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	2,310,789,600	0	0
1	5,006,710,800	0	0
2	8,611,542,576	0	0
3	15,636,342,960	0-1	0.3202
4	24,419,055,136	0-2	0.8037
5	32,933,031,040	0-2	1.0609
6	41,619,399,184	0-2	1.3554
7	50,979,441,968	0-3	1.8017
8	56,466,608,128	0-4	2.1906
9	59,413,313,872	0-4	2.5389
10	59,723,754,816	0-4	2.9355
11	56,799,933,520	0-5	3.3723
12	50,971,682,080	0-6	3.7524
13	43,906,944,752	1-6	4.1519
14	36,153,374,224	1-6	4.5803
15	28,090,962,724	1-7	4.9899
16	21,024,781,756	2-8	5.3901
17	14,997,082,848	2-8	5.8111
18	10,192,504,020	2-8	6.2344
19	6,579,838,440	3-9	6.6273
20	4,086,538,404	3-9	7.0491
21	2,399,507,844	3-9	7.4640
22	1,333,800,036	4-10	7.8600
23	710,603,628	4-10	8.2587
24	354,993,864	4-10	8.6729
25	167,819,892	5-11	9.0569
26	74,095,248	6-11	9.4182
27	31,157,940	6-11	9.8359
28	11,790,760	6-12	10.1650
29	4,236,588	7-12	10.5083
30	1,396,068	8-12	10.8810
31	388,196	8-12	11.1218
32	109,156	9-12	11.4631
33	22,360	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	635,013,559,600	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	51,915,526,432	0-12	3.5455
1	84,362,730,452	3-15	6.2727
2	130,378,765,244	4-18	7.8824
3	132,634,453,224	7-21	10.1293
4	106,275,127,972	8-24	11.9909
5	70,893,050,800	11-25	14.0036
6	36,155,455,908	12-28	16.0143
7	15,596,471,176	15-29	17.9256
8	5,192,436,964	16-31	20.0225
9	1,322,059,596	19-32	21.9829
10	258,159,616	22-34	24.0980
11	28,236,208	25-35	26.6364
12	1,086,008	28-37	29.3636
0-12	635,013,559,600	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	1,258,903,296	0	0
1	2,551,590,720	0	0
2	4,389,323,904	0	0
3	7,724,154,816	0-1	0.3303
4	12,008,470,320	0-2	0.8091
5	15,905,447,712	0-2	1.0552
6	19,871,903,664	0-2	1.3576
7	24,098,511,528	0-3	1.7960
8	26,622,237,600	0-4	2.1873
9	27,794,443,680	0-4	2.5323
10	27,806,095,800	0-4	2.9296
11	26,536,540,680	0-5	3.3663
12	23,847,368,760	0-6	3.7502
13	20,587,593,744	1-6	4.1476
14	17,062,981,992	1-6	4.5762
15	13,429,620,828	1-7	4.9940
16	10,135,417,140	2-8	5.3927
17	7,332,174,216	2-8	5.8133
18	5,076,423,252	2-8	6.2414
19	3,342,413,316	3-9	6.6411
20	2,117,203,068	3-9	7.0568
21	1,275,996,648	3-9	7.4749
22	730,416,516	4-10	7.8782
23	399,746,964	4-10	8.2728
24	206,919,732	4-10	8.6845
25	101,379,876	5-11	9.0722
26	46,516,656	6-11	9.4341
27	20,389,980	6-11	9.8456
28	8,101,900	6-12	10.1760
29	3,044,844	7-12	10.5183
30	1,058,604	8-12	10.8937
31	312,688	8-12	11.1288
32	93,348	9-12	11.4764
33	19,980	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	302,292,822,832	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	26,090,262,000	0-12	3.5455
1	40,202,721,900	3-15	6.2727
2	62,392,621,500	4-18	7.8870
3	60,949,551,300	7-21	10.1478
4	50,121,892,920	8-24	11.9777
5	33,214,253,160	11-25	14.0248
6	17,662,662,820	12-28	15.9860
7	7,922,143,944	15-29	17.9344
8	2,781,316,164	16-31	19.9969
9	773,901,964	19-32	21.9665
10	160,997,760	22-34	24.1190
11	19,565,700	25-35	26.6364
12	931,700	28-37	29.3636
0-12	302,292,822,832	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	1,051,886,304	0	0
1	2,455,120,080	0	0
2	4,222,218,672	0	0
3	7,912,188,144	0-1	0.3103
4	12,410,584,816	0-2	0.7985
5	17,027,583,328	0-2	1.0662
6	21,747,495,520	0-2	1.3534
7	26,880,930,440	0-3	1.8067
8	29,844,370,528	0-4	2.1935
9	31,618,870,192	0-4	2.5447
10	31,917,659,016	0-4	2.9406
11	30,263,392,840	0-5	3.3774
12	27,124,313,320	0-6	3.7543
13	23,319,351,008	1-6	4.1558
14	19,090,392,232	1-6	4.5839
15	14,661,341,896	1-7	4.9863
16	10,889,364,616	2-8	5.3876
17	7,664,908,632	2-8	5.8090
18	5,116,080,768	2-8	6.2275
19	3,237,425,124	3-9	6.6131
20	1,969,335,336	3-9	7.0408
21	1,123,511,196	4-9	7.4518
22	603,383,520	4-10	7.8379
23	310,856,664	5-10	8.2406
24	148,074,132	5-10	8.6566
25	66,440,016	6-11	9.0335
26	27,578,592	6-11	9.3914
27	10,767,960	7-11	9.8176
28	3,688,860	7-12	10.1408
29	1,191,744	8-12	10.4828
30	337,464	8-12	10.8409
31	75,508	9-12	11.0930
32	15,808	9-12	11.3844
33	2380	10-12	11.7697
34	112	11-12	11.9643
0-34	332,720,736,768	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	25,825,264,432	0-12	3.5455
1	44,160,008,552	3-15	6.2727
2	67,986,143,744	4-18	7.8781
3	71,684,901,924	7-20	10.1135
4	56,153,235,052	8-22	12.0027
5	37,678,797,640	11-24	13.9850
6	18,492,793,088	12-26	16.0413
7	7,674,327,232	15-28	17.9166
8	2,411,120,800	16-30	20.0520
9	548,157,632	19-32	22.0060
10	97,161,856	22-33	24.0632
11	8,670,508	25-34	26.6364
12	154,308	28-34	29.3636
0-12	332,720,736,768	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	2,046,339,936	0	0
1	4,319,337,312	0	0
2	7,426,786,320	0	0
3	13,309,544,160	0-1	0.3245
4	20,740,666,032	0-2	0.8063
5	27,766,490,688	0-2	1.0586
6	34,890,285,600	0-2	1.3567
7	42,559,540,992	0-3	1.7994
8	47,071,459,800	0-4	2.1891
9	49,362,273,432	0-4	2.5361
10	49,482,685,848	0-4	2.9327
11	47,153,411,544	0-5	3.3696
12	42,334,154,904	0-6	3.7513
13	36,504,121,416	1-6	4.1500
14	30,144,202,608	1-6	4.5780
15	23,567,774,556	1-7	4.9920
16	17,705,857,932	2-8	5.3913
17	12,711,756,264	2-8	5.8121
18	8,713,861,836	2-8	6.2375
19	5,674,847,712	3-9	6.6339
20	3,556,301,748	3-9	7.0530
21	2,111,792,784	3-9	7.4689
22	1,188,569,904	4-10	7.8685
23	640,180,896	4-10	8.2659
24	324,431,592	4-10	8.6789
25	155,400,900	5-11	9.0634
26	69,483,828	6-11	9.4252
27	29,637,876	6-11	9.8406
28	11,364,952	6-12	10.1681
29	4,129,560	7-12	10.5102
30	1,372,704	8-12	10.8818
31	386,360	8-12	11.1224
32	109,156	9-12	11.4631
33	22,360	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	531,578,588,684	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	44,493,999,000	0-12	3.5455
1	70,687,679,700	3-15	6.2727
2	109,422,015,780	4-18	7.8842
3	109,311,569,400	7-21	10.1373
4	88,574,786,388	8-24	11.9849
5	58,946,311,116	11-25	14.0136
6	30,606,586,516	12-28	16.0014
7	13,470,932,904	15-29	17.9291
8	4,580,164,116	16-31	20.0124
9	1,213,672,944	19-32	21.9739
10	242,438,416	22-34	24.1039
11	27,346,396	25-35	26.6364
12	1,086,008	28-37	29.3636
0-12	531,578,588,684	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	264,449,664	0	0
1	687,373,488	0	0
2	1,184,756,256	0	0
3	2,326,798,800	0-1	0.2954
4	3,678,389,104	0-2	0.7893
5	5,166,540,352	0-2	1.0734
6	6,729,113,584	0-2	1.3487
7	8,419,900,976	0-3	1.8129
8	9,395,148,328	0-4	2.1982
9	10,051,040,440	0-4	2.5525
10	10,241,068,968	0-4	2.9487
11	9,646,521,976	0-5	3.3850
12	8,637,527,176	1-6	3.7574
13	7,402,823,336	1-6	4.1613
14	6,009,171,616	1-6	4.5915
15	4,523,188,168	2-7	4.9795
16	3,318,923,824	2-8	5.3833
17	2,285,326,584	2-8	5.8057
18	1,478,642,184	3-8	6.2164
19	904,990,728	3-9	6.5859
20	530,236,656	4-9	7.0227
21	287,715,060	4-9	7.4282
22	145,230,132	5-10	7.7900
23	70,422,732	5-10	8.1933
24	30,562,272	6-10	8.6092
25	12,418,992	6-11	8.9751
26	4,611,420	7-11	9.3132
27	1,520,064	7-11	9.7451
28	425,808	8-11	10.0809
29	107,028	9-11	10.4353
30	23,364	9-11	10.8336
31	1836	11	11.0000
0-31	103,434,970,916	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	7,421,527,432	0-11	3.5455
1	13,675,050,752	3-14	6.2727
2	20,956,749,464	4-17	7.8729
3	23,322,883,824	7-19	10.0917
4	17,700,341,584	8-21	12.0211
5	11,946,739,684	11-23	13.9547
6	5,548,869,392	12-25	16.0851
7	2,125,538,272	15-27	17.9037
8	612,272,848	16-28	20.0976
9	108,386,652	19-30	22.0828
10	15,721,200	22-30	24.0069
11	889,812	25-31	26.6364
0-11	103,434,970,916	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	298,722,816	0	0
1	583,220,736	0	0
2	1,003,871,232	0	0
3	1,739,138,688	0-1	0.3354
4	2,698,012,800	0-2	0.8114
5	3,539,168,640	0-2	1.0522
6	4,403,572,128	0-2	1.3580
7	5,311,985,184	0-3	1.7927
8	5,863,612,032	0-4	2.1858
9	6,098,710,968	0-4	2.5289
10	6,094,244,088	0-4	2.9269
11	5,820,897,816	0-5	3.3634
12	5,236,272,216	0-6	3.7494
13	4,525,112,736	1-6	4.1455
14	3,762,309,384	1-6	4.5752
15	2,976,568,236	1-7	4.9956
16	2,254,937,832	2-8	5.3939
17	1,641,613,500	2-8	5.8145
18	1,145,716,128	2-8	6.2448
19	761,091,672	3-9	6.6464
20	486,317,352	3-9	7.0591
21	296,791,896	3-9	7.4794
22	172,256,424	4-10	7.8850
23	95,566,800	4-10	8.2768
24	50,363,112	4-10	8.6872
25	25,179,360	5-11	9.0786
26	11,820,648	6-11	9.4386
27	5,307,456	6-11	9.8457
28	2,183,392	6-12	10.1786
29	846,960	7-12	10.5192
30	308,448	8-12	10.8906
31	95,632	8-12	11.1131
32	30,720	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	66,905,856,160	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	5,929,605,000	0-12	3.5455
1	8,894,407,500	3-15	6.2727
2	13,835,745,000	4-18	7.8896
3	13,264,746,000	7-21	10.1573
4	11,046,634,500	8-24	11.9718
5	7,291,218,000	11-25	14.0342
6	3,958,926,400	12-28	15.9723
7	1,800,843,000	15-29	17.9390
8	650,060,400	16-31	19.9834
9	187,697,620	19-32	21.9660
10	40,409,160	22-34	24.1344
11	5,270,760	25-35	26.6364
12	292,820	28-37	29.3636
0-12	66,905,856,160	0-37	10.0000

Study 7Z80 Main

Top HCP and Controls

4-4-3-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	576,108,288	0	0
1	1,159,075,008	0	0
2	1,998,089,856	0	0
3	3,500,086,464	0-1	0.3312
4	5,447,418,480	0-2	0.8083
5	7,201,988,640	0-2	1.0541
6	8,995,078,512	0-2	1.3576
7	10,896,685,056	0-3	1.7949
8	12,048,600,960	0-4	2.1872
9	12,566,324,448	0-4	2.5319
10	12,574,353,168	0-4	2.9296
11	12,003,625,008	0-5	3.3665
12	10,792,467,648	0-6	3.7508
13	9,314,807,760	1-6	4.1477
14	7,725,746,736	1-6	4.5768
15	6,084,044,784	1-7	4.9944
16	4,593,528,252	2-8	5.3930
17	3,323,621,808	2-8	5.8130
18	2,303,233,056	2-8	6.2412
19	1,517,291,568	3-9	6.6402
20	961,283,664	3-9	7.0556
21	579,570,336	3-9	7.4725
22	331,988,400	4-10	7.8756
23	181,741,248	4-10	8.2699
24	93,978,144	5-10	8.6797
25	46,084,320	5-11	9.0663
26	21,121,560	6-11	9.4286
27	9,244,080	6-11	9.8374
28	3,659,760	7-12	10.1640
29	1,376,688	7-12	10.5106
30	473,136	8-12	10.8791
31	139,152	8-12	11.1149
32	40,992	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	136,852,887,600	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	11,859,210,000	0-12	3.5455
1	18,184,122,000	3-15	6.2727
2	28,264,450,500	4-18	7.8887
3	27,491,805,000	7-21	10.1490
4	22,714,579,800	8-23	11.9758
5	15,026,457,600	11-25	14.0250
6	8,024,732,100	12-27	15.9848
7	3,592,102,800	15-29	17.9365
8	1,263,784,500	16-31	19.9990
9	349,786,800	19-32	21.9745
10	72,672,600	22-34	24.1179
11	8,784,600	25-35	26.6364
12	399,300	28-36	29.3636
0-12	136,852,887,600	0-36	10.0000

Study 7Z80 Main

Top HCP and Controls

5-3-3-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	384,072,192	0	0
1	809,294,976	0	0
2	1,387,362,816	0	0
3	2,484,929,664	0-1	0.3257
4	3,863,039,040	0-2	0.8086
5	5,164,290,432	0-2	1.0589
6	6,473,253,024	0-2	1.3574
7	7,889,841,288	0-3	1.7997
8	8,710,024,608	0-4	2.1885
9	9,129,408,264	0-4	2.5352
10	9,137,498,544	0-4	2.9313
11	8,712,017,856	0-5	3.3681
12	7,818,628,896	0-6	3.7499
13	6,747,673,248	1-6	4.1488
14	5,574,925,872	1-6	4.5761
15	4,369,007,808	1-7	4.9921
16	3,286,951,056	2-8	5.3915
17	2,366,938,908	2-8	5.8130
18	1,627,474,068	2-8	6.2392
19	1,064,030,076	3-9	6.6384
20	669,602,052	3-9	7.0569
21	399,634,416	3-9	7.4749
22	226,171,692	4-10	7.8768
23	122,438,916	4-10	8.2740
24	62,578,476	5-10	8.6896
25	30,116,196	5-11	9.0759
26	13,574,448	6-11	9.4387
27	5,838,444	6-11	9.8585
28	2,258,748	7-12	10.1928
29	821,196	8-12	10.5303
30	277,020	8-12	10.9222
31	77,904	9-12	11.1728
32	21,636	10-12	11.5008
33	4428	10-12	11.7317
34	756	11-12	11.8571
35	108	12	12.0000
0-35	98,534,079,072	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	8,301,447,000	0-12	3.5455
1	13,124,192,400	3-15	6.2727
2	20,292,426,000	4-18	7.8829
3	20,193,000,300	7-21	10.1398
4	16,360,678,620	8-23	11.9844
5	10,896,577,560	11-25	14.0183
6	5,679,004,320	12-27	15.9973
7	2,529,198,144	15-28	17.9280
8	867,471,264	16-30	20.0039
9	236,417,544	19-31	21.9551
10	47,916,000	22-33	24.1077
11	5,510,340	25-34	26.6364
12	239,580	28-35	29.3636
0-12	98,534,079,072	0-35	10.0000

Study 7Z80 Main

Top HCP and Controls

5-4-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	246,903,552	0	0
1	534,957,696	0	0
2	920,744,496	0	0
3	1,663,414,704	0-1	0.3216
4	2,599,672,320	0-2	0.8041
5	3,498,126,912	0-2	1.0604
6	4,406,978,016	0-2	1.3566
7	5,389,847,568	0-3	1.8015
8	5,968,963,224	0-4	2.1901
9	6,267,660,768	0-4	2.5381
10	6,288,743,232	0-4	2.9346
11	5,988,505,392	0-5	3.3717
12	5,376,127,896	0-6	3.7515
13	4,629,605,760	1-6	4.1509
14	3,817,654,200	1-6	4.5783
15	2,974,849,200	1-7	4.9899
16	2,231,960,400	2-8	5.3903
17	1,594,443,744	2-8	5.8108
18	1,088,865,180	2-8	6.2348
19	705,038,724	3-9	6.6311
20	439,647,696	3-9	7.0530
21	258,562,800	4-9	7.4674
22	144,483,192	4-10	7.8680
23	76,884,012	5-10	8.2661
24	38,504,268	5-10	8.6847
25	18,089,424	6-11	9.0664
26	7,959,168	6-11	9.4313
27	3,302,208	7-11	9.8535
28	1,223,244	7-12	10.1906
29	427,356	8-12	10.5345
30	135,648	8-12	10.9379
31	34,272	9-12	11.2216
32	8640	10-12	11.5750
33	1620	11-12	11.8667
34	108	12	12.0000
0-34	67,182,326,640	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	5,534,298,000	0-12	3.5455
1	8,933,938,200	3-15	6.2727
2	13,819,932,720	4-18	7.8834
3	13,931,577,000	7-20	10.1313
4	11,234,624,940	8-22	11.9882
5	7,481,364,660	11-24	14.0070
6	3,841,817,760	12-26	16.0143
7	1,667,542,140	15-28	17.9266
8	560,617,200	16-30	20.0177
9	144,815,220	19-31	21.9518
10	28,749,600	22-32	24.0857
11	2,940,300	25-33	26.6364
12	108,900	28-34	29.3636
0-12	67,182,326,640	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	72,013,536	0	0
1	152,028,576	0	0
2	264,049,632	0	0
3	469,802,592	0-1	0.3236
4	737,366,112	0-2	0.7999
5	987,952,896	0-2	1.0552
6	1,244,046,384	0-2	1.3560
7	1,518,005,664	0-3	1.7963
8	1,687,649,040	0-4	2.1891
9	1,768,663,296	0-4	2.5370
10	1,776,222,000	0-4	2.9355
11	1,695,428,928	0-5	3.3735
12	1,524,045,240	1-6	3.7563
13	1,312,019,208	1-6	4.1537
14	1,083,496,608	1-6	4.5835
15	845,748,000	2-7	4.9948
16	633,339,864	2-8	5.3923
17	452,355,840	2-8	5.8094
18	308,297,340	3-8	6.2323
19	199,296,720	3-9	6.6205
20	123,431,040	3-9	7.0384
21	72,363,024	4-9	7.4436
22	39,978,396	5-10	7.8327
23	21,212,568	5-10	8.2326
24	10,350,936	5-10	8.6250
25	4,855,824	6-11	8.9976
26	2,060,532	7-11	9.3568
27	837,936	7-11	9.7514
28	293,040	7-11	10.0243
29	100,224	8-11	10.3890
30	26,604	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	19,007,345,500	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1,581,228,000	0-11	3.5455
1	2,515,590,000	3-14	6.2727
2	3,917,133,000	4-17	7.8907
3	3,899,164,500	7-20	10.1353
4	3,198,393,000	8-21	11.9801
5	2,120,283,000	11-24	14.0054
6	1,102,068,000	12-25	16.0040
7	473,170,500	15-28	17.9356
8	155,727,000	16-29	20.0490
9	37,268,000	19-32	22.0763
10	6,655,000	22-33	24.0818
11	665,500	25-34	26.6364
0-11	19,007,345,500	0-34	10.0000

Study 7Z80 Main

Top HCP and Controls

5-4-3-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	288,054,144	0	0
1	635,548,032	0	0
2	1,100,397,312	0	0
3	1,996,946,784	0-1	0.3183
4	3,137,188,320	0-2	0.7988
5	4,244,734,368	0-2	1.0595
6	5,370,642,144	0-2	1.3554
7	6,588,576,288	0-3	1.8007
8	7,323,861,888	0-4	2.1907
9	7,706,183,184	0-4	2.5402
10	7,749,400,896	0-4	2.9377
11	7,383,262,320	0-5	3.3755
12	6,630,108,768	1-6	3.7556
13	5,702,287,680	1-6	4.1547
14	4,693,321,440	1-6	4.5833
15	3,641,808,816	2-7	4.9915
16	2,719,135,008	2-8	5.3907
17	1,929,268,368	2-8	5.8087
18	1,304,790,336	3-8	6.2294
19	835,879,176	3-9	6.6173
20	513,892,584	3-9	7.0391
21	297,351,000	4-9	7.4450
22	162,337,464	5-10	7.8336
23	84,834,648	5-10	8.2354
24	40,853,664	5-10	8.6378
25	18,688,320	6-11	9.0097
26	7,809,120	7-11	9.3695
27	3,074,976	7-11	9.7773
28	1,044,864	7-11	10.0618
29	340,632	8-11	10.4149
30	87,768	9-11	10.6555
31	18,792	9-11	10.8046
32	3240	10-11	10.9333
33	216	11	11.0000
0-33	82,111,732,560	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	6,641,157,600	0-11	3.5455
1	10,881,723,600	3-14	6.2727
2	16,876,015,200	4-17	7.8862
3	17,160,636,240	7-20	10.1259
4	13,848,203,160	8-21	11.9886
5	9,220,475,880	11-24	13.9967
6	4,685,226,480	12-25	16.0209
7	1,981,805,760	15-28	17.9281
8	639,199,440	16-29	20.0523
9	148,539,600	19-31	22.0455
10	26,353,800	22-32	24.0661
11	2,395,800	25-33	26.6364
0-11	82,111,732,560	0-33	10.0000

Study 7Z80 Main

Top HCP and Controls

6-3-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	109,734,912	0	0
1	266,499,072	0	0
2	449,717,184	0	0
3	863,890,272	0-1	0.3085
4	1,338,156,288	0-2	0.8085
5	1,847,667,024	0-2	1.0726
6	2,350,716,984	0-2	1.3549
7	2,913,941,520	0-3	1.8127
8	3,205,597,248	0-4	2.1935
9	3,408,949,152	0-4	2.5449
10	3,424,218,840	0-4	2.9367
11	3,244,906,656	0-5	3.3726
12	2,898,328,752	0-6	3.7481
13	2,499,992,640	1-6	4.1520
14	2,042,896,320	1-6	4.5757
15	1,573,412,976	1-7	4.9844
16	1,170,675,936	2-8	5.3867
17	830,508,048	2-8	5.8133
18	556,662,096	2-8	6.2346
19	354,639,744	3-9	6.6305
20	218,278,656	3-9	7.0603
21	126,158,832	4-9	7.4838
22	68,465,232	4-10	7.8802
23	35,695,728	5-10	8.2841
24	17,525,952	5-10	8.7201
25	7,927,488	6-11	9.1079
26	3,352,680	6-11	9.4637
27	1,358,496	7-11	9.9185
28	483,120	8-12	10.2851
29	154,080	8-12	10.5846
30	48,168	9-12	11.0523
31	11,376	10-12	11.4051
32	2304	11-12	11.6250
33	432	12	12.0000
0-33	35,830,574,208	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	2,767,149,000	0-12	3.5455
1	4,796,391,600	3-15	6.2727
2	7,305,273,360	4-18	7.8659
3	7,795,933,200	7-20	10.1144
4	5,957,396,280	8-22	12.0106
5	4,043,343,744	11-24	13.9971
6	1,957,900,032	12-26	16.0345
7	853,357,824	15-27	17.9032
8	270,237,528	16-29	20.0208
9	69,364,944	19-30	21.9021
10	12,946,032	22-31	24.0741
11	1,237,104	25-32	26.6364
12	43,560	28-33	29.3636
0-12	35,830,574,208	0-33	10.0000

Study 7Z80 Main

Top HCP and Controls

6-3-3-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	64,012,032	0	0
1	157,997,952	0	0
2	268,821,504	0	0
3	517,466,880	0-1	0.3053
4	807,371,712	0-2	0.8018
5	1,119,557,376	0-2	1.0713
6	1,431,860,976	0-2	1.3536
7	1,779,410,808	0-3	1.8114
8	1,967,529,312	0-4	2.1941
9	2,094,792,840	0-4	2.5469
10	2,110,824,576	0-4	2.9403
11	2,000,693,520	0-5	3.3770
12	1,788,624,288	1-6	3.7526
13	1,539,727,200	1-6	4.1559
14	1,256,282,784	1-6	4.5812
15	962,553,888	2-7	4.9850
16	712,974,672	2-8	5.3867
17	501,522,624	2-8	5.8104
18	332,747,136	3-8	6.2281
19	209,448,144	3-9	6.6151
20	126,998,208	3-9	7.0456
21	71,982,576	4-9	7.4605
22	38,137,392	5-10	7.8447
23	19,456,992	5-10	8.2531
24	9,171,936	5-10	8.6776
25	4,002,336	6-11	9.0532
26	1,612,800	7-11	9.4038
27	607,752	7-11	9.8479
28	197,280	8-11	10.1577
29	57,384	9-11	10.4605
30	14,400	9-11	10.7500
31	2304	10-11	10.8125
32	432	11	11.0000
0-32	21,896,462,016	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1,660,289,400	0-11	3.5455
1	2,918,084,400	3-14	6.2727
2	4,460,979,600	4-17	7.8701
3	4,794,954,120	7-20	10.1087
4	3,678,990,480	8-21	12.0108
5	2,490,673,680	11-24	13.9848
6	1,195,216,704	12-25	16.0453
7	502,543,008	15-27	17.9055
8	153,427,032	16-28	20.0545
9	34,882,848	19-30	21.9838
10	5,941,584	22-31	24.0484
11	479,160	25-32	26.6364
0-11	21,896,462,016	0-32	10.0000

Study 7Z80 Main

Top HCP and Controls

5-5-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	61,725,888	0	0
1	145,741,680	0	0
2	253,761,984	0	0
3	471,517,200	0-1	0.3091
4	748,331,136	0-2	0.7905
5	1,026,669,168	0-2	1.0646
6	1,314,750,528	0-2	1.3533
7	1,624,967,568	0-3	1.8059
8	1,816,432,128	0-4	2.1943
9	1,919,571,696	0-4	2.5459
10	1,941,202,368	0-4	2.9443
11	1,842,063,552	0-5	3.3820
12	1,655,365,680	1-6	3.7570
13	1,417,246,848	1-6	4.1577
14	1,160,905,392	1-6	4.5867
15	888,961,824	2-7	4.9838
16	660,369,024	2-8	5.3869
17	460,066,608	2-8	5.8041
18	306,517,824	3-8	6.2198
19	192,340,656	3-9	6.6033
20	115,912,080	4-9	7.0343
21	64,890,828	4-9	7.4380
22	34,538,616	5-10	7.8269
23	17,330,544	5-10	8.2266
24	8,001,288	6-10	8.6512
25	3,445,200	6-11	9.0230
26	1,376,352	7-11	9.3839
27	492,480	7-11	9.8039
28	148,392	8-11	10.1288
29	42,768	9-11	10.4773
30	9720	10-11	10.8000
31	972	11	11.0000
0-31	20,154,697,992	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	1,549,603,440	0-11	3.5455
1	2,664,512,928	3-14	6.2727
2	4,127,292,576	4-17	7.8849
3	4,330,839,744	7-19	10.1078
4	3,443,313,456	8-21	12.0007
5	2,291,813,568	11-23	13.9727
6	1,126,265,580	12-25	16.0641
7	446,402,880	15-27	17.9218
8	140,023,620	16-28	20.0649
9	29,076,300	19-29	21.9775
10	5,227,200	22-30	24.0170
11	326,700	25-31	26.6364
0-11	20,154,697,992	0-31	10.0000

Study 7Z80 Main

Top HCP and Controls

6-4-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	82,301,184	0	0
1	208,039,104	0	0
2	357,019,488	0	0
3	689,925,600	0-1	0.3015
4	1,086,390,144	0-2	0.7946
5	1,512,689,472	0-2	1.0719
6	1,948,375,296	0-2	1.3521
7	2,426,856,768	0-3	1.8122
8	2,698,584,336	0-4	2.1960
9	2,874,342,240	0-4	2.5494
10	2,908,319,904	0-4	2.9447
11	2,751,350,112	0-5	3.3815
12	2,463,525,792	1-6	3.7547
13	2,113,475,328	1-6	4.1578
14	1,721,571,264	1-6	4.5848
15	1,309,621,536	2-7	4.9806
16	967,753,728	2-8	5.3845
17	673,095,456	2-8	5.8064
18	443,031,264	3-8	6.2214
19	275,793,408	3-9	6.6043
20	165,054,240	4-9	7.0405
21	91,737,216	4-9	7.4522
22	47,920,320	5-10	7.8371
23	23,848,992	5-10	8.2416
24	10,904,832	6-10	8.6787
25	4,602,528	6-11	9.0545
26	1,796,544	7-11	9.4045
27	635,040	7-11	9.8478
28	187,344	8-11	10.1868
29	50,976	9-11	10.4972
30	11,520	10-11	10.8500
31	864	11	11.0000
0-31	29,858,811,840	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	2,213,719,200	0-11	3.5455
1	3,964,569,840	3-14	6.2727
2	6,077,665,440	4-17	7.8733
3	6,598,991,520	7-19	10.1001
4	5,071,255,200	8-21	12.0144
5	3,416,933,520	11-23	13.9694
6	1,621,825,920	12-25	16.0717
7	648,608,400	15-27	17.9065
8	196,542,720	16-28	20.0639
9	41,120,640	19-29	21.9466
10	7,143,840	22-30	24.0144
11	435,600	25-31	26.6364
0-11	29,858,811,840	0-31	10.0000

Study 7Z80 Main

Top HCP and Controls

7-2-2-2 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	6,718,464	0	0
1	20,715,264	0	0
2	33,732,288	0	0
3	73,868,112	0-1	0.2804
4	112,440,960	0-2	0.8141
5	163,004,400	0-2	1.0962
6	214,137,432	0-2	1.3472
7	271,247,616	0-3	1.8319
8	295,621,488	0-4	2.2043
9	321,580,512	0-4	2.5588
10	327,180,504	0-4	2.9423
11	304,074,048	0-5	3.3742
12	269,551,200	0-6	3.7411
13	232,895,184	1-6	4.1531
14	187,569,264	1-6	4.5749
15	139,780,848	1-7	4.9707
16	102,354,912	2-8	5.3778
17	71,483,424	2-8	5.8198
18	46,076,496	3-8	6.2406
19	28,131,888	3-9	6.6266
20	16,850,496	4-9	7.0756
21	9,377,904	4-9	7.5239
22	4,751,712	5-10	7.9119
23	2,349,984	5-10	8.3176
24	1,105,104	6-10	8.7960
25	457,632	6-11	9.2074
26	172,872	7-11	9.5248
27	66,528	8-11	10.0530
28	21,504	9-12	10.5234
29	5040	10-12	10.7000
30	1512	11-12	11.3333
31	336	12	12.0000
0-31	3,257,324,928	0-12	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	219,615,000	0-12	3.5455
1	439,230,000	3-15	6.2727
2	650,060,400	4-17	7.8329
3	779,753,040	7-19	10.0856
4	535,285,608	8-21	12.0549
5	375,916,992	11-23	13.9750
6	161,694,720	12-25	16.0751
7	70,369,728	15-26	17.8583
8	19,639,752	16-27	20.0299
9	4,900,368	19-28	21.8057
10	794,640	22-29	24.0457
11	62,832	25-30	26.6364
12	1848	28-31	29.3636
0-12	3,257,324,928	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	24,004,512	0	0
1	56,010,528	0	0
2	98,685,216	0	0
3	181,748,448	0-1	0.3082
4	289,959,264	0-2	0.7832
5	398,805,120	0-2	1.0567
6	511,388,640	0-2	1.3513
7	633,298,176	0-3	1.7977
8	711,807,264	0-4	2.1915
9	754,028,352	0-4	2.5455
10	763,599,312	1-4	2.9462
11	728,808,192	1-5	3.3862
12	655,299,720	1-6	3.7678
13	561,789,432	2-6	4.1668
14	459,690,768	2-6	4.5992
15	352,176,768	2-7	4.9980
16	258,943,608	3-7	5.3939
17	179,644,176	3-7	5.8044
18	117,527,544	3-8	6.2122
19	72,518,544	4-8	6.5687
20	42,273,576	5-8	6.9813
21	22,965,552	5-9	7.3464
22	11,394,972	5-9	7.6585
23	5,509,872	6-9	8.0577
24	2,202,156	7-9	8.3125
25	893,664	7-9	8.6087
26	284,940	7-9	8.8365
27	79,200	8-9	8.9700
28	18,900	9	9.0000
29	2376	9	9.0000
30	108	9	9.0000
0-30	7,895,358,900	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	603,741,600	0-9	3.5455
1	1,034,985,600	3-12	6.2727
2	1,617,165,000	4-15	7.8945
3	1,689,039,000	7-18	10.1103
4	1,365,606,000	8-19	11.9909
5	909,206,100	11-22	13.9662
6	448,014,600	12-23	16.0389
7	173,695,500	15-26	17.9310
8	47,916,000	18-27	20.1818
9	5,989,500	21-30	22.9091
0-9	7,895,358,900	0-30	10.0000

Study 7Z80 Main

Top HCP and Controls

7-3-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	23,514,624	0	0
1	73,436,544	0	0
2	121,056,768	0	0
3	264,446,208	0-1	0.2777
4	406,967,328	0-2	0.8049
5	591,197,184	0-2	1.0939
6	781,627,968	0-2	1.3456
7	992,222,352	0-3	1.8295
8	1,089,256,896	0-4	2.2045
9	1,184,984,208	0-4	2.5603
10	1,210,560,768	0-4	2.9470
11	1,125,952,128	0-5	3.3795
12	999,507,456	1-6	3.7465
13	861,315,264	1-6	4.1569
14	692,336,736	1-6	4.5819
15	512,714,592	2-7	4.9690
16	373,514,688	2-8	5.3767
17	258,083,424	2-8	5.8150
18	164,003,328	3-8	6.2311
19	98,909,568	3-9	6.6070
20	58,073,760	4-9	7.0601
21	31,538,304	4-9	7.5001
22	15,507,072	5-10	7.8747
23	7,471,296	5-10	8.2858
24	3,330,432	6-10	8.7651
25	1,312,416	7-11	9.1636
26	467,712	7-11	9.4677
27	160,272	8-11	9.9874
28	44,352	9-11	10.4091
29	9072	10-11	10.5556
30	2016	11	11.0000
0-30	11,943,524,736	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	790,614,000	0-11	3.5455
1	1,600,394,400	3-14	6.2727
2	2,382,383,520	4-17	7.8397
3	2,870,168,400	7-19	10.0796
4	1,991,737,440	8-21	12.0549
5	1,388,727,648	11-23	13.9582
6	593,740,224	12-24	16.0950
7	243,099,648	15-26	17.8625
8	66,193,776	16-27	20.0609
9	14,148,288	19-28	21.8519
10	2,195,424	22-29	24.0051
11	121,968	25-30	26.6364
0-11	11,943,524,736	0-30	10.0000

Study 7Z80 Main

Top HCP and Controls

5-5-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	16,003,008	0	0
1	38,864,448	0	0
2	68,584,320	0	0
3	128,214,576	0-1	0.3031
4	205,562,448	0-2	0.7794
5	284,815,440	0-2	1.0602
6	367,751,664	0-2	1.3500
7	457,274,160	0-3	1.8012
8	515,217,024	0-4	2.1935
9	547,132,320	0-4	2.5483
10	555,823,296	1-4	2.9494
11	529,060,896	1-5	3.3891
12	475,892,928	1-6	3.7676
13	407,021,760	2-6	4.1678
14	332,133,264	2-6	4.6003
15	252,522,576	2-7	4.9929
16	185,235,984	3-7	5.3914
17	127,169,136	3-7	5.8021
18	82,486,944	3-8	6.2068
19	50,289,984	4-8	6.5607
20	28,983,312	5-8	6.9780
21	15,414,192	5-9	7.3430
22	7,533,648	5-9	7.6515
23	3,545,964	6-9	8.0456
24	1,376,028	7-9	8.3176
25	530,712	7-9	8.6087
26	167,832	7-9	8.8436
27	40,824	8-9	8.9762
28	8748	9	9.0000
29	972	9	9.0000
0-29	5,684,658,408	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	422,619,120	0-9	3.5455
1	744,614,640	3-12	6.2727
2	1,161,483,840	4-15	7.8927
3	1,235,657,808	7-18	10.1005
4	988,986,240	8-19	11.9992
5	658,365,840	11-22	13.9536
6	318,401,820	12-23	16.0646
7	118,592,100	15-26	17.9256
8	32,343,300	18-27	20.1818
9	3,593,700	21-29	22.9091
0-9	5,684,658,408	0-29	10.0000

Study 7Z80 Main

Top HCP and Controls

6-5-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	10,287,648	0	0
1	28,005,264	0	0
2	49,279,104	0	0
3	96,589,584	0-1	0.2899
4	156,219,840	0-2	0.7736
5	220,253,040	0-2	1.0734
6	289,977,408	0-2	1.3467
7	363,899,088	0-3	1.8136
8	411,233,760	0-4	2.2006
9	439,323,696	0-4	2.5555
10	449,962,128	0-4	2.9574
11	423,636,696	1-5	3.3947
12	381,013,416	1-6	3.7619
13	323,992,872	1-6	4.1644
14	262,155,096	2-6	4.5981
15	195,270,264	2-7	4.9682
16	142,861,536	2-8	5.3765
17	95,867,280	3-8	5.7944
18	61,181,136	4-8	6.1973
19	36,770,976	4-9	6.5603
20	20,893,680	4-9	7.0125
21	10,846,440	5-9	7.4226
22	5,357,880	6-10	7.8006
23	2,447,928	6-10	8.1886
24	979,560	6-10	8.6670
25	358,344	7-10	9.0705
26	121,824	8-10	9.4043
27	32,400	9-10	9.7600
28	3888	10	10.0000
0-28	4,478,821,776	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	309,920,688	0-10	3.5455
1	587,641,824	3-13	6.2727
2	908,173,728	4-16	7.8824
3	1,017,761,976	7-17	10.0758
4	785,465,208	8-20	12.0264
5	522,040,464	11-21	13.9223
6	240,137,568	12-24	16.1494
7	79,976,160	15-25	17.9089
8	23,522,400	16-26	20.0955
9	3,528,360	19-27	21.8215
10	653,400	22-28	23.9091
0-10	4,478,821,776	0-28	10.0000

Study 7Z80 Main

Top HCP and Controls

6-4-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	21,337,344	0	0
1	55,375,488	0	0
2	96,526,080	0	0
3	187,209,792	0-1	0.2958
4	298,414,368	0-2	0.7823
5	419,126,400	0-2	1.0671
6	544,737,312	0-2	1.3487
7	682,311,168	0-3	1.8071
8	765,761,472	0-4	2.1952
9	818,893,152	0-4	2.5516
10	833,066,640	1-4	2.9503
11	790,398,000	1-5	3.3890
12	708,825,600	1-6	3.7655
13	607,037,760	2-6	4.1680
14	492,804,000	2-6	4.5990
15	371,841,840	2-7	4.9890
16	271,408,176	3-7	5.3889
17	185,666,976	3-7	5.8038
18	118,867,680	3-8	6.2067
19	71,718,336	4-8	6.5589
20	41,009,328	5-8	6.9815
21	21,532,176	5-9	7.3544
22	10,289,664	5-9	7.6520
23	4,778,496	6-9	8.0563
24	1,835,136	7-9	8.3475
25	671,184	7-9	8.6145
26	214,704	7-9	8.8645
27	46,368	8-9	8.9814
28	10,656	9	9.0000
29	864	9	9.0000
0-29	8,421,716,160	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	603,741,600	0-9	3.5455
1	1,106,859,600	3-12	6.2727
2	1,710,601,200	4-15	7.8824
3	1,880,223,840	7-18	10.0924
4	1,459,521,360	8-19	12.0128
5	981,319,680	11-22	13.9482
6	459,035,280	12-23	16.0759
7	170,580,960	15-26	17.9106
8	45,041,040	18-27	20.1818
9	4,791,600	21-29	22.9091
0-9	8,421,716,160	0-29	10.0000

Study 7Z80 Main

Top HCP and Controls

7-4-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	4,408,992	0	0
1	14,206,752	0	0
2	24,058,944	0	0
3	52,289,712	0-1	0.2717
4	82,537,488	0-2	0.7852
5	120,271,824	0-2	1.0907
6	161,467,776	0-2	1.3418
7	205,755,120	0-3	1.8262
8	229,419,648	0-4	2.2063
9	249,487,560	0-4	2.5632
10	257,250,384	0-4	2.9576
11	239,196,024	1-5	3.3909
12	213,122,880	1-6	3.7553
13	182,487,096	1-6	4.1624
14	145,933,056	2-6	4.5957
15	106,565,544	2-7	4.9592
16	76,905,216	2-8	5.3697
17	51,774,120	3-8	5.8034
18	31,915,728	4-8	6.2090
19	18,857,160	4-9	6.5662
20	10,538,640	4-9	7.0360
21	5,435,640	5-9	7.4701
22	2,536,128	6-10	7.8362
23	1,146,600	6-10	8.2325
24	444,528	6-10	8.7494
25	159,768	7-10	9.1703
26	48,384	8-10	9.4375
27	12,600	9-10	9.8400
28	1008	10	10.0000
0-28	2,488,234,320	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	158,122,800	0-10	3.5455
1	329,182,920	3-13	6.2727
2	495,799,920	4-16	7.8532
3	603,567,360	7-17	10.0647
4	427,977,000	8-20	12.0585
5	292,984,560	11-21	13.9191
6	123,971,760	12-24	16.1566
7	42,906,600	15-25	17.8719
8	11,586,960	16-26	20.0909
9	1,829,520	19-27	21.7576
10	304,920	22-28	23.9091
0-10	2,488,234,320	0-28	10.0000

Study 7Z80 Main

Top HCP and Controls

6-5-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	9,144,576	0	0
1	25,147,584	0	0
2	44,579,808	0	0
3	87,508,512	0-1	0.2874
4	142,248,960	0-2	0.7679
5	201,434,688	0-2	1.0700
6	266,196,672	0-2	1.3448
7	335,077,344	0-3	1.8098
8	380,255,904	0-4	2.1991
9	407,332,800	0-4	2.5558
10	418,158,720	1-4	2.9592
11	394,759,008	1-5	3.3978
12	355,286,736	1-6	3.7682
13	302,182,272	2-6	4.1708
14	244,100,304	2-6	4.6068
15	181,270,656	2-7	4.9764
16	131,593,248	3-7	5.3812
17	87,571,584	3-7	5.7950
18	54,883,872	4-8	6.1890
19	32,309,280	4-8	6.5283
20	17,767,296	5-8	6.9632
21	8,830,080	5-9	7.3386
22	4,060,368	6-9	7.6290
23	1,753,056	6-9	7.9975
24	592,272	7-9	8.3173
25	186,624	7-9	8.6111
26	57,024	8-9	8.8636
27	7776	9	9.0000
0-27	4,134,297,024	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	281,746,080	0-9	3.5455
1	539,342,496	3-12	6.2727
2	837,188,352	4-15	7.8872
3	942,934,608	7-17	10.0737
4	732,121,632	8-19	12.0246
5	486,809,136	11-21	13.9137
6	222,678,720	12-23	16.1423
7	71,351,280	15-25	17.9101
8	18,817,920	18-26	20.1818
9	1,306,800	21-27	22.9091
0-9	4,134,297,024	0-27	10.0000

Study 7Z80 Main

Top HCP and Controls

7-3-3-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	3,048,192	0	0
1	9,725,184	0	0
2	16,381,440	0	0
3	35,665,920	0-1	0.2727
4	55,883,520	0-2	0.7889
5	81,616,896	0-2	1.0877
6	109,049,328	0-2	1.3421
7	139,132,944	0-3	1.8230
8	154,681,920	0-4	2.2031
9	168,623,208	0-4	2.5619
10	173,449,080	1-4	2.9540
11	161,955,288	1-5	3.3885
12	144,129,672	1-6	3.7584
13	123,826,464	2-6	4.1673
14	99,195,624	2-6	4.5983
15	72,718,776	2-7	4.9751
16	52,284,456	3-7	5.3799
17	35,383,176	3-7	5.8101
18	21,724,848	3-8	6.2110
19	12,636,792	4-8	6.5518
20	7,041,384	5-8	6.9931
21	3,557,736	5-9	7.3950
22	1,566,936	5-9	7.6526
23	697,536	6-9	8.0853
24	258,552	7-9	8.4444
25	78,120	7-9	8.6323
26	25,704	8-9	8.9216
27	3528	9	9.0000
28	1008	9	9.0000
0-28	1,684,343,232	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	107,811,000	0-9	3.5455
1	222,809,400	3-12	6.2727
2	335,412,000	4-15	7.8526
3	407,286,000	7-18	10.0711
4	288,454,320	8-19	12.0530
5	199,330,560	11-22	13.9307
6	84,332,160	12-23	16.1111
7	30,857,904	15-25	17.8676
8	7,379,064	18-26	20.1818
9	670,824	21-28	22.9091
0-9	1,684,343,232	0-28	10.0000

Study 7Z80 Main

Top HCP and Controls

8-2-2-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	1,259,712	0	0
1	5,808,672	0	0
2	9,036,684	0	0
3	24,695,604	0-1	0.2352
4	36,656,064	0-2	0.8157
5	56,799,792	0-2	1.1294
6	80,710,992	0-2	1.3255
7	104,434,380	0-3	1.8531
8	113,165,532	0-4	2.2290
9	126,554,400	0-4	2.5801
10	135,262,800	0-4	2.9537
11	118,990,656	0-5	3.3748
12	104,751,828	1-6	3.7281
13	90,612,396	1-6	4.1524
14	71,952,336	1-6	4.5876
15	49,735,872	2-7	4.9451
16	35,518,176	2-8	5.3613
17	24,166,692	3-8	5.8350
18	14,505,660	3-8	6.2651
19	8,080,992	4-9	6.6098
20	4,605,696	4-9	7.0966
21	2,394,720	5-9	7.5981
22	1,045,728	5-10	7.9685
23	460,656	6-10	8.3567
24	197,568	7-10	8.9209
25	67,536	8-11	9.4104
26	18,144	9-11	9.5833
27	6048	10-11	10.2500
28	1512	11	11.0000
0-28	1,221,496,848	0-11	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	65,884,500	0-11	3.5455
1	164,112,300	3-14	6.2727
2	233,830,080	4-16	7.7877
3	336,609,900	7-18	10.0529
4	197,152,560	8-20	12.1207
5	144,397,044	11-22	13.9359
6	51,714,432	12-23	16.1358
7	21,712,284	15-24	17.7943
8	4,875,948	16-25	20.0567
9	1,070,784	19-26	21.6865
10	131,472	22-27	23.9819
11	5544	25-28	26.6364
0-11	1,221,496,848	0-28	10.0000

Study 7Z80 Main

Top HCP and Controls

7-4-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	3,919,104	0	0
1	12,737,088	0	0
2	21,772,800	0	0
3	47,278,080	0-1	0.2694
4	75,155,040	0-2	0.7783
5	109,873,152	0-2	1.0869
6	148,119,840	0-2	1.3399
7	189,294,624	0-3	1.8221
8	212,209,632	0-4	2.2046
9	231,222,816	0-4	2.5632
10	239,084,784	1-4	2.9599
11	222,994,512	1-5	3.3945
12	198,910,080	1-6	3.7619
13	170,249,472	2-6	4.1690
14	135,959,328	2-6	4.6050
15	98,897,040	2-7	4.9670
16	70,805,520	3-7	5.3743
17	47,185,344	3-7	5.8034
18	28,496,160	4-8	6.1983
19	16,428,384	4-8	6.5295
20	8,873,424	5-8	6.9816
21	4,347,504	5-9	7.3830
22	1,862,784	6-9	7.6364
23	794,304	6-9	8.0368
24	262,080	7-9	8.4077
25	73,584	7-9	8.6301
26	23,184	8-9	8.9130
27	2016	9	9.0000
0-27	2,296,831,680	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	143,748,000	0-9	3.5455
1	301,870,800	3-12	6.2727
2	457,118,640	4-15	7.8593
3	558,439,200	7-17	10.0622
4	399,793,680	8-19	12.0565
5	273,208,320	11-21	13.9085
6	115,085,520	12-23	16.1525
7	37,810,080	15-25	17.8724
8	9,147,600	18-26	20.1818
9	609,840	21-27	22.9091
0-9	2,296,831,680	0-27	10.0000

Study 7Z80 Main

Top HCP and Controls

8-3-1-1 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	734,832	0	0
1	3,417,552	0	0
2	5,409,504	0	0
3	14,658,732	0-1	0.2331
4	22,102,308	0-2	0.8034
5	34,225,524	0-2	1.1255
6	48,950,892	0-2	1.3241
7	63,536,508	0-3	1.8486
8	69,490,656	0-4	2.2276
9	77,698,656	0-4	2.5804
10	83,309,904	0-4	2.9599
11	73,648,800	1-5	3.3818
12	64,854,144	1-6	3.7358
13	56,016,324	1-6	4.1561
14	44,245,404	2-6	4.5984
15	30,400,236	2-7	4.9386
16	21,488,292	2-8	5.3561
17	14,467,860	3-8	5.8267
18	8,408,736	4-8	6.2481
19	4,671,720	4-9	6.5799
20	2,556,000	4-9	7.0831
21	1,292,184	5-9	7.5779
22	534,240	6-10	7.9358
23	229,320	6-10	8.3187
24	85,680	7-10	8.9235
25	28,728	8-10	9.4211
26	6048	9-10	9.5000
27	1512	10	10.0000
0-27	746,470,296	0-10	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	39,530,700	0-10	3.5455
1	99,425,700	3-13	6.2727
2	142,876,800	4-16	7.7980
3	205,777,440	7-17	10.0466
4	123,100,560	8-20	12.1206
5	88,905,960	11-21	13.9113
6	31,794,444	12-23	16.1718
7	11,861,388	15-24	17.8022
8	2,665,872	16-25	20.0802
9	470,448	19-26	21.6296
10	60,984	22-27	23.9091
0-10	746,470,296	0-27	10.0000

Study 7Z80 Main

Top HCP and Controls

6-6-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	762,048	0	0
1	2,370,816	0	0
2	4,339,440	0	0
3	8,784,720	0-1	0.2699
4	14,817,600	0-2	0.7400
5	21,337,344	0-2	1.0744
6	29,211,840	0-2	1.3348
7	37,192,176	0-3	1.8127
8	43,076,880	0-4	2.2054
9	46,484,928	1-4	2.5610
10	48,577,536	1-4	2.9765
11	45,505,152	1-5	3.4149
12	41,189,904	2-6	3.7755
13	34,700,400	2-6	4.1778
14	27,615,168	2-6	4.6297
15	19,885,824	3-7	4.9521
16	14,164,416	4-7	5.3582
17	8,881,488	4-7	5.7770
18	5,198,256	4-8	6.1408
19	2,915,136	5-8	6.4232
20	1,410,048	6-8	6.8750
21	596,160	6-8	7.3188
22	245,376	6-8	7.5775
23	88,128	7-8	7.8235
24	15,552	8	8.0000
0-24	459,366,336	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	28,174,608	0-8	3.5455
1	58,910,544	3-11	6.2727
2	92,207,808	4-14	7.8965
3	109,405,296	7-15	10.0404
4	84,889,728	8-18	12.0498
5	55,251,504	11-19	13.8417
6	24,254,208	12-22	16.2721
7	4,965,840	15-23	17.9091
8	1,306,800	18-24	20.1818
0-8	459,366,336	0-24	10.0000

Study 7Z80 Main

Top HCP and Controls

7-5-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	979,776	0	0
1	3,374,784	0	0
2	6,023,808	0	0
3	13,009,248	0-1	0.2594
4	21,573,216	0-2	0.7477
5	31,649,184	0-2	1.0841
6	43,843,680	0-2	1.3320
7	56,345,760	0-3	1.8187
8	64,680,768	0-4	2.2082
9	70,542,144	1-4	2.5652
10	74,040,480	1-4	2.9764
11	68,909,184	1-5	3.4117
12	61,904,736	2-6	3.7723
13	52,490,160	2-6	4.1756
14	41,436,576	2-6	4.6295
15	29,484,000	3-7	4.9456
16	20,762,784	4-7	5.3530
17	13,130,208	4-7	5.7837
18	7,432,992	4-8	6.1485
19	4,161,024	5-8	6.4266
20	1,971,648	6-8	6.8988
21	840,672	6-8	7.3525
22	326,592	6-8	7.5833
23	117,936	7-8	7.8462
24	18,144	8	8.0000
0-24	689,049,504	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	40,249,440	0-8	3.5455
1	88,757,856	3-11	6.2727
2	136,743,552	4-14	7.8789
3	170,354,448	7-15	10.0371
4	125,766,432	8-18	12.0682
5	83,269,296	11-19	13.8411
6	34,760,880	12-22	16.2727
7	7,318,080	15-23	17.8864
8	1,829,520	18-24	20.1818
0-8	689,049,504	0-24	10.0000

Study 7Z80 Main

Top HCP and Controls

8-3-2-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	653,184	0	0
1	3,055,968	0	0
2	4,898,880	0	0
3	13,206,240	0-1	0.2314
4	20,123,640	0-2	0.7942
5	31,203,792	0-2	1.1206
6	44,810,712	0-2	1.3226
7	58,365,792	0-3	1.8434
8	64,296,288	0-4	2.2246
9	71,976,816	0-4	2.5798
10	77,356,080	1-4	2.9632
11	68,789,952	1-5	3.3865
12	60,628,032	1-6	3.7436
13	52,336,800	2-6	4.1629
14	41,243,832	2-6	4.6095
15	28,209,312	2-7	4.9448
16	19,728,360	3-7	5.3599
17	13,131,360	3-7	5.8254
18	7,394,400	4-8	6.2324
19	3,988,224	4-8	6.5316
20	2,094,480	5-8	7.0177
21	992,880	5-9	7.4853
22	356,832	6-9	7.6497
23	147,168	7-9	8.1164
24	48,384	7-9	8.6250
25	9072	8-9	8.6667
26	3024	9	9.0000
0-26	689,049,504	0-9	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	35,937,000	0-9	3.5455
1	91,040,400	3-12	6.2727
2	131,769,000	4-15	7.8066
3	189,921,600	7-17	10.0436
4	115,564,680	8-19	12.1185
5	82,938,240	11-21	13.8960
6	29,577,240	12-22	16.1747
7	10,140,768	15-24	17.8018
8	2,038,608	18-25	20.1818
9	121,968	21-26	22.9091
0-9	689,049,504	0-26	10.0000

Study 7Z80 Main

Top HCP and Controls

8-4-1-0 Shape

Controls per HCP

HCP	Hands	Controls	Average
0	244,944	0	0
1	1,170,288	0	0
2	1,950,480	0	0
3	5,159,376	0-1	0.2268
4	8,150,544	0-2	0.7677
5	12,600,576	0-2	1.1137
6	18,387,000	0-2	1.3184
7	24,084,432	0-3	1.8355
8	27,055,944	0-4	2.2232
9	30,288,384	1-4	2.5790
10	32,788,152	1-4	2.9768
11	29,397,600	1-5	3.4011
12	25,957,368	2-6	3.7570
13	22,343,904	2-6	4.1678
14	17,366,040	2-6	4.6342
15	11,739,744	3-7	4.9250
16	8,026,416	4-7	5.3388
17	5,184,576	4-7	5.8073
18	2,675,088	4-8	6.1819
19	1,459,584	5-8	6.4385
20	660,240	6-8	6.9679
21	286,272	6-8	7.4613
22	90,720	6-8	7.6000
23	33,264	7-8	7.9091
24	3024	8	8.0000
0-24	287,103,960	0-8	3.0000

HCP per Controls

Controls	Hands	HCP	Average
0	14,374,800	0-8	3.5455
1	37,243,800	3-11	6.2727
2	54,885,600	4-14	7.8279
3	79,235,640	7-15	10.0285
4	50,355,360	8-18	12.1221
5	34,978,680	11-19	13.8391
6	12,545,280	12-22	16.2746
7	2,874,960	15-23	17.8209
8	609,840	18-24	20.1818
0-8	287,103,960	0-24	10.0000