0.043431105341	0.923658347418
20	795	19080	165054240	0.025992238670	0.552782344068
21	643	15432	91737216	0.014446497183	0.307236659287
22	494	11856	47920320	0.007546345944	0.160489708220
23	361	8664	23848992	0.003755666574	0.079872541908
24	249	5976	10904832	0.001717259708	0.036521319262
25	160	3840	4602528	0.000724792082	0.015414303907
26	96	2304	1796544	0.000282914274	0.006016796682
27	53	1272	635040	0.000100004164	0.002126809343
28	26	624	187344	0.000029502362	0.000627432870
29	11	264	50976	0.000008027545	0.000170723471
30	4	96	11520	0.000001814134	0.000038581575
31	1	24	864	0.000000136060	0.000002893618
Totals	14080	337920	29858811840	4.702074686217	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

6-4-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	21337344	0.003360139902	0.253360996674
1	3	72	55375488	0.008720363079	0.657532110415
2	6	144	96526080	0.015200632891	1.146156889714
3	13	312	187209792	0.029481227475	2.222941125577
4	24	576	298414368	0.046993385179	3.543391422016
5	39	936	419126400	0.066002748077	4.976733863232
6	61	1464	544737312	0.085783571668	6.468245921031
7	90	2160	682311168	0.107448283219	8.101806746239
8	123	2952	765761472	0.120589782757	9.092701029715
9	161	3864	818893152	0.128956797791	9.723590019448
10	203	4872	833066640	0.131188795484	9.891886928661
11	241	5784	790398000	0.124469468100	9.385236749656
12	275	6600	708825600	0.111623695161	8.416640819203
13	303	7272	607037760	0.095594456342	7.208005452418
14	318	7632	492804000	0.077605271974	5.851586430099
15	320	7680	371841840	0.058556519680	4.415273952904
16	311	7464	271408176	0.042740532371	3.222718159145
17	289	6936	185666976	0.029238269513	2.204621629043
18	256	6144	118867680	0.018718919967	1.411442486801
19	219	5256	71718336	0.011293984973	0.851588139964
20	178	4272	41009328	0.006458023987	0.486947401466
21	137	3288	21532176	0.003390821452	0.255674444388
22	101	2424	10289664	0.001620384926	0.122180132939
23	70	1680	4778496	0.000752502986	0.056740169215
24	45	1080	1835136	0.000288991624	0.021790523038
25	27	648	671184	0.000105696011	0.007969682037
26	15	360	214704	0.000033810932	0.002549409122
27	7	168	46368	0.000007301891	0.000550576618
28	3	72	10656	0.000001678074	0.000126530030
29	1	24	864	0.000000136060	0.000010259192
Totals	3840	92160	8421716160	1.326226193549	100.000000000000

6-5-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	10287648	0.001620067453	0.229695409072
1	4	48	28005264	0.004410183622	0.625281946919
2	10	120	49279104	0.007760323107	1.100269366914
3	22	264	96589584	0.015210633307	2.156584674067
4	43	516	156219840	0.024601024283	3.487967322949
5	74	888	220253040	0.034684777462	4.917655825919
6	117	1404	289977408	0.045664758432	6.474412747430
7	174	2088	363899088	0.057305719303	8.124884315558
8	241	2892	411233760	0.064759839185	9.181739764766
9	314	3768	439323696	0.069183356695	9.808912208879
10	390	4680	449962128	0.070858664543	10.046439677755
11	460	5520	423636696	0.066713015745	9.458663844810
12	515	6180	381013416	0.060000831516	8.507001060897
13	552	6624	323992872	0.051021410032	7.233886236245
14	566	6792	262155096	0.041283385534	5.853215624805
15	552	6624	195270264	0.030750566039	4.359857877051
16	515	6180	142861536	0.022497399282	3.189712454412
17	460	5520	95867280	0.015096887074	2.140457575555
18	390	4680	61181136	0.009634618832	1.366009612792
19	314	3768	36770976	0.005790581232	0.820996633468
20	241	2892	20893680	0.003290273048	0.466499473410
21	174	2088	10846440	0.001708064314	0.242171726013
22	117	1404	5357880	0.000843742613	0.119626997187
23	74	888	2447928	0.000385492241	0.054655624234
24	43	516	979560	0.000154258123	0.021870930548
25	22	264	358344	0.000056430921	0.008000854196
26	10	120	121824	0.000019184472	0.002720001065
27	4	48	32400	0.000005102253	0.000723404539
28	1	12	3888	0.000000612270	0.000086808545
Totals	6400	76800	4478821776	0.705311202933	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

6-5-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	9144576	0.001440059958	0.221188171699
1	3	72	25147584	0.003960164885	0.608267472173
2	6	144	44579808	0.007020292296	1.078292337034
3	13	312	87508512	0.013780573765	2.116647920844
4	24	576	142248960	0.022400932681	3.440704893099
5	39	936	201434688	0.031721320743	4.872283893263
6	60	1440	266196672	0.041919840604	6.438740865852
7	87	2088	335077344	0.052766958899	8.104820288790
8	117	2808	380255904	0.059881540835	9.197595184685
9	149	3576	407332800	0.064145527893	9.852528679855
10	183	4392	418158720	0.065850360780	10.114385047145
11	211	5064	394759008	0.062165445451	9.548394943769
12	232	5568	355286736	0.055949472358	8.593643222476
13	246	5904	302182272	0.047586743217	7.309157282261
14	248	5952	244100304	0.038440171916	5.904275928482
15	238	5712	181270656	0.028545950438	4.384558123127
16	219	5256	131593248	0.020722903631	3.182965501416
17	193	4632	87571584	0.013790506152	2.118173500637
18	160	3840	54883872	0.008642944890	1.327526098909
19	127	3048	32309280	0.005087966944	0.781493922968
20	96	2304	17767296	0.002797939624	0.429753737984
21	67	1608	8830080	0.001390534086	0.213581171085
22	44	1056	4060368	0.000639414378	0.098211811499
23	27	648	1753056	0.000276065916	0.042402758917
24	15	360	592272	0.000093269189	0.014325821211
25	7	168	186624	0.000029388979	0.004514044320
26	3	72	57024	0.000008979966	0.001379291320
27	1	24	7776	0.000001224541	0.000188085180
Totals	2816	67584	4134297024	0.651056495015	100.000000000000

6-6-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	762048	0.000120004997	0.165891128774
1	3	36	2370816	0.000373348878	0.516105733965
2	6	72	4339440	0.000683361786	0.944657816632
3	12	144	8784720	0.001383390932	1.912356067816
4	21	252	14817600	0.002333430488	3.225660837280
5	32	384	21337344	0.003360139902	4.644951605683
6	46	552	29211840	0.004600191533	6.359159936352
7	63	756	37192176	0.005856910524	8.096408701573
8	79	948	43076880	0.006783615775	9.377456862664
9	94	1128	46484928	0.007320304787	10.119358855238
10	108	1296	48577536	0.007649842317	10.574901161238
11	116	1392	45505152	0.007166012648	9.906070261100
12	118	1416	41189904	0.006486460545	8.966678829508
13	116	1392	34700400	0.005464513234	7.553971042406
14	108	1296	27615168	0.004348752492	6.011578523682
15	94	1128	19885824	0.003131558956	4.328968503256
16	79	948	14164416	0.002230569062	3.083468441188
17	63	756	8881488	0.001398629662	1.933421607978
18	46	552	5198256	0.000818605512	1.131614485568
19	32	384	2915136	0.000459066733	0.634599397375
20	21	252	1410048	0.000222050062	0.306955013787
21	12	144	596160	0.000093881460	0.129778774211
22	6	72	245376	0.000038641065	0.053416191125
23	3	36	88128	0.000013878129	0.019184688362
24	1	12	15552	0.000002449082	0.003385533240
Totals	1280	15360	459366336	0.072339610557	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

7-2-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	4	6718464	0.001058003234	0.206257102024
1	4	16	20715264	0.003262176640	0.635959397908
2	10	40	33732288	0.005312057906	1.035582533079
3	24	96	73868112	0.011632525146	2.267753866525
4	51	204	112440960	0.017706859688	3.451941776930
5	96	384	163004400	0.025669436115	5.004241320809
6	167	668	214137432	0.033721710153	6.574027360896
7	272	1088	271247616	0.042715247871	8.327312196224
8	415	1660	295621488	0.046553570948	9.075590999806
9	595	2380	321580512	0.050641518931	9.872534030477
10	811	3244	327180504	0.051523388604	10.044453999279
11	1049	4196	304074048	0.047884654336	9.335084915422
12	1290	5160	269551200	0.042448101450	8.275232160075
13	1515	6060	232895184	0.036675623769	7.149891065458
14	1699	6796	187569264	0.029537836030	5.758383586103
15	1820	7280	139780848	0.022012261925	4.291277385269
16	1862	7448	102354912	0.016118539589	3.142299717175
17	1823	7292	71483424	0.011256991748	2.194543853624
18	1703	6812	46076496	0.007255986160	1.414550191291
19	1517	6068	28131888	0.004430123983	0.863650038661
20	1288	5152	16850496	0.002653564754	0.517310872340
21	1038	4152	9377904	0.001476803740	0.287902011844
22	792	3168	4751712	0.000748285124	0.145877740325
23	569	2276	2349984	0.000370068318	0.072144598772
24	384	1536	1105104	0.000174028410	0.033926735110
25	240	960	457632	0.000072066493	0.014049319921
26	138	552	172872	0.000027223356	0.005307177019
27	72	288	66528	0.000010476627	0.002042412147
28	33	132	21504	0.000003386384	0.000660173623
29	13	52	5040	0.000000793684	0.000154728193
30	4	16	1512	0.000000238105	0.000046418458
31	1	4	336	0.000000052912	0.000010315213
Totals	21296	85184	3257324928	0.512953602133	100.000000000000

7-3-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	23514624	0.003703011321	0.196881779205
1	4	96	73436544	0.011564563133	0.614864921564
2	10	240	121056768	0.019063650873	1.013576567017
3	23	552	264446208	0.041644182869	2.214138739152
4	47	1128	406967328	0.064087974477	3.407430695675
5	85	2040	591197184	0.093099930712	4.949938959125
6	142	3408	781627968	0.123088390190	6.544365966305
7	223	5352	992222352	0.156252151942	8.307617507663
8	327	7848	1089256896	0.171532856194	9.120062293812
9	452	10848	1184984208	0.186607701534	9.921561969292
10	595	14280	1210560768	0.190635420252	10.135707797809
11	744	17856	1125952128	0.177311509491	9.427301846717
12	886	21264	999507456	0.157399387917	8.368613772677
13	1009	24216	861315264	0.135637302697	7.211566794883
14	1099	26376	692336736	0.109027079112	5.796753900573
15	1143	27432	512714592	0.080740731320	4.292824801163
16	1138	27312	373514688	0.058819954685	3.127340515101
17	1084	26016	258083424	0.040642191036	2.160864817587
18	985	23640	164003328	0.025826744251	1.373156849633
19	854	20496	98909568	0.015575977317	0.828143870309
20	705	16920	58073760	0.009145278730	0.486236360569
21	552	13248	31538304	0.004966555993	0.264061947349
22	408	9792	15507072	0.002442006437	0.129836646574
23	284	6816	7471296	0.001176556923	0.062555201795
24	184	4416	3330432	0.000524466281	0.027884833612
25	110	2640	1312416	0.000206675272	0.010988514940
26	60	1440	467712	0.000073653860	0.003916029902
27	29	696	160272	0.000025239146	0.001341915419
28	12	288	44352	0.000006984418	0.000371347663
29	4	96	9072	0.000001428631	0.000075957477
30	1	24	2016	0.000000317474	0.000016879439
Totals	13200	316800	11943524736	1.880829874487	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

7-3-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	3048192	0.000480019986	0.180972140481
1	3	36	9725184	0.001531492336	0.577387305345
2	6	72	16381440	0.002579699245	0.972571367212
3	13	156	35665920	0.005616560381	2.117497153929
4	24	288	55883520	0.008800366410	3.317822575488
5	39	468	81616896	0.012852780034	4.845621394108
6	61	732	109049328	0.017172755818	6.474293714501
7	90	1080	139132944	0.021910231978	8.260367682589
8	123	1476	154681920	0.024358837329	9.183515394088
9	161	1932	168623208	0.026554268874	10.011214151392
10	202	2424	173449080	0.027314232488	10.297727725842
11	239	2868	161955288	0.025504225154	9.615337594090
12	272	3264	144129672	0.022697101475	8.557025032770
13	297	3564	123826464	0.019499814158	7.351617036687
14	309	3708	99195624	0.015621024544	5.889276135376
15	308	3696	72718776	0.011451531215	4.317337144737
16	295	3540	52284456	0.008233596781	3.104144987000
17	269	3228	35383176	0.005572034717	2.100710551613
18	234	2808	21724848	0.003421162851	1.289811220615
19	195	2340	12636792	0.001990003490	0.750250409769
20	153	1836	7041384	0.001108855692	0.418049235229
21	114	1368	3557736	0.000560261422	0.211223931822
22	80	960	1566936	0.000246756306	0.093029494834
23	52	624	697536	0.000109845843	0.041412936909
24	31	372	258552	0.000040715981	0.015350315487
25	17	204	78120	0.000012302100	0.004638009553
26	8	96	25704	0.000004047788	0.001526054756
27	3	36	3528	0.000000555579	0.000209458496
28	1	12	1008	0.000000158737	0.000059845285
Totals	3600	43200	1684343232	0.265245238710	100.000000000000

7-4-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	4408992	0.000694314623	0.177193601284
1	4	48	14206752	0.002237236006	0.570957159694
2	10	120	24058944	0.003788729175	0.966908293428
3	22	264	52289712	0.008234424480	2.101478609941
4	43	516	82537488	0.012997752056	3.317110745422
5	74	888	120271824	0.018940040284	4.833621296567
6	117	1404	161467776	0.025427453250	6.489251221324
7	174	2088	205755120	0.032401689206	8.269121535145
8	241	2892	229419648	0.036128306952	9.220178588325
9	314	3768	249487560	0.039288540572	10.026690733853
10	390	4680	257250384	0.040511006436	10.338671962374
11	460	5520	239196024	0.037667860849	9.613082742143
12	515	6180	213122880	0.033561941596	8.565225480854
13	552	6624	182487096	0.028737511702	7.333999637140
14	566	6792	145933056	0.022981092891	5.864924168396
15	552	6624	106565544	0.016781617083	4.282777676662
16	515	6180	76905216	0.012110799027	3.090754571700
17	460	5520	51774120	0.008153230623	2.080757410339
18	390	4680	31915728	0.005025991574	1.282665693639
19	314	3768	18857160	0.002969568085	0.757853062649
20	241	2892	10538640	0.001659592908	0.423538889215
21	174	2088	5435640	0.000855988021	0.218453702544
22	117	1404	2536128	0.000399381708	0.101924805860
23	74	888	1146600	0.000180563073	0.046080869104
24	43	516	444528	0.000070002915	0.017865198483
25	22	264	159768	0.000025159778	0.006420938684
26	10	120	48384	0.000007619365	0.001944511400
27	4	48	12600	0.000001984210	0.000506383177
28	1	12	1008	0.000000158737	0.000040510654
Totals	6400	76800	2488234320	0.391839557185	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

7-4-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	3919104	0.000617168553	0.170630875311
1	3	72	12737088	0.002005797799	0.554550344760
2	6	144	21772800	0.003428714186	0.947949307282
3	13	312	47278080	0.007445207946	2.058404210099
4	24	576	75155040	0.011835186645	3.272117876744
5	39	936	109873152	0.017302489111	4.783683234463
6	60	1440	148119840	0.023325460970	6.448876567220
7	87	2088	189294624	0.029809540464	8.241554034991
8	117	2808	212209632	0.033418126084	9.239233063870
9	149	3576	231222816	0.036412264353	10.067033558158
10	183	4392	239084784	0.037650343112	10.409329777270
11	211	5064	222994512	0.035116496117	9.708787715781
12	232	5568	198910080	0.031323753169	8.660194028672
13	246	5904	170249472	0.026810367972	7.412361710371
14	248	5952	135959328	0.021410460603	5.919429324486
15	238	5712	98897040	0.015574004445	4.305802678584
16	219	5256	70805520	0.011150237492	3.082747447998
17	193	4632	47185344	0.007430604164	2.054366648234
18	160	3840	28496160	0.004487488427	1.240672542448
19	127	3048	16428384	0.002587091843	0.715262861578
20	96	2304	8873424	0.001397359767	0.386333229260
21	67	1608	4347504	0.000684631680	0.189282655662
22	44	1056	1862784	0.000293345547	0.081102329623
23	27	648	794304	0.000125084573	0.034582595099
24	15	360	262080	0.000041271560	0.011410500921
25	7	168	73584	0.000011587784	0.003203717566
26	3	72	23184	0.000003650946	0.001009390466
27	1	24	2016	0.000000317474	0.000087773084
Totals	2816	67584	2296831680	0.361698052786	100.000000000000

7-5-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	979776	0.000154292138	0.142192396092
1	3	72	3374784	0.000531450699	0.489773808763
2	6	144	6023808	0.000948610925	0.874219916716
3	12	288	13009248	0.002048656726	1.887999037004
4	21	504	21573216	0.003397284306	3.130865906552
5	32	768	31649184	0.004984017037	4.593165486119
6	46	1104	43843680	0.006904369102	6.362921639952
7	63	1512	56345760	0.008873158557	8.177316676510
8	79	1896	64680768	0.010185730214	9.386955164255
9	94	2256	70542144	0.011108761842	10.237601738409
10	108	2592	74040480	0.011659669133	10.745306334333
11	116	2784	68909184	0.010851608278	10.000614411588
12	118	2832	61904736	0.009748569155	8.984076708660
13	116	2784	52490160	0.008265990420	7.617763265961
14	108	2592	41436576	0.006525305700	6.013584765602
15	94	2256	29484000	0.004643050460	4.278937845371
16	79	1896	20762784	0.003269659944	3.013249973982
17	63	1512	13130208	0.002067705138	1.905553653805
18	46	1104	7432992	0.001170524926	1.078731202454
19	32	768	4161024	0.000655265378	0.603878817972
20	21	504	1971648	0.000310489118	0.286140253865
21	12	288	840672	0.000132386464	0.122004586771
22	6	144	326592	0.000051430713	0.047397465364
23	3	72	117936	0.000018572202	0.017115751381
24	1	24	18144	0.000002857262	0.002633192520
Totals	1280	30720	689049504	0.108509415836	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

7-6-0-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	36288	0.000005714524	0.102694508289
1	2	24	139104	0.000021905674	0.393662281774
2	3	36	266112	0.000041906507	0.753093060785
3	6	72	574560	0.000090479958	1.625996381241
4	9	108	1019088	0.000160482872	2.884004107780
5	12	144	1505952	0.000237152731	4.261822093990
6	16	192	2186352	0.000344300049	6.187344124407
7	20	240	2842560	0.000447637685	8.044403149298
8	22	264	3380832	0.000532403119	9.567705022250
9	24	288	3719520	0.000585738673	10.526187099614
10	26	312	3995136	0.000629141841	11.306176341141
11	24	288	3719520	0.000585738673	10.526187099614
12	22	264	3380832	0.000532403119	9.567705022250
13	20	240	2842560	0.000447637685	8.044403149298
14	16	192	2186352	0.000344300049	6.187344124407
15	12	144	1505952	0.000237152731	4.261822093990
16	9	108	1019088	0.000160482872	2.884004107780
17	6	72	574560	0.000090479958	1.625996381241
18	3	36	266112	0.000041906507	0.753093060785
19	2	24	139104	0.000021905674	0.393662281774
20	1	12	36288	0.000005714524	0.102694508289
Totals	256	3072	35335872	0.005564585427	100.000000000000

8-2-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	1259712	0.000198375606	0.103128551012
1	4	48	5808672	0.000914731963	0.475537207444
2	10	120	9036684	0.001423069455	0.739804119413
3	23	276	24695604	0.003888988452	2.021749302132
4	47	564	36656064	0.005772485240	3.000913515251
5	85	1020	56799792	0.008944658132	4.650015437453
6	141	1692	80710992	0.012710121033	6.607548118700
7	219	2628	104434380	0.016446007872	8.549705238372
8	317	3804	113165532	0.017820963079	9.264496440191
9	430	5160	126554400	0.019929401205	10.360599800745
10	553	6636	135262800	0.021300773496	11.073528369842
11	673	8076	118990656	0.018738285853	9.741380519715
12	776	9312	104751828	0.016495998616	8.575693680382
13	851	10212	90612396	0.014269363958	7.418144070397
14	889	10668	71952336	0.011330834580	5.890505253273
15	882	10584	49735872	0.007832253540	4.071715132252
16	832	9984	35518176	0.005593294106	2.907758301477
17	747	8964	24166692	0.003805697002	1.978448985732
18	635	7620	14505660	0.002284307127	1.187531512975
19	510	6120	8080992	0.001272569991	0.661564703440
20	386	4632	4605696	0.000725290969	0.377053449425
21	274	3288	2394720	0.000377113207	0.196047988492
22	180	2160	1045728	0.000164678058	0.085610372365
23	109	1308	460656	0.000072542703	0.037712418231
24	60	720	197568	0.000031112407	0.016174253771
25	29	348	67536	0.000010635363	0.005528954095
26	12	144	18144	0.000002857262	0.001485390652
27	4	48	6048	0.000000952421	0.000495130217
28	1	12	1512	0.000000238105	0.000123782554
Totals	9680	116160	1221496848	0.192357600800	100.000000000000

8-3-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	734832	0.000115719104	0.098440889602
1	4	48	3417552	0.000538185673	0.457828264341
2	10	120	5409504	0.000851872203	0.724677730512
3	22	264	14658732	0.002308412439	1.963739492187
4	43	516	22102308	0.003480604101	2.960909244271
5	74	888	34225524	0.005389731209	4.584981369440
6	117	1404	48950892	0.007708637282	6.557647673632
7	174	2088	63536508	0.010005535636	8.511592268368
8	241	2892	69490656	0.010943176716	9.309232580636
9	314	3768	77698656	0.012235747540	10.408807479193
10	389	4668	83309904	0.013119389774	11.160511603264
11	457	5484	73648800	0.011597988560	9.866273366087
12	509	6108	64854144	0.010213032938	8.688107798465
13	541	6492	56016324	0.008821279979	7.504159817231
14	548	6576	44245404	0.006967631373	5.927282604156
15	527	6324	30400236	0.004787336513	4.072531239743
16	483	5796	21488292	0.003383910733	2.878653325544
17	421	5052	14467860	0.002278354498	1.938169553099
18	347	4164	8408736	0.001324182118	1.126466256602
19	270	3240	4671720	0.000735688227	0.625841379762
20	198	2376	2556000	0.000402511090	0.342411481568
21	135	1620	1292184	0.000203489198	0.173105883372
22	85	1020	534240	0.000084130487	0.071568822345
23	49	588	229320	0.000036112615	0.030720579403
24	25	300	85680	0.000013492625	0.011478018678
25	11	132	28728	0.000004523998	0.003848512145
26	4	48	6048	0.000000952421	0.000810213083
27	1	12	1512	0.000000238105	0.000202553271
Totals	6000	72000	746470296	0.117551867155	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

8-3-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	653184	0.000102861426	0.094794930728
1	3	72	3055968	0.000481244527	0.443504854478
2	6	144	4898880	0.000771460692	0.710961980462
3	13	312	13206240	0.002079678426	1.916587984366
4	24	576	20123640	0.003169009495	2.920492632703
5	39	936	31203792	0.004913878063	4.528526879253
6	60	1440	44810712	0.007056654354	6.503264531774
7	87	2088	58365792	0.009191267040	8.470478777095
8	117	2808	64296288	0.010125183475	9.331156560850
9	149	3576	71976816	0.011334689616	10.445812032687
10	182	4368	77356080	0.012181799716	11.226490919874
11	209	5016	68789952	0.010832831986	9.983310575027
12	229	5496	60628032	0.009547517700	8.798791907990
13	240	5760	52336800	0.008241839754	7.595506519659
14	239	5736	41243832	0.006494952962	5.985612319663
15	226	5424	28209312	0.004442316479	4.093945621649
16	204	4896	19728360	0.003106762006	2.863126652799
17	175	4200	13131360	0.002067886552	1.905720840632
18	141	3384	7394400	0.001164447576	1.073130443760
19	108	2592	3988224	0.000628053360	0.578800793970
20	77	1848	2094480	0.000329832327	0.303966549260
21	51	1224	992880	0.000156355716	0.144094146246
22	31	744	356832	0.000056192816	0.051786119564
23	17	408	147168	0.000023175568	0.021358117109
24	8	192	48384	0.000007619365	0.007021846721
25	3	72	9072	0.000001428631	0.001316596260
26	1	24	3024	0.000000476210	0.000438865420
Totals	2640	63360	689049504	0.108509415836	100.000000000000

8-4-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	244944	0.000038573035	0.085315437655
1	3	72	1170288	0.000184293387	0.407618202131
2	6	144	1950480	0.000307155646	0.679363670219
3	12	288	5159376	0.000812482808	1.797041043948
4	21	504	8150544	0.001283522828	2.838882473094
5	32	768	12600576	0.001984300305	4.388854824573
6	46	1104	18387000	0.002895528721	6.404300379556
7	63	1512	24084432	0.003792742948	8.388749496872
8	79	1896	27055944	0.004260687601	9.423744625466
9	94	2256	30288384	0.004769722401	10.549622513044
10	108	2592	32788152	0.005163378247	11.420306428375
11	116	2784	29397600	0.004629444451	10.239357200089
12	118	2832	25957368	0.004087687201	9.041104135241
13	116	2784	22343904	0.003518649903	7.782513344644
14	108	2592	17366040	0.002734751052	6.048693999205
15	94	2256	11739744	0.001848739105	4.089021969603
16	79	1896	8026416	0.001263975529	2.795647959715
17	63	1512	5184576	0.000816451227	1.805818352349
18	46	1104	2675088	0.000421264705	0.931748903777
19	32	768	1459584	0.000229850840	0.508381702572
20	21	504	660240	0.000103972583	0.229965480100
21	12	288	286272	0.000045081242	0.099710223433
22	6	144	90720	0.000014286309	0.031598310243
23	3	72	33264	0.000005238313	0.011586047089
24	1	24	3024	0.000000476210	0.001053277008
Totals	1280	30720	287103960	0.045212256598	100.000000000000

8-5-0-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	13608	0.000002142946	0.068463005526
1	2	24	68040	0.000010714732	0.342315027630
2	3	36	122472	0.000019286517	0.616167049733
3	6	72	312984	0.000049287766	1.574649127097
4	9	108	530712	0.000083574908	2.670057215512
5	12	144	816480	0.000128576782	4.107780331557
6	16	192	1231632	0.000193953654	6.196445357285
7	20	240	1631232	0.000256881444	8.206866948126
8	22	264	1900800	0.000299332191	9.563086486163
9	24	288	2137104	0.000336544625	10.751952010693
10	26	312	2346300	0.000369488173	11.804434881358
11	24	288	2137104	0.000336544625	10.751952010693
12	22	264	1900800	0.000299332191	9.563086486163
13	20	240	1631232	0.000256881444	8.206866948126
14	16	192	1231632	0.000193953654	6.196445357285
15	12	144	816480	0.000128576782	4.107780331557
16	9	108	530712	0.000083574908	2.670057215512
17	6	72	312984	0.000049287766	1.574649127097
18	3	36	122472	0.000019286517	0.616167049733
19	2	24	68040	0.000010714732	0.342315027630
20	1	12	13608	0.000002142946	0.068463005526
Totals	256	3072	19876428	0.003130079303	100.000000000000

Study 7Z76   Main

Top   High Card Expectancy

9-2-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	34992	0.000005510434	0.030938565304
1	4	48	331452	0.000052196051	0.293056965793
2	10	120	482544	0.000075989558	0.426646635113
3	22	264	1915812	0.000301696235	1.693886450373
4	43	516	2714688	0.000427500793	2.400221535406
5	74	888	4553724	0.000717106577	4.026225632962
6	116	1392	7594704	0.001195990839	6.714941862871
7	170	2040	9892884	0.001557901221	8.746903225738
8	231	2772	10665792	0.001679616417	9.430278415258
9	293	3516	12227628	0.001925569591	10.811193055162
10	351	4212	14876352	0.002342682573	13.153091787593
11	397	4764	11417988	0.001798069951	10.095340860020
12	423	5076	10011672	0.001576607593	8.851930954799
13	427	5124	8691564	0.001368721009	7.684742809913
14	409	4908	6888456	0.001084773057	6.090504852453
15	369	4428	4096740	0.000645142129	3.622178155633
16	314	3768	2848896	0.000448635459	2.518883028669
17	252	3024	1888884	0.000297455695	1.670077760201
18	189	2268	1031472	0.000162433067	0.911987420863
19	131	1572	482940	0.000076051919	0.426996762909
20	84	1008	261216	0.000041135500	0.230957026587
21	49	588	126216	0.000019876111	0.111595277731
22	25	300	43272	0.000006814343	0.038259419233
23	11	132	14616	0.000002301683	0.012922898676
24	4	48	5544	0.000000873052	0.004901789153
25	1	12	1512	0.000000238105	0.001336851587
Totals	4400	52800	113101560	0.017810888963	100.000000000000