Study 7Z80   Main

HCP and Controls

by Richard Pavlicek

Every bridge player is familiar with HCP and most are familiar with controls (ace = 2, king = 1). The 88 tables in this study show the correlation between the two; more specifically, the control range and average for each number of HCP, and the HCP range and average for each number of controls. Further, all statistics are broken down by shape (hand pattern) because of its significant influence. Click on a shape to jump to it:

Any

Balanced

Unbal

Tame

Untame

4333

4432

5332

5422

4441

5431

6322

6311

5521

6421

(etc)

The general relationship between HCP and controls is obvious: For 10 HCP composed of an ace, king, queen and jack, there are 3 controls, so the average controls-to-HCP ratio is 3:10, but this varies considerably with each hand’s high-card makeup. A hand with a higher ratio is often described as “control rich” — not to be confused with attempts to stop my son from overbidding — while a lower ratio is often called “junky.” Experts are well aware that an abundance of controls suggests being aggressive, and a deficiency suggests being conservative.

Any Shape

The 635,013,559,600 possible bridge hands as a whole, comprising 39 generic shapes, or 560 specific shapes.

Controls per HCP

HCP	Hands	Controls	Average
0	2310789600	0	0
1	5006710800	0	0
2	8611542576	0	0
3	15636342960	0-1	0.3202
4	24419055136	0-2	0.8037
5	32933031040	0-2	1.0609
6	41619399184	0-2	1.3554
7	50979441968	0-3	1.8017
8	56466608128	0-4	2.1906
9	59413313872	0-4	2.5389
10	59723754816	0-4	2.9355
11	56799933520	0-5	3.3723
12	50971682080	0-6	3.7524
13	43906944752	1-6	4.1519
14	36153374224	1-6	4.5803
15	28090962724	1-7	4.9899
16	21024781756	2-8	5.3901
17	14997082848	2-8	5.8111
18	10192504020	2-8	6.2344
19	6579838440	3-9	6.6273
20	4086538404	3-9	7.0491
21	2399507844	3-9	7.4640
22	1333800036	4-10	7.8600
23	710603628	4-10	8.2587
24	354993864	4-10	8.6729
25	167819892	5-11	9.0569
26	74095248	6-11	9.4182
27	31157940	6-11	9.8359
28	11790760	6-12	10.1650
29	4236588	7-12	10.5083
30	1396068	8-12	10.8810
31	388196	8-12	11.1218
32	109156	9-12	11.4631
33	22360	10-12	11.6723
34	4484	10-12	11.8466
35	624	11-12	11.9615
36	60	12	12.0000
37	4	12	12.0000
0-37	635013559600	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	51915526432	0-12	3.5455
1	84362730452	3-15	6.2727
2	130378765244	4-18	7.8824
3	132634453224	7-21	10.1293
4	106275127972	8-24	11.9909
5	70893050800	11-25	14.0036
6	36155455908	12-28	16.0143
7	15596471176	15-29	17.9256
8	5192436964	16-31	20.0225
9	1322059596	19-32	21.9829
10	258159616	22-34	24.0980
11	28236208	25-35	26.6364
12	1086008	28-37	29.3636
0-12	635013559600	0-37	10.0000

Study 7Z80   Main

Top   HCP and Controls

Balanced Shape

Three generic patterns: 4-3-3-3, 4-4-3-2 and 5-3-3-2.

Controls per HCP

HCP	Hands	Controls	Average
0	1258903296	0	0
1	2551590720	0	0
2	4389323904	0	0
3	7724154816	0-1	0.3303
4	12008470320	0-2	0.8091
5	15905447712	0-2	1.0552
6	19871903664	0-2	1.3576
7	24098511528	0-3	1.7960
8	26622237600	0-4	2.1873
9	27794443680	0-4	2.5323
10	27806095800	0-4	2.9296
11	26536540680	0-5	3.3663
12	23847368760	0-6	3.7502
13	20587593744	1-6	4.1476
14	17062981992	1-6	4.5762
15	13429620828	1-7	4.9940
16	10135417140	2-8	5.3927
17	7332174216	2-8	5.8133
18	5076423252	2-8	6.2414
19	3342413316	3-9	6.6411
20	2117203068	3-9	7.0568
21	1275996648	3-9	7.4749
22	730416516	4-10	7.8782
23	399746964	4-10	8.2728
24	206919732	4-10	8.6845
25	101379876	5-11	9.0722
26	46516656	6-11	9.4341
27	20389980	6-11	9.8456
28	8101900	6-12	10.1760
29	3044844	7-12	10.5183
30	1058604	8-12	10.8937
31	312688	8-12	11.1288
32	93348	9-12	11.4764
33	19980	10-12	11.6607
34	4372	10-12	11.8435
35	624	11-12	11.9615
36	60	12	12.0000
37	4	12	12.0000
0-37	302292822832	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	26090262000	0-12	3.5455
1	40202721900	3-15	6.2727
2	62392621500	4-18	7.8870
3	60949551300	7-21	10.1478
4	50121892920	8-24	11.9777
5	33214253160	11-25	14.0248
6	17662662820	12-28	15.9860
7	7922143944	15-29	17.9344
8	2781316164	16-31	19.9969
9	773901964	19-32	21.9665
10	160997760	22-34	24.1190
11	19565700	25-35	26.6364
12	931700	28-37	29.3636
0-12	302292822832	0-37	10.0000

Study 7Z80   Main

Top   HCP and Controls

Unbalanced Shape

Any generic pattern except 4-3-3-3, 4-4-3-2 or 5-3-3-2.

Controls per HCP

HCP	Hands	Controls	Average
0	1051886304	0	0
1	2455120080	0	0
2	4222218672	0	0
3	7912188144	0-1	0.3103
4	12410584816	0-2	0.7985
5	17027583328	0-2	1.0662
6	21747495520	0-2	1.3534
7	26880930440	0-3	1.8067
8	29844370528	0-4	2.1935
9	31618870192	0-4	2.5447
10	31917659016	0-4	2.9406
11	30263392840	0-5	3.3774
12	27124313320	0-6	3.7543
13	23319351008	1-6	4.1558
14	19090392232	1-6	4.5839
15	14661341896	1-7	4.9863
16	10889364616	2-8	5.3876
17	7664908632	2-8	5.8090
18	5116080768	2-8	6.2275
19	3237425124	3-9	6.6131
20	1969335336	3-9	7.0408
21	1123511196	4-9	7.4518
22	603383520	4-10	7.8379
23	310856664	5-10	8.2406
24	148074132	5-10	8.6566
25	66440016	6-11	9.0335
26	27578592	6-11	9.3914
27	10767960	7-11	9.8176
28	3688860	7-12	10.1408
29	1191744	8-12	10.4828
30	337464	8-12	10.8409
31	75508	9-12	11.0930
32	15808	9-12	11.3844
33	2380	10-12	11.7697
34	112	11-12	11.9643
0-34	332720736768	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	25825264432	0-12	3.5455
1	44160008552	3-15	6.2727
2	67986143744	4-18	7.8781
3	71684901924	7-20	10.1135
4	56153235052	8-22	12.0027
5	37678797640	11-24	13.9850
6	18492793088	12-26	16.0413
7	7674327232	15-28	17.9166
8	2411120800	16-30	20.0520
9	548157632	19-32	22.0060
10	97161856	22-33	24.0632
11	8670508	25-34	26.6364
12	154308	28-34	29.3636
0-12	332720736768	0-34	10.0000

Study 7Z80   Main

Top   HCP and Controls

Tame Shape

Nine generic patterns: 4-3-3-3, 4-4-3-2, 5-3-3-2, 5-4-2-2, 4-4-4-1, 5-4-3-1, 6-3-2-2, 6-3-3-1 or 7-2-2-2.

Controls per HCP

HCP	Hands	Controls	Average
0	2046339936	0	0
1	4319337312	0	0
2	7426786320	0	0
3	13309544160	0-1	0.3245
4	20740666032	0-2	0.8063
5	27766490688	0-2	1.0586
6	34890285600	0-2	1.3567
7	42559540992	0-3	1.7994
8	47071459800	0-4	2.1891
9	49362273432	0-4	2.5361
10	49482685848	0-4	2.9327
11	47153411544	0-5	3.3696
12	42334154904	0-6	3.7513
13	36504121416	1-6	4.1500
14	30144202608	1-6	4.5780
15	23567774556	1-7	4.9920
16	17705857932	2-8	5.3913
17	12711756264	2-8	5.8121
18	8713861836	2-8	6.2375
19	5674847712	3-9	6.6339
20	3556301748	3-9	7.0530
21	2111792784	3-9	7.4689
22	1188569904	4-10	7.8685
23	640180896	4-10	8.2659
24	324431592	4-10	8.6789
25	155400900	5-11	9.0634
26	69483828	6-11	9.4252
27	29637876	6-11	9.8406
28	11364952	6-12	10.1681
29	4129560	7-12	10.5102
30	1372704	8-12	10.8818
31	386360	8-12	11.1224
32	109156	9-12	11.4631
33	22360	10-12	11.6723
34	4484	10-12	11.8466
35	624	11-12	11.9615
36	60	12	12.0000
37	4	12	12.0000
0-37	531578588684	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	44493999000	0-12	3.5455
1	70687679700	3-15	6.2727
2	109422015780	4-18	7.8842
3	109311569400	7-21	10.1373
4	88574786388	8-24	11.9849
5	58946311116	11-25	14.0136
6	30606586516	12-28	16.0014
7	13470932904	15-29	17.9291
8	4580164116	16-31	20.0124
9	1213672944	19-32	21.9739
10	242438416	22-34	24.1039
11	27346396	25-35	26.6364
12	1086008	28-37	29.3636
0-12	531578588684	0-37	10.0000

Study 7Z80   Main

Top   HCP and Controls

Untame Shape

Any generic pattern except 4-3-3-3, 4-4-3-2, 5-3-3-2, 5-4-2-2, 4-4-4-1, 5-4-3-1, 6-3-2-2, 6-3-3-1 or 7-2-2-2.

Controls per HCP

HCP	Hands	Controls	Average
0	264449664	0	0
1	687373488	0	0
2	1184756256	0	0
3	2326798800	0-1	0.2954
4	3678389104	0-2	0.7893
5	5166540352	0-2	1.0734
6	6729113584	0-2	1.3487
7	8419900976	0-3	1.8129
8	9395148328	0-4	2.1982
9	10051040440	0-4	2.5525
10	10241068968	0-4	2.9487
11	9646521976	0-5	3.3850
12	8637527176	1-6	3.7574
13	7402823336	1-6	4.1613
14	6009171616	1-6	4.5915
15	4523188168	2-7	4.9795
16	3318923824	2-8	5.3833
17	2285326584	2-8	5.8057
18	1478642184	3-8	6.2164
19	904990728	3-9	6.5859
20	530236656	4-9	7.0227
21	287715060	4-9	7.4282
22	145230132	5-10	7.7900
23	70422732	5-10	8.1933
24	30562272	6-10	8.6092
25	12418992	6-11	8.9751
26	4611420	7-11	9.3132
27	1520064	7-11	9.7451
28	425808	8-11	10.0809
29	107028	9-11	10.4353
30	23364	9-11	10.8336
31	1836	11	11.0000
0-31	103434970916	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	7421527432	0-11	3.5455
1	13675050752	3-14	6.2727
2	20956749464	4-17	7.8729
3	23322883824	7-19	10.0917
4	17700341584	8-21	12.0211
5	11946739684	11-23	13.9547
6	5548869392	12-25	16.0851
7	2125538272	15-27	17.9037
8	612272848	16-28	20.0976
9	108386652	19-30	22.0828
10	15721200	22-30	24.0069
11	889812	25-31	26.6364
0-11	103434970916	0-31	10.0000

Study 7Z80   Main

Top   HCP and Controls

4-3-3-3 Shape

This is the only generic hand pattern that allows 37 HCP. Subsequent patterns gradually reduce the maximum: 36, 35, 34, etc.

Controls per HCP

HCP	Hands	Controls	Average
0	298722816	0	0
1	583220736	0	0
2	1003871232	0	0
3	1739138688	0-1	0.3354
4	2698012800	0-2	0.8114
5	3539168640	0-2	1.0522
6	4403572128	0-2	1.3580
7	5311985184	0-3	1.7927
8	5863612032	0-4	2.1858
9	6098710968	0-4	2.5289
10	6094244088	0-4	2.9269
11	5820897816	0-5	3.3634
12	5236272216	0-6	3.7494
13	4525112736	1-6	4.1455
14	3762309384	1-6	4.5752
15	2976568236	1-7	4.9956
16	2254937832	2-8	5.3939
17	1641613500	2-8	5.8145
18	1145716128	2-8	6.2448
19	761091672	3-9	6.6464
20	486317352	3-9	7.0591
21	296791896	3-9	7.4794
22	172256424	4-10	7.8850
23	95566800	4-10	8.2768
24	50363112	4-10	8.6872
25	25179360	5-11	9.0786
26	11820648	6-11	9.4386
27	5307456	6-11	9.8457
28	2183392	6-12	10.1786
29	846960	7-12	10.5192
30	308448	8-12	10.8906
31	95632	8-12	11.1131
32	30720	9-12	11.4688
33	6960	10-12	11.6155
34	1840	10-12	11.8370
35	276	11-12	11.9565
36	48	12	12.0000
37	4	12	12.0000
0-37	66905856160	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	5929605000	0-12	3.5455
1	8894407500	3-15	6.2727
2	13835745000	4-18	7.8896
3	13264746000	7-21	10.1573
4	11046634500	8-24	11.9718
5	7291218000	11-25	14.0342
6	3958926400	12-28	15.9723
7	1800843000	15-29	17.9390
8	650060400	16-31	19.9834
9	187697620	19-32	21.9660
10	40409160	22-34	24.1344
11	5270760	25-35	26.6364
12	292820	28-37	29.3636
0-12	66905856160	0-37	10.0000

Study 7Z80   Main

Top   HCP and Controls

4-4-3-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	576108288	0	0
1	1159075008	0	0
2	1998089856	0	0
3	3500086464	0-1	0.3312
4	5447418480	0-2	0.8083
5	7201988640	0-2	1.0541
6	8995078512	0-2	1.3576
7	10896685056	0-3	1.7949
8	12048600960	0-4	2.1872
9	12566324448	0-4	2.5319
10	12574353168	0-4	2.9296
11	12003625008	0-5	3.3665
12	10792467648	0-6	3.7508
13	9314807760	1-6	4.1477
14	7725746736	1-6	4.5768
15	6084044784	1-7	4.9944
16	4593528252	2-8	5.3930
17	3323621808	2-8	5.8130
18	2303233056	2-8	6.2412
19	1517291568	3-9	6.6402
20	961283664	3-9	7.0556
21	579570336	3-9	7.4725
22	331988400	4-10	7.8756
23	181741248	4-10	8.2699
24	93978144	5-10	8.6797
25	46084320	5-11	9.0663
26	21121560	6-11	9.4286
27	9244080	6-11	9.8374
28	3659760	7-12	10.1640
29	1376688	7-12	10.5106
30	473136	8-12	10.8791
31	139152	8-12	11.1149
32	40992	9-12	11.4693
33	8592	10-12	11.6606
34	1776	10-12	11.8446
35	240	11-12	11.9500
36	12	12	12.0000
0-36	136852887600	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	11859210000	0-12	3.5455
1	18184122000	3-15	6.2727
2	28264450500	4-18	7.8887
3	27491805000	7-21	10.1490
4	22714579800	8-23	11.9758
5	15026457600	11-25	14.0250
6	8024732100	12-27	15.9848
7	3592102800	15-29	17.9365
8	1263784500	16-31	19.9990
9	349786800	19-32	21.9745
10	72672600	22-34	24.1179
11	8784600	25-35	26.6364
12	399300	28-36	29.3636
0-12	136852887600	0-36	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-3-3-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	384072192	0	0
1	809294976	0	0
2	1387362816	0	0
3	2484929664	0-1	0.3257
4	3863039040	0-2	0.8086
5	5164290432	0-2	1.0589
6	6473253024	0-2	1.3574
7	7889841288	0-3	1.7997
8	8710024608	0-4	2.1885
9	9129408264	0-4	2.5352
10	9137498544	0-4	2.9313
11	8712017856	0-5	3.3681
12	7818628896	0-6	3.7499
13	6747673248	1-6	4.1488
14	5574925872	1-6	4.5761
15	4369007808	1-7	4.9921
16	3286951056	2-8	5.3915
17	2366938908	2-8	5.8130
18	1627474068	2-8	6.2392
19	1064030076	3-9	6.6384
20	669602052	3-9	7.0569
21	399634416	3-9	7.4749
22	226171692	4-10	7.8768
23	122438916	4-10	8.2740
24	62578476	5-10	8.6896
25	30116196	5-11	9.0759
26	13574448	6-11	9.4387
27	5838444	6-11	9.8585
28	2258748	7-12	10.1928
29	821196	8-12	10.5303
30	277020	8-12	10.9222
31	77904	9-12	11.1728
32	21636	10-12	11.5008
33	4428	10-12	11.7317
34	756	11-12	11.8571
35	108	12	12.0000
0-35	98534079072	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	8301447000	0-12	3.5455
1	13124192400	3-15	6.2727
2	20292426000	4-18	7.8829
3	20193000300	7-21	10.1398
4	16360678620	8-23	11.9844
5	10896577560	11-25	14.0183
6	5679004320	12-27	15.9973
7	2529198144	15-28	17.9280
8	867471264	16-30	20.0039
9	236417544	19-31	21.9551
10	47916000	22-33	24.1077
11	5510340	25-34	26.6364
12	239580	28-35	29.3636
0-12	98534079072	0-35	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-4-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	246903552	0	0
1	534957696	0	0
2	920744496	0	0
3	1663414704	0-1	0.3216
4	2599672320	0-2	0.8041
5	3498126912	0-2	1.0604
6	4406978016	0-2	1.3566
7	5389847568	0-3	1.8015
8	5968963224	0-4	2.1901
9	6267660768	0-4	2.5381
10	6288743232	0-4	2.9346
11	5988505392	0-5	3.3717
12	5376127896	0-6	3.7515
13	4629605760	1-6	4.1509
14	3817654200	1-6	4.5783
15	2974849200	1-7	4.9899
16	2231960400	2-8	5.3903
17	1594443744	2-8	5.8108
18	1088865180	2-8	6.2348
19	705038724	3-9	6.6311
20	439647696	3-9	7.0530
21	258562800	4-9	7.4674
22	144483192	4-10	7.8680
23	76884012	5-10	8.2661
24	38504268	5-10	8.6847
25	18089424	6-11	9.0664
26	7959168	6-11	9.4313
27	3302208	7-11	9.8535
28	1223244	7-12	10.1906
29	427356	8-12	10.5345
30	135648	8-12	10.9379
31	34272	9-12	11.2216
32	8640	10-12	11.5750
33	1620	11-12	11.8667
34	108	12	12.0000
0-34	67182326640	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	5534298000	0-12	3.5455
1	8933938200	3-15	6.2727
2	13819932720	4-18	7.8834
3	13931577000	7-20	10.1313
4	11234624940	8-22	11.9882
5	7481364660	11-24	14.0070
6	3841817760	12-26	16.0143
7	1667542140	15-28	17.9266
8	560617200	16-30	20.0177
9	144815220	19-31	21.9518
10	28749600	22-32	24.0857
11	2940300	25-33	26.6364
12	108900	28-34	29.3636
0-12	67182326640	0-34	10.0000

Study 7Z80   Main

Top   HCP and Controls

4-4-4-1 Shape

Note that only 11 controls are possible, because each singleton reduces the maximum by 1.

Controls per HCP

HCP	Hands	Controls	Average
0	72013536	0	0
1	152028576	0	0
2	264049632	0	0
3	469802592	0-1	0.3236
4	737366112	0-2	0.7999
5	987952896	0-2	1.0552
6	1244046384	0-2	1.3560
7	1518005664	0-3	1.7963
8	1687649040	0-4	2.1891
9	1768663296	0-4	2.5370
10	1776222000	0-4	2.9355
11	1695428928	0-5	3.3735
12	1524045240	1-6	3.7563
13	1312019208	1-6	4.1537
14	1083496608	1-6	4.5835
15	845748000	2-7	4.9948
16	633339864	2-8	5.3923
17	452355840	2-8	5.8094
18	308297340	3-8	6.2323
19	199296720	3-9	6.6205
20	123431040	3-9	7.0384
21	72363024	4-9	7.4436
22	39978396	5-10	7.8327
23	21212568	5-10	8.2326
24	10350936	5-10	8.6250
25	4855824	6-11	8.9976
26	2060532	7-11	9.3568
27	837936	7-11	9.7514
28	293040	7-11	10.0243
29	100224	8-11	10.3890
30	26604	9-11	10.6035
31	6592	9-11	10.7858
32	1192	9-11	10.9027
33	112	10-11	10.9643
34	4	11	11.0000
0-34	19007345500	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1581228000	0-11	3.5455
1	2515590000	3-14	6.2727
2	3917133000	4-17	7.8907
3	3899164500	7-20	10.1353
4	3198393000	8-21	11.9801
5	2120283000	11-24	14.0054
6	1102068000	12-25	16.0040
7	473170500	15-28	17.9356
8	155727000	16-29	20.0490
9	37268000	19-32	22.0763
10	6655000	22-33	24.0818
11	665500	25-34	26.6364
0-11	19007345500	0-34	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-4-3-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	288054144	0	0
1	635548032	0	0
2	1100397312	0	0
3	1996946784	0-1	0.3183
4	3137188320	0-2	0.7988
5	4244734368	0-2	1.0595
6	5370642144	0-2	1.3554
7	6588576288	0-3	1.8007
8	7323861888	0-4	2.1907
9	7706183184	0-4	2.5402
10	7749400896	0-4	2.9377
11	7383262320	0-5	3.3755
12	6630108768	1-6	3.7556
13	5702287680	1-6	4.1547
14	4693321440	1-6	4.5833
15	3641808816	2-7	4.9915
16	2719135008	2-8	5.3907
17	1929268368	2-8	5.8087
18	1304790336	3-8	6.2294
19	835879176	3-9	6.6173
20	513892584	3-9	7.0391
21	297351000	4-9	7.4450
22	162337464	5-10	7.8336
23	84834648	5-10	8.2354
24	40853664	5-10	8.6378
25	18688320	6-11	9.0097
26	7809120	7-11	9.3695
27	3074976	7-11	9.7773
28	1044864	7-11	10.0618
29	340632	8-11	10.4149
30	87768	9-11	10.6555
31	18792	9-11	10.8046
32	3240	10-11	10.9333
33	216	11	11.0000
0-33	82111732560	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	6641157600	0-11	3.5455
1	10881723600	3-14	6.2727
2	16876015200	4-17	7.8862
3	17160636240	7-20	10.1259
4	13848203160	8-21	11.9886
5	9220475880	11-24	13.9967
6	4685226480	12-25	16.0209
7	1981805760	15-28	17.9281
8	639199440	16-29	20.0523
9	148539600	19-31	22.0455
10	26353800	22-32	24.0661
11	2395800	25-33	26.6364
0-11	82111732560	0-33	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-3-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	109734912	0	0
1	266499072	0	0
2	449717184	0	0
3	863890272	0-1	0.3085
4	1338156288	0-2	0.8085
5	1847667024	0-2	1.0726
6	2350716984	0-2	1.3549
7	2913941520	0-3	1.8127
8	3205597248	0-4	2.1935
9	3408949152	0-4	2.5449
10	3424218840	0-4	2.9367
11	3244906656	0-5	3.3726
12	2898328752	0-6	3.7481
13	2499992640	1-6	4.1520
14	2042896320	1-6	4.5757
15	1573412976	1-7	4.9844
16	1170675936	2-8	5.3867
17	830508048	2-8	5.8133
18	556662096	2-8	6.2346
19	354639744	3-9	6.6305
20	218278656	3-9	7.0603
21	126158832	4-9	7.4838
22	68465232	4-10	7.8802
23	35695728	5-10	8.2841
24	17525952	5-10	8.7201
25	7927488	6-11	9.1079
26	3352680	6-11	9.4637
27	1358496	7-11	9.9185
28	483120	8-12	10.2851
29	154080	8-12	10.5846
30	48168	9-12	11.0523
31	11376	10-12	11.4051
32	2304	11-12	11.6250
33	432	12	12.0000
0-33	35830574208	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	2767149000	0-12	3.5455
1	4796391600	3-15	6.2727
2	7305273360	4-18	7.8659
3	7795933200	7-20	10.1144
4	5957396280	8-22	12.0106
5	4043343744	11-24	13.9971
6	1957900032	12-26	16.0345
7	853357824	15-27	17.9032
8	270237528	16-29	20.0208
9	69364944	19-30	21.9021
10	12946032	22-31	24.0741
11	1237104	25-32	26.6364
12	43560	28-33	29.3636
0-12	35830574208	0-33	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-3-3-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	64012032	0	0
1	157997952	0	0
2	268821504	0	0
3	517466880	0-1	0.3053
4	807371712	0-2	0.8018
5	1119557376	0-2	1.0713
6	1431860976	0-2	1.3536
7	1779410808	0-3	1.8114
8	1967529312	0-4	2.1941
9	2094792840	0-4	2.5469
10	2110824576	0-4	2.9403
11	2000693520	0-5	3.3770
12	1788624288	1-6	3.7526
13	1539727200	1-6	4.1559
14	1256282784	1-6	4.5812
15	962553888	2-7	4.9850
16	712974672	2-8	5.3867
17	501522624	2-8	5.8104
18	332747136	3-8	6.2281
19	209448144	3-9	6.6151
20	126998208	3-9	7.0456
21	71982576	4-9	7.4605
22	38137392	5-10	7.8447
23	19456992	5-10	8.2531
24	9171936	5-10	8.6776
25	4002336	6-11	9.0532
26	1612800	7-11	9.4038
27	607752	7-11	9.8479
28	197280	8-11	10.1577
29	57384	9-11	10.4605
30	14400	9-11	10.7500
31	2304	10-11	10.8125
32	432	11	11.0000
0-32	21896462016	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1660289400	0-11	3.5455
1	2918084400	3-14	6.2727
2	4460979600	4-17	7.8701
3	4794954120	7-20	10.1087
4	3678990480	8-21	12.0108
5	2490673680	11-24	13.9848
6	1195216704	12-25	16.0453
7	502543008	15-27	17.9055
8	153427032	16-28	20.0545
9	34882848	19-30	21.9838
10	5941584	22-31	24.0484
11	479160	25-32	26.6364
0-11	21896462016	0-32	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-5-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	61725888	0	0
1	145741680	0	0
2	253761984	0	0
3	471517200	0-1	0.3091
4	748331136	0-2	0.7905
5	1026669168	0-2	1.0646
6	1314750528	0-2	1.3533
7	1624967568	0-3	1.8059
8	1816432128	0-4	2.1943
9	1919571696	0-4	2.5459
10	1941202368	0-4	2.9443
11	1842063552	0-5	3.3820
12	1655365680	1-6	3.7570
13	1417246848	1-6	4.1577
14	1160905392	1-6	4.5867
15	888961824	2-7	4.9838
16	660369024	2-8	5.3869
17	460066608	2-8	5.8041
18	306517824	3-8	6.2198
19	192340656	3-9	6.6033
20	115912080	4-9	7.0343
21	64890828	4-9	7.4380
22	34538616	5-10	7.8269
23	17330544	5-10	8.2266
24	8001288	6-10	8.6512
25	3445200	6-11	9.0230
26	1376352	7-11	9.3839
27	492480	7-11	9.8039
28	148392	8-11	10.1288
29	42768	9-11	10.4773
30	9720	10-11	10.8000
31	972	11	11.0000
0-31	20154697992	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1549603440	0-11	3.5455
1	2664512928	3-14	6.2727
2	4127292576	4-17	7.8849
3	4330839744	7-19	10.1078
4	3443313456	8-21	12.0007
5	2291813568	11-23	13.9727
6	1126265580	12-25	16.0641
7	446402880	15-27	17.9218
8	140023620	16-28	20.0649
9	29076300	19-29	21.9775
10	5227200	22-30	24.0170
11	326700	25-31	26.6364
0-11	20154697992	0-31	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-4-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	82301184	0	0
1	208039104	0	0
2	357019488	0	0
3	689925600	0-1	0.3015
4	1086390144	0-2	0.7946
5	1512689472	0-2	1.0719
6	1948375296	0-2	1.3521
7	2426856768	0-3	1.8122
8	2698584336	0-4	2.1960
9	2874342240	0-4	2.5494
10	2908319904	0-4	2.9447
11	2751350112	0-5	3.3815
12	2463525792	1-6	3.7547
13	2113475328	1-6	4.1578
14	1721571264	1-6	4.5848
15	1309621536	2-7	4.9806
16	967753728	2-8	5.3845
17	673095456	2-8	5.8064
18	443031264	3-8	6.2214
19	275793408	3-9	6.6043
20	165054240	4-9	7.0405
21	91737216	4-9	7.4522
22	47920320	5-10	7.8371
23	23848992	5-10	8.2416
24	10904832	6-10	8.6787
25	4602528	6-11	9.0545
26	1796544	7-11	9.4045
27	635040	7-11	9.8478
28	187344	8-11	10.1868
29	50976	9-11	10.4972
30	11520	10-11	10.8500
31	864	11	11.0000
0-31	29858811840	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	2213719200	0-11	3.5455
1	3964569840	3-14	6.2727
2	6077665440	4-17	7.8733
3	6598991520	7-19	10.1001
4	5071255200	8-21	12.0144
5	3416933520	11-23	13.9694
6	1621825920	12-25	16.0717
7	648608400	15-27	17.9065
8	196542720	16-28	20.0639
9	41120640	19-29	21.9466
10	7143840	22-30	24.0144
11	435600	25-31	26.6364
0-11	29858811840	0-31	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-2-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	6718464	0	0
1	20715264	0	0
2	33732288	0	0
3	73868112	0-1	0.2804
4	112440960	0-2	0.8141
5	163004400	0-2	1.0962
6	214137432	0-2	1.3472
7	271247616	0-3	1.8319
8	295621488	0-4	2.2043
9	321580512	0-4	2.5588
10	327180504	0-4	2.9423
11	304074048	0-5	3.3742
12	269551200	0-6	3.7411
13	232895184	1-6	4.1531
14	187569264	1-6	4.5749
15	139780848	1-7	4.9707
16	102354912	2-8	5.3778
17	71483424	2-8	5.8198
18	46076496	3-8	6.2406
19	28131888	3-9	6.6266
20	16850496	4-9	7.0756
21	9377904	4-9	7.5239
22	4751712	5-10	7.9119
23	2349984	5-10	8.3176
24	1105104	6-10	8.7960
25	457632	6-11	9.2074
26	172872	7-11	9.5248
27	66528	8-11	10.0530
28	21504	9-12	10.5234
29	5040	10-12	10.7000
30	1512	11-12	11.3333
31	336	12	12.0000
0-31	3257324928	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	219615000	0-12	3.5455
1	439230000	3-15	6.2727
2	650060400	4-17	7.8329
3	779753040	7-19	10.0856
4	535285608	8-21	12.0549
5	375916992	11-23	13.9750
6	161694720	12-25	16.0751
7	70369728	15-26	17.8583
8	19639752	16-27	20.0299
9	4900368	19-28	21.8057
10	794640	22-29	24.0457
11	62832	25-30	26.6364
12	1848	28-31	29.3636
0-12	3257324928	0-31	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-4-4-0 Shape

Note that only 9 controls are possible, because each void reduces the maximum by 3.

Controls per HCP

HCP	Hands	Controls	Average
0	24004512	0	0
1	56010528	0	0
2	98685216	0	0
3	181748448	0-1	0.3082
4	289959264	0-2	0.7832
5	398805120	0-2	1.0567
6	511388640	0-2	1.3513
7	633298176	0-3	1.7977
8	711807264	0-4	2.1915
9	754028352	0-4	2.5455
10	763599312	1-4	2.9462
11	728808192	1-5	3.3862
12	655299720	1-6	3.7678
13	561789432	2-6	4.1668
14	459690768	2-6	4.5992
15	352176768	2-7	4.9980
16	258943608	3-7	5.3939
17	179644176	3-7	5.8044
18	117527544	3-8	6.2122
19	72518544	4-8	6.5687
20	42273576	5-8	6.9813
21	22965552	5-9	7.3464
22	11394972	5-9	7.6585
23	5509872	6-9	8.0577
24	2202156	7-9	8.3125
25	893664	7-9	8.6087
26	284940	7-9	8.8365
27	79200	8-9	8.9700
28	18900	9	9.0000
29	2376	9	9.0000
30	108	9	9.0000
0-30	7895358900	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	603741600	0-9	3.5455
1	1034985600	3-12	6.2727
2	1617165000	4-15	7.8945
3	1689039000	7-18	10.1103
4	1365606000	8-19	11.9909
5	909206100	11-22	13.9662
6	448014600	12-23	16.0389
7	173695500	15-26	17.9310
8	47916000	18-27	20.1818
9	5989500	21-30	22.9091
0-9	7895358900	0-30	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-3-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	23514624	0	0
1	73436544	0	0
2	121056768	0	0
3	264446208	0-1	0.2777
4	406967328	0-2	0.8049
5	591197184	0-2	1.0939
6	781627968	0-2	1.3456
7	992222352	0-3	1.8295
8	1089256896	0-4	2.2045
9	1184984208	0-4	2.5603
10	1210560768	0-4	2.9470
11	1125952128	0-5	3.3795
12	999507456	1-6	3.7465
13	861315264	1-6	4.1569
14	692336736	1-6	4.5819
15	512714592	2-7	4.9690
16	373514688	2-8	5.3767
17	258083424	2-8	5.8150
18	164003328	3-8	6.2311
19	98909568	3-9	6.6070
20	58073760	4-9	7.0601
21	31538304	4-9	7.5001
22	15507072	5-10	7.8747
23	7471296	5-10	8.2858
24	3330432	6-10	8.7651
25	1312416	7-11	9.1636
26	467712	7-11	9.4677
27	160272	8-11	9.9874
28	44352	9-11	10.4091
29	9072	10-11	10.5556
30	2016	11	11.0000
0-30	11943524736	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	790614000	0-11	3.5455
1	1600394400	3-14	6.2727
2	2382383520	4-17	7.8397
3	2870168400	7-19	10.0796
4	1991737440	8-21	12.0549
5	1388727648	11-23	13.9582
6	593740224	12-24	16.0950
7	243099648	15-26	17.8625
8	66193776	16-27	20.0609
9	14148288	19-28	21.8519
10	2195424	22-29	24.0051
11	121968	25-30	26.6364
0-11	11943524736	0-30	10.0000

Study 7Z80   Main

Top   HCP and Controls

5-5-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	16003008	0	0
1	38864448	0	0
2	68584320	0	0
3	128214576	0-1	0.3031
4	205562448	0-2	0.7794
5	284815440	0-2	1.0602
6	367751664	0-2	1.3500
7	457274160	0-3	1.8012
8	515217024	0-4	2.1935
9	547132320	0-4	2.5483
10	555823296	1-4	2.9494
11	529060896	1-5	3.3891
12	475892928	1-6	3.7676
13	407021760	2-6	4.1678
14	332133264	2-6	4.6003
15	252522576	2-7	4.9929
16	185235984	3-7	5.3914
17	127169136	3-7	5.8021
18	82486944	3-8	6.2068
19	50289984	4-8	6.5607
20	28983312	5-8	6.9780
21	15414192	5-9	7.3430
22	7533648	5-9	7.6515
23	3545964	6-9	8.0456
24	1376028	7-9	8.3176
25	530712	7-9	8.6087
26	167832	7-9	8.8436
27	40824	8-9	8.9762
28	8748	9	9.0000
29	972	9	9.0000
0-29	5684658408	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	422619120	0-9	3.5455
1	744614640	3-12	6.2727
2	1161483840	4-15	7.8927
3	1235657808	7-18	10.1005
4	988986240	8-19	11.9992
5	658365840	11-22	13.9536
6	318401820	12-23	16.0646
7	118592100	15-26	17.9256
8	32343300	18-27	20.1818
9	3593700	21-29	22.9091
0-9	5684658408	0-29	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-5-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	10287648	0	0
1	28005264	0	0
2	49279104	0	0
3	96589584	0-1	0.2899
4	156219840	0-2	0.7736
5	220253040	0-2	1.0734
6	289977408	0-2	1.3467
7	363899088	0-3	1.8136
8	411233760	0-4	2.2006
9	439323696	0-4	2.5555
10	449962128	0-4	2.9574
11	423636696	1-5	3.3947
12	381013416	1-6	3.7619
13	323992872	1-6	4.1644
14	262155096	2-6	4.5981
15	195270264	2-7	4.9682
16	142861536	2-8	5.3765
17	95867280	3-8	5.7944
18	61181136	4-8	6.1973
19	36770976	4-9	6.5603
20	20893680	4-9	7.0125
21	10846440	5-9	7.4226
22	5357880	6-10	7.8006
23	2447928	6-10	8.1886
24	979560	6-10	8.6670
25	358344	7-10	9.0705
26	121824	8-10	9.4043
27	32400	9-10	9.7600
28	3888	10	10.0000
0-28	4478821776	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	309920688	0-10	3.5455
1	587641824	3-13	6.2727
2	908173728	4-16	7.8824
3	1017761976	7-17	10.0758
4	785465208	8-20	12.0264
5	522040464	11-21	13.9223
6	240137568	12-24	16.1494
7	79976160	15-25	17.9089
8	23522400	16-26	20.0955
9	3528360	19-27	21.8215
10	653400	22-28	23.9091
0-10	4478821776	0-28	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-4-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	21337344	0	0
1	55375488	0	0
2	96526080	0	0
3	187209792	0-1	0.2958
4	298414368	0-2	0.7823
5	419126400	0-2	1.0671
6	544737312	0-2	1.3487
7	682311168	0-3	1.8071
8	765761472	0-4	2.1952
9	818893152	0-4	2.5516
10	833066640	1-4	2.9503
11	790398000	1-5	3.3890
12	708825600	1-6	3.7655
13	607037760	2-6	4.1680
14	492804000	2-6	4.5990
15	371841840	2-7	4.9890
16	271408176	3-7	5.3889
17	185666976	3-7	5.8038
18	118867680	3-8	6.2067
19	71718336	4-8	6.5589
20	41009328	5-8	6.9815
21	21532176	5-9	7.3544
22	10289664	5-9	7.6520
23	4778496	6-9	8.0563
24	1835136	7-9	8.3475
25	671184	7-9	8.6145
26	214704	7-9	8.8645
27	46368	8-9	8.9814
28	10656	9	9.0000
29	864	9	9.0000
0-29	8421716160	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	603741600	0-9	3.5455
1	1106859600	3-12	6.2727
2	1710601200	4-15	7.8824
3	1880223840	7-18	10.0924
4	1459521360	8-19	12.0128
5	981319680	11-22	13.9482
6	459035280	12-23	16.0759
7	170580960	15-26	17.9106
8	45041040	18-27	20.1818
9	4791600	21-29	22.9091
0-9	8421716160	0-29	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-4-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	4408992	0	0
1	14206752	0	0
2	24058944	0	0
3	52289712	0-1	0.2717
4	82537488	0-2	0.7852
5	120271824	0-2	1.0907
6	161467776	0-2	1.3418
7	205755120	0-3	1.8262
8	229419648	0-4	2.2063
9	249487560	0-4	2.5632
10	257250384	0-4	2.9576
11	239196024	1-5	3.3909
12	213122880	1-6	3.7553
13	182487096	1-6	4.1624
14	145933056	2-6	4.5957
15	106565544	2-7	4.9592
16	76905216	2-8	5.3697
17	51774120	3-8	5.8034
18	31915728	4-8	6.2090
19	18857160	4-9	6.5662
20	10538640	4-9	7.0360
21	5435640	5-9	7.4701
22	2536128	6-10	7.8362
23	1146600	6-10	8.2325
24	444528	6-10	8.7494
25	159768	7-10	9.1703
26	48384	8-10	9.4375
27	12600	9-10	9.8400
28	1008	10	10.0000
0-28	2488234320	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	158122800	0-10	3.5455
1	329182920	3-13	6.2727
2	495799920	4-16	7.8532
3	603567360	7-17	10.0647
4	427977000	8-20	12.0585
5	292984560	11-21	13.9191
6	123971760	12-24	16.1566
7	42906600	15-25	17.8719
8	11586960	16-26	20.0909
9	1829520	19-27	21.7576
10	304920	22-28	23.9091
0-10	2488234320	0-28	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-5-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	9144576	0	0
1	25147584	0	0
2	44579808	0	0
3	87508512	0-1	0.2874
4	142248960	0-2	0.7679
5	201434688	0-2	1.0700
6	266196672	0-2	1.3448
7	335077344	0-3	1.8098
8	380255904	0-4	2.1991
9	407332800	0-4	2.5558
10	418158720	1-4	2.9592
11	394759008	1-5	3.3978
12	355286736	1-6	3.7682
13	302182272	2-6	4.1708
14	244100304	2-6	4.6068
15	181270656	2-7	4.9764
16	131593248	3-7	5.3812
17	87571584	3-7	5.7950
18	54883872	4-8	6.1890
19	32309280	4-8	6.5283
20	17767296	5-8	6.9632
21	8830080	5-9	7.3386
22	4060368	6-9	7.6290
23	1753056	6-9	7.9975
24	592272	7-9	8.3173
25	186624	7-9	8.6111
26	57024	8-9	8.8636
27	7776	9	9.0000
0-27	4134297024	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	281746080	0-9	3.5455
1	539342496	3-12	6.2727
2	837188352	4-15	7.8872
3	942934608	7-17	10.0737
4	732121632	8-19	12.0246
5	486809136	11-21	13.9137
6	222678720	12-23	16.1423
7	71351280	15-25	17.9101
8	18817920	18-26	20.1818
9	1306800	21-27	22.9091
0-9	4134297024	0-27	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-3-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	3048192	0	0
1	9725184	0	0
2	16381440	0	0
3	35665920	0-1	0.2727
4	55883520	0-2	0.7889
5	81616896	0-2	1.0877
6	109049328	0-2	1.3421
7	139132944	0-3	1.8230
8	154681920	0-4	2.2031
9	168623208	0-4	2.5619
10	173449080	1-4	2.9540
11	161955288	1-5	3.3885
12	144129672	1-6	3.7584
13	123826464	2-6	4.1673
14	99195624	2-6	4.5983
15	72718776	2-7	4.9751
16	52284456	3-7	5.3799
17	35383176	3-7	5.8101
18	21724848	3-8	6.2110
19	12636792	4-8	6.5518
20	7041384	5-8	6.9931
21	3557736	5-9	7.3950
22	1566936	5-9	7.6526
23	697536	6-9	8.0853
24	258552	7-9	8.4444
25	78120	7-9	8.6323
26	25704	8-9	8.9216
27	3528	9	9.0000
28	1008	9	9.0000
0-28	1684343232	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	107811000	0-9	3.5455
1	222809400	3-12	6.2727
2	335412000	4-15	7.8526
3	407286000	7-18	10.0711
4	288454320	8-19	12.0530
5	199330560	11-22	13.9307
6	84332160	12-23	16.1111
7	30857904	15-25	17.8676
8	7379064	18-26	20.1818
9	670824	21-28	22.9091
0-9	1684343232	0-28	10.0000

Study 7Z80   Main

Top   HCP and Controls

8-2-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	1259712	0	0
1	5808672	0	0
2	9036684	0	0
3	24695604	0-1	0.2352
4	36656064	0-2	0.8157
5	56799792	0-2	1.1294
6	80710992	0-2	1.3255
7	104434380	0-3	1.8531
8	113165532	0-4	2.2290
9	126554400	0-4	2.5801
10	135262800	0-4	2.9537
11	118990656	0-5	3.3748
12	104751828	1-6	3.7281
13	90612396	1-6	4.1524
14	71952336	1-6	4.5876
15	49735872	2-7	4.9451
16	35518176	2-8	5.3613
17	24166692	3-8	5.8350
18	14505660	3-8	6.2651
19	8080992	4-9	6.6098
20	4605696	4-9	7.0966
21	2394720	5-9	7.5981
22	1045728	5-10	7.9685
23	460656	6-10	8.3567
24	197568	7-10	8.9209
25	67536	8-11	9.4104
26	18144	9-11	9.5833
27	6048	10-11	10.2500
28	1512	11	11.0000
0-28	1221496848	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	65884500	0-11	3.5455
1	164112300	3-14	6.2727
2	233830080	4-16	7.7877
3	336609900	7-18	10.0529
4	197152560	8-20	12.1207
5	144397044	11-22	13.9359
6	51714432	12-23	16.1358
7	21712284	15-24	17.7943
8	4875948	16-25	20.0567
9	1070784	19-26	21.6865
10	131472	22-27	23.9819
11	5544	25-28	26.6364
0-11	1221496848	0-28	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-4-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	3919104	0	0
1	12737088	0	0
2	21772800	0	0
3	47278080	0-1	0.2694
4	75155040	0-2	0.7783
5	109873152	0-2	1.0869
6	148119840	0-2	1.3399
7	189294624	0-3	1.8221
8	212209632	0-4	2.2046
9	231222816	0-4	2.5632
10	239084784	1-4	2.9599
11	222994512	1-5	3.3945
12	198910080	1-6	3.7619
13	170249472	2-6	4.1690
14	135959328	2-6	4.6050
15	98897040	2-7	4.9670
16	70805520	3-7	5.3743
17	47185344	3-7	5.8034
18	28496160	4-8	6.1983
19	16428384	4-8	6.5295
20	8873424	5-8	6.9816
21	4347504	5-9	7.3830
22	1862784	6-9	7.6364
23	794304	6-9	8.0368
24	262080	7-9	8.4077
25	73584	7-9	8.6301
26	23184	8-9	8.9130
27	2016	9	9.0000
0-27	2296831680	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	143748000	0-9	3.5455
1	301870800	3-12	6.2727
2	457118640	4-15	7.8593
3	558439200	7-17	10.0622
4	399793680	8-19	12.0565
5	273208320	11-21	13.9085
6	115085520	12-23	16.1525
7	37810080	15-25	17.8724
8	9147600	18-26	20.1818
9	609840	21-27	22.9091
0-9	2296831680	0-27	10.0000

Study 7Z80   Main

Top   HCP and Controls

8-3-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	734832	0	0
1	3417552	0	0
2	5409504	0	0
3	14658732	0-1	0.2331
4	22102308	0-2	0.8034
5	34225524	0-2	1.1255
6	48950892	0-2	1.3241
7	63536508	0-3	1.8486
8	69490656	0-4	2.2276
9	77698656	0-4	2.5804
10	83309904	0-4	2.9599
11	73648800	1-5	3.3818
12	64854144	1-6	3.7358
13	56016324	1-6	4.1561
14	44245404	2-6	4.5984
15	30400236	2-7	4.9386
16	21488292	2-8	5.3561
17	14467860	3-8	5.8267
18	8408736	4-8	6.2481
19	4671720	4-9	6.5799
20	2556000	4-9	7.0831
21	1292184	5-9	7.5779
22	534240	6-10	7.9358
23	229320	6-10	8.3187
24	85680	7-10	8.9235
25	28728	8-10	9.4211
26	6048	9-10	9.5000
27	1512	10	10.0000
0-27	746470296	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	39530700	0-10	3.5455
1	99425700	3-13	6.2727
2	142876800	4-16	7.7980
3	205777440	7-17	10.0466
4	123100560	8-20	12.1206
5	88905960	11-21	13.9113
6	31794444	12-23	16.1718
7	11861388	15-24	17.8022
8	2665872	16-25	20.0802
9	470448	19-26	21.6296
10	60984	22-27	23.9091
0-10	746470296	0-27	10.0000

Study 7Z80   Main

Top   HCP and Controls

6-6-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	762048	0	0
1	2370816	0	0
2	4339440	0	0
3	8784720	0-1	0.2699
4	14817600	0-2	0.7400
5	21337344	0-2	1.0744
6	29211840	0-2	1.3348
7	37192176	0-3	1.8127
8	43076880	0-4	2.2054
9	46484928	1-4	2.5610
10	48577536	1-4	2.9765
11	45505152	1-5	3.4149
12	41189904	2-6	3.7755
13	34700400	2-6	4.1778
14	27615168	2-6	4.6297
15	19885824	3-7	4.9521
16	14164416	4-7	5.3582
17	8881488	4-7	5.7770
18	5198256	4-8	6.1408
19	2915136	5-8	6.4232
20	1410048	6-8	6.8750
21	596160	6-8	7.3188
22	245376	6-8	7.5775
23	88128	7-8	7.8235
24	15552	8	8.0000
0-24	459366336	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	28174608	0-8	3.5455
1	58910544	3-11	6.2727
2	92207808	4-14	7.8965
3	109405296	7-15	10.0404
4	84889728	8-18	12.0498
5	55251504	11-19	13.8417
6	24254208	12-22	16.2721
7	4965840	15-23	17.9091
8	1306800	18-24	20.1818
0-8	459366336	0-24	10.0000

Study 7Z80   Main

Top   HCP and Controls

7-5-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	979776	0	0
1	3374784	0	0
2	6023808	0	0
3	13009248	0-1	0.2594
4	21573216	0-2	0.7477
5	31649184	0-2	1.0841
6	43843680	0-2	1.3320
7	56345760	0-3	1.8187
8	64680768	0-4	2.2082
9	70542144	1-4	2.5652
10	74040480	1-4	2.9764
11	68909184	1-5	3.4117
12	61904736	2-6	3.7723
13	52490160	2-6	4.1756
14	41436576	2-6	4.6295
15	29484000	3-7	4.9456
16	20762784	4-7	5.3530
17	13130208	4-7	5.7837
18	7432992	4-8	6.1485
19	4161024	5-8	6.4266
20	1971648	6-8	6.8988
21	840672	6-8	7.3525
22	326592	6-8	7.5833
23	117936	7-8	7.8462
24	18144	8	8.0000
0-24	689049504	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	40249440	0-8	3.5455
1	88757856	3-11	6.2727
2	136743552	4-14	7.8789
3	170354448	7-15	10.0371
4	125766432	8-18	12.0682
5	83269296	11-19	13.8411
6	34760880	12-22	16.2727
7	7318080	15-23	17.8864
8	1829520	18-24	20.1818
0-8	689049504	0-24	10.0000

Study 7Z80   Main

Top   HCP and Controls

8-3-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	653184	0	0
1	3055968	0	0
2	4898880	0	0
3	13206240	0-1	0.2314
4	20123640	0-2	0.7942
5	31203792	0-2	1.1206
6	44810712	0-2	1.3226
7	58365792	0-3	1.8434
8	64296288	0-4	2.2246
9	71976816	0-4	2.5798
10	77356080	1-4	2.9632
11	68789952	1-5	3.3865
12	60628032	1-6	3.7436
13	52336800	2-6	4.1629
14	41243832	2-6	4.6095
15	28209312	2-7	4.9448
16	19728360	3-7	5.3599
17	13131360	3-7	5.8254
18	7394400	4-8	6.2324
19	3988224	4-8	6.5316
20	2094480	5-8	7.0177
21	992880	5-9	7.4853
22	356832	6-9	7.6497
23	147168	7-9	8.1164
24	48384	7-9	8.6250
25	9072	8-9	8.6667
26	3024	9	9.0000
0-26	689049504	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	35937000	0-9	3.5455
1	91040400	3-12	6.2727
2	131769000	4-15	7.8066
3	189921600	7-17	10.0436
4	115564680	8-19	12.1185
5	82938240	11-21	13.8960
6	29577240	12-22	16.1747
7	10140768	15-24	17.8018
8	2038608	18-25	20.1818
9	121968	21-26	22.9091
0-9	689049504	0-26	10.0000

Study 7Z80   Main

Top   HCP and Controls

8-4-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	244944	0	0
1	1170288	0	0
2	1950480	0	0
3	5159376	0-1	0.2268
4	8150544	0-2	0.7677
5	12600576	0-2	1.1137
6	18387000	0-2	1.3184
7	24084432	0-3	1.8355
8	27055944	0-4	2.2232
9	30288384	1-4	2.5790
10	32788152	1-4	2.9768
11	29397600	1-5	3.4011
12	25957368	2-6	3.7570
13	22343904	2-6	4.1678
14	17366040	2-6	4.6342
15	11739744	3-7	4.9250
16	8026416	4-7	5.3388
17	5184576	4-7	5.8073
18	2675088	4-8	6.1819
19	1459584	5-8	6.4385
20	660240	6-8	6.9679
21	286272	6-8	7.4613
22	90720	6-8	7.6000
23	33264	7-8	7.9091
24	3024	8	8.0000
0-24	287103960	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	14374800	0-8	3.5455
1	37243800	3-11	6.2727
2	54885600	4-14	7.8279
3	79235640	7-15	10.0285
4	50355360	8-18	12.1221
5	34978680	11-19	13.8391
6	12545280	12-22	16.2746
7	2874960	15-23	17.8209
8	609840	18-24	20.1818
0-8	287103960	0-24	10.0000