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

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	2,310,789,600	0.363896103487
1	1	4	5,006,710,800	0.788441557556
2	2	10	8,611,542,576	1.356119478996
3	3	24	15,636,342,960	2.462363633597
4	5	51	24,419,055,136	3.845438379518
5	5	96	32,933,031,040	5.186193356366
6	8	170	41,619,399,184	6.554096137761
7	9	284	50,979,441,968	8.028087148267
8	12	445	56,466,608,128	8.892189351605
9	13	664	59,413,313,872	9.356227591333
10	16	952	59,723,754,816	9.405114885046
11	17	1304	56,799,933,520	8.944680418443
12	21	1716	50,971,682,080	8.026865144755
13	21	2184	43,906,944,752	6.914331841931
14	24	2680	36,153,374,224	5.693323186165
15	25	3176	28,090,962,724	4.423679195401
16	28	3650	21,024,781,756	3.310918552550
17	27	4064	14,997,082,848	2.361694899468
18	30	4380	10,192,504,020	1.605084468814
19	29	4584	6,579,838,440	1.036172903795
20	31	4658	4,086,538,404	0.643535613094
21	29	4584	2,399,507,844	0.377867182161
22	30	4380	1,333,800,036	0.210042764574
23	27	4064	710,603,628	0.111903693592
24	28	3650	354,993,864	0.055903351769
25	25	3176	167,819,892	0.026427765118
26	24	2680	74,095,248	0.011668293831
27	21	2184	31,157,940	0.004906657430
28	21	1716	11,790,760	0.001856772950
29	17	1304	4,236,588	0.000667164966
30	16	952	1,396,068	0.000219848534
31	13	664	388,196	0.000061131923
32	11	439	109,156	0.000017189554
33	8	268	22,360	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	65,399	635,013,559,600	100

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	7,317,500,400	1.152337661043
1-2	3	14	13,618,253,376	2.144561036551
2-3	5	34	24,247,885,536	3.818483112593
3-4	8	75	40,055,398,096	6.307802013115
4-5	10	147	57,352,086,176	9.031631735884
5-6	13	266	74,552,430,224	11.740289494127
6-7	17	454	92,598,841,152	14.582183286028
7-8	21	729	107,446,050,096	16.920276499872
8-9	25	1109	115,879,922,000	18.248416942938
9-10	29	1616	119,137,068,688	18.761342476379
10-11	33	2256	116,523,688,336	18.349795303489
11-12	38	3020	107,771,615,600	16.971545563198
12-13	42	3900	94,878,626,832	14.941196986686
13-14	45	4864	80,060,318,976	12.607655028096
14-15	49	5856	64,244,336,948	10.117002381566
15-16	53	6826	49,115,744,480	7.734597747950
16-17	55	7714	36,021,864,604	5.672613452017
17-18	57	8444	25,189,586,868	3.966779368281
18-19	59	8964	16,772,342,460	2.641257372609
19-20	60	9242	10,666,376,844	1.679708516889
20-21	60	9242	6,486,046,248	1.021402795255
21-22	59	8964	3,733,307,880	0.587909946734
22-23	57	8444	2,044,403,664	0.321946458165
23-24	55	7714	1,065,597,492	0.167807045360
24-25	53	6826	522,813,756	0.082331116887
25-26	49	5856	241,915,140	0.038096058949
26-27	45	4864	105,253,188	0.016574951260
27-28	42	3900	42,948,700	0.006763430379
28-29	38	3020	16,027,348	0.002523937916
29-30	33	2256	5,632,656	0.000887013500
30-31	29	1616	1,784,264	0.000280980457
31-32	24	1103	497,352	0.000078321477
32-33	19	707	131,516	0.000020710739
33-34	14	416	26,844	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	15,929,042,976	2.508457140039
1-3	6	38	29,254,596,336	4.606924670148
2-4	10	85	48,666,940,672	7.663921492110
3-5	13	171	72,988,429,136	11.493995369481
4-6	18	317	98,971,485,360	15.585727873645
5-7	22	550	125,531,872,192	19.768376642394
6-8	29	899	149,065,449,280	23.474372637633
7-9	34	1393	166,859,363,968	26.276504091205
8-10	41	2061	175,603,676,816	27.653531827984
9-11	46	2920	175,937,002,208	27.706022894822
10-12	54	3972	167,495,370,416	26.376660448244
11-13	59	5204	151,678,560,352	23.885877405129
12-14	66	6580	131,032,001,056	20.634520172851
13-15	70	8040	108,151,281,700	17.031334223497
14-16	77	9506	85,269,118,704	13.427920934115
15-17	80	10,890	64,112,827,328	10.096292647418
16-18	85	12,094	46,214,368,624	7.277697920830
17-19	86	13,028	31,769,425,308	5.002952272076
18-20	90	13,622	20,858,880,864	3.284792985702
19-21	89	13,826	13,065,884,688	2.057575699050
20-22	90	13,622	7,819,846,284	1.231445559828
21-23	86	13,028	4,443,911,508	0.699813640326
22-24	85	12,094	2,399,397,528	0.377849809933
23-25	80	10,890	1,233,417,384	0.194234810478
24-26	77	9506	596,909,004	0.093999410717
25-27	70	8040	273,073,080	0.043002716379
26-28	66	6580	117,043,948	0.018431724210
27-29	59	5204	47,185,288	0.007430595345
28-30	54	3972	17,423,416	0.002743786449
29-31	46	2920	6,020,852	0.000948145423
30-32	40	2055	1,893,420	0.000298170011
31-33	32	1371	519,712	0.000081842662
32-34	25	855	136,000	0.000021416866
33-35	17	480	27,468	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	31,565,385,936	4.970820773636
1-4	11	89	53,673,651,472	8.452363049666
2-5	15	181	81,599,971,712	12.850114848477
3-6	21	341	114,607,828,320	18.048091507242
4-7	27	601	149,950,927,328	23.613815021912
5-8	34	995	181,998,480,320	28.660565993999
6-9	42	1563	208,478,763,152	32.830600228966
7-10	50	2345	226,583,118,784	35.681618976251
8-11	58	3365	232,403,610,336	36.598212246427
9-12	67	4636	226,908,684,288	35.732888039577
10-13	75	6156	211,402,315,168	33.290992290175
11-14	83	7884	187,831,934,576	29.579200591294
12-15	91	9756	159,122,963,780	25.058199368252
13-16	98	11,690	129,176,063,456	20.342252776046
14-17	104	13,570	100,266,201,552	15.789615833583
15-18	110	15,270	74,305,331,348	11.701377116231
16-19	114	16,678	52,794,207,064	8.313870824625
17-20	117	17,686	35,855,963,712	5.646487885170
18-21	119	18,206	23,258,388,708	3.662660167863
19-22	119	18,206	14,399,684,724	2.267618463623
20-23	117	17,686	8,530,449,912	1.343349253420
21-24	114	16,678	4,798,905,372	0.755716992094
22-25	110	15,270	2,567,217,420	0.404277575052
23-26	104	13,570	1,307,512,632	0.205903104309
24-27	98	11,690	628,066,944	0.098906068147
25-28	91	9756	284,863,840	0.044859489328
26-29	83	7884	121,280,536	0.019098889176
27-30	75	6156	48,581,356	0.007650443879
28-31	67	4636	17,811,612	0.002804918372
29-32	57	3359	6,130,008	0.000965334977
30-33	48	2323	1,915,780	0.000301691196
31-34	38	1519	524,196	0.000082548788
32-35	28	919	136,624	0.000021515131
33-36	19	505	27,528	0.000004335026
34-37	12	241	5172	0.000000814471

5-Point Ranges

Range	Ways	Specific	Hands	Percent
0-4	12	90	55,984,441,072	8.816259153153
1-5	16	185	86,606,682,512	13.638556406032
2-6	23	351	123,219,370,896	19.404210986237
3-7	30	625	165,587,270,288	26.076178655509
4-8	39	1046	206,417,535,456	32.506004373517
5-9	47	1659	241,411,794,192	38.016793585332
6-10	58	2515	268,202,517,968	42.235715114012
7-11	67	3649	283,383,052,304	44.626299394694
8-12	79	5081	283,375,292,416	44.625077391182
9-13	88	6820	270,815,629,040	42.647219881508
10-14	99	8836	247,555,689,392	38.984315476340
11-15	108	11,060	215,922,897,300	34.002879786695
12-16	119	13,406	180,147,745,536	28.369117920801
13-17	125	15,754	144,173,146,304	22.703947675514
14-18	134	17,950	110,458,705,572	17.394700302397
15-19	139	19,854	80,885,169,788	12.737550020026
16-20	145	21,336	56,880,745,468	8.957406437719
17-21	146	22,270	38,255,471,556	6.024355067331
18-22	149	22,586	24,592,188,744	3.872702932437
19-23	146	22,270	15,110,288,352	2.379522157215
20-24	145	21,336	8,885,443,776	1.399252605188
21-25	139	19,854	4,966,725,264	0.782144757213
22-26	134	17,950	2,641,312,668	0.415945868883
23-27	125	15,754	1,338,670,572	0.210809761739
24-28	119	13,406	639,857,704	0.100762841096
25-29	108	11,060	289,100,428	0.045526654294
26-30	99	8836	122,676,604	0.019318737710
27-31	88	6820	48,969,552	0.007711575802
28-32	78	5075	17,920,768	0.002822107927
29-33	65	3627	6,152,368	0.000968856162
30-34	54	2471	1,920,264	0.000302397322
31-35	41	1583	524,820	0.000082647054
32-36	30	944	136,684	0.000021524580
33-37	20	509	27,532	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.

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	298,722,816	0.047041958630	0.446482315816
1	4	16	583,220,736	0.091843823991	0.871703568975
2	10	40	1,003,871,232	0.158086582062	1.500423564717
3	24	96	1,739,138,688	0.273874260117	2.599381859551
4	51	204	2,698,012,800	0.424874832862	4.032551042390
5	96	384	3,539,168,640	0.557337490908	5.289774084254
6	170	680	4,403,572,128	0.693461117708	6.581743932055
7	284	1136	5,311,985,184	0.836515237146	7.939492129503
8	445	1780	5,863,612,032	0.923383751946	8.763974289452
9	664	2656	6,098,710,968	0.960406415863	9.115361969833
10	949	3796	6,094,244,088	0.959702985215	9.108685603583
11	1295	5180	5,820,897,816	0.916657247393	8.700132021448
12	1698	6792	5,236,272,216	0.824592189700	7.826328690089
13	2145	8580	4,525,112,736	0.712600962230	6.763403079662
14	2608	10,432	3,762,309,384	0.592477015195	5.623288602724
15	3059	12,236	2,976,568,236	0.468740893954	4.448890436260
16	3467	13,868	2,254,937,832	0.355100737285	3.370314590411
17	3794	15,176	1,641,613,500	0.258516290744	2.453617058683
18	4011	16,044	1,145,716,128	0.180423883975	1.712430262099
19	4101	16,404	761,091,672	0.119854396886	1.137556135863
20	4049	16,196	486,317,352	0.076583774417	0.726868139669
21	3861	15,444	296,791,896	0.046737883233	0.443596290421
22	3555	14,220	172,256,424	0.027126416656	0.257460906842
23	3155	12,620	95,566,800	0.015049568400	0.142837720769
24	2696	10,784	50,363,112	0.007931029383	0.075274594618
25	2216	8864	25,179,360	0.003965168872	0.037634015085
26	1747	6988	11,820,648	0.001861479621	0.017667583495
27	1317	5268	5,307,456	0.000835801995	0.007932722641
28	948	3792	2,183,392	0.000343833918	0.003263379509
29	647	2588	846,960	0.000133376679	0.001265898157
30	417	1668	308,448	0.000048573451	0.000461017940
31	252	1008	95,632	0.000015059836	0.000142935171
32	141	564	30,720	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	54,000	216,000	66,905,856,160	10.536130315413	100

4-4-3-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	576,108,288	0.090723777357	0.420969040627
1	4	48	1,159,075,008	0.182527599683	0.846949617452
2	10	120	1,998,089,856	0.314653100834	1.460027545666
3	24	288	3,500,086,464	0.551182948944	2.557553973015
4	51	612	5,447,418,480	0.857842859833	3.980492173407
5	96	1152	7,201,988,640	1.134147221130	5.262577038966
6	169	2028	8,995,078,512	1.416517549273	6.572808707034
7	280	3360	10,896,685,056	1.715976752192	7.962334772102
8	435	5220	12,048,600,960	1.897376957996	8.804053148821
9	641	7692	12,566,324,448	1.978906474992	9.182359735609
10	904	10,848	12,574,353,168	1.980170813348	9.188226414888
11	1216	14,592	12,003,625,008	1.890294282151	8.771188696496
12	1567	18,804	10,792,467,648	1.699564912409	7.886181897414
13	1944	23,328	9,314,807,760	1.466867536792	6.806438595016
14	2319	27,828	7,725,746,736	1.216627049801	5.645293184153
15	2663	31,956	6,084,044,784	0.958096829906	4.445682433668
16	2951	35,412	4,593,528,252	0.723374829176	3.356544631653
17	3156	37,872	3,323,621,808	0.523393832739	2.428609192167
18	3254	39,048	2,303,233,056	0.362706121969	1.682999238373
19	3240	38,880	1,517,291,568	0.238938451796	1.108702632885
20	3114	37,368	961,283,664	0.151380021650	0.702421177118
21	2884	34,608	579,570,336	0.091268970125	0.423498799451
22	2575	30,900	331,988,400	0.052280521413	0.242587793230
23	2214	26,568	181,741,248	0.028620057832	0.132800448121
24	1829	21,948	93,978,144	0.014799391695	0.068670925143
25	1449	17,388	46,084,320	0.007257218260	0.033674349740
26	1100	13,200	21,121,560	0.003326158895	0.015433770065
27	796	9552	9,244,080	0.001455729545	0.006754756996
28	547	6564	3,659,760	0.000576327851	0.002674229287
29	356	4272	1,376,688	0.000216796630	0.001005961967
30	217	2604	473,136	0.000074508015	0.000345725990
31	123	1476	139,152	0.000021913233	0.000101679988
32	64	768	40,992	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	42,240	506,880	136,852,887,600	21.551175645163	100

4-4-4-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	4	72,013,536	0.011340472170	0.378872136564
1	4	16	152,028,576	0.023940996803	0.799841177191
2	10	40	264,049,632	0.041581731289	1.389197834069
3	23	92	469,802,592	0.073983080345	2.471689652824
4	47	188	737,366,112	0.116118168006	3.879374487090
5	85	340	987,952,896	0.155579811024	5.197742609561
6	143	572	1,244,046,384	0.195908633004	6.545082184148
7	227	908	1,518,005,664	0.239050905457	7.986415904314
8	337	1348	1,687,649,040	0.265765827278	8.878930727071
9	474	1896	1,768,663,296	0.278523705402	9.305156766893
10	639	2556	1,776,222,000	0.279714027070	9.344924045286
11	821	3284	1,695,428,928	0.266990980329	8.919861681896
12	1009	4036	1,524,045,240	0.240001999479	8.018190862054
13	1195	4780	1,312,019,208	0.206612786163	6.902695634169
14	1361	5444	1,083,496,608	0.170625743596	5.700409917839
15	1489	5956	845,748,000	0.133185817407	4.449585030166
16	1573	6292	633,339,864	0.099736431518	3.332079505789
17	1604	6416	452,355,840	0.071235619013	2.379900128611
18	1573	6292	308,297,340	0.048549725488	1.621990508880
19	1489	5956	199,296,720	0.031384640058	1.048524740080
20	1361	5444	123,431,040	0.019437543992	0.649385996587
21	1195	4780	72,363,024	0.011395508475	0.380710836240
22	1009	4036	39,978,396	0.006295675958	0.210331295341
23	821	3284	21,212,568	0.003340490558	0.111601948836
24	639	2556	10,350,936	0.001630033854	0.054457556948
25	474	1896	4,855,824	0.000764680364	0.025547091781
26	337	1348	2,060,532	0.000324486299	0.010840714186
27	227	908	837,936	0.000131955607	0.004408485130
28	143	572	293,040	0.000046147046	0.001541719753
29	85	340	100,224	0.000015782970	0.000527290883
30	47	188	26,604	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	20,480	81,920	19,007,345,500	2.993218839606	100

5-3-3-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	384,072,192	0.060482518238	0.389786148729
1	4	48	809,294,976	0.127445306288	0.821335099107
2	10	120	1,387,362,816	0.218477667922	1.408003027040
3	24	288	2,484,929,664	0.391319150030	2.521898704898
4	51	612	3,863,039,040	0.608339614422	3.920510625747
5	96	1152	5,164,290,432	0.813256717739	5.241121123410
6	169	2028	6,473,253,024	1.019388157330	6.569557542898
7	280	3360	7,889,841,288	1.242468159730	8.007220813659
8	435	5220	8,710,024,608	1.371628129246	8.839606245912
9	641	7692	9,129,408,264	1.437671389214	9.265229197838
10	903	10,836	9,137,498,544	1.438945421851	9.273439839351
11	1213	14,556	8,712,017,856	1.371942019866	8.841629148058
12	1561	18,732	7,818,628,896	1.231253849276	7.934948973631
13	1931	23,172	6,747,673,248	1.062603017840	6.848060398544
14	2295	27,540	5,574,925,872	0.877922335314	5.657865709514
15	2624	31,488	4,369,007,808	0.688018033938	4.434006842249
16	2891	34,692	3,286,951,056	0.517619034477	3.335852008723
17	3069	36,828	2,366,938,908	0.372738325382	2.402152565175
18	3137	37,644	1,627,474,068	0.256289656086	1.651686485861
19	3091	37,092	1,064,030,076	0.167560213465	1.079859969283
20	2932	35,184	669,602,052	0.105446890366	0.679563921748
21	2675	32,100	399,634,416	0.062933209844	0.405579896584
22	2346	28,152	226,171,692	0.035616828740	0.229536515823
23	1974	23,688	122,438,916	0.019281307328	0.124260476328
24	1590	19,080	62,578,476	0.009854667677	0.063509474681
25	1223	14,676	30,116,196	0.004742606759	0.030564243644
26	896	10,752	13,574,448	0.002137662699	0.013776399118
27	621	7452	5,838,444	0.000919420367	0.005925304275
28	406	4872	2,258,748	0.000355700751	0.002292352069
29	248	2976	821,196	0.000129319443	0.000833413178
30	140	1680	277,020	0.000043624265	0.000281141309
31	72	864	77,904	0.000012268084	0.000079063001
32	33	396	21,636	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	39,600	475,200	98,534,079,072	15.516846464518	100

5-4-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	246,903,552	0.038881618867	0.367512654516
1	4	48	534,957,696	0.084243507546	0.796277418117
2	10	120	920,744,496	0.144996037026	1.370515940798
3	24	288	1,663,414,704	0.261949477905	2.475970671444
4	51	612	2,599,672,320	0.409388473789	3.869577685111
5	96	1152	3,498,126,912	0.550874364668	5.206915400154
6	168	2016	4,406,978,016	0.693997466570	6.559728185085
7	276	3312	5,389,847,568	0.848776768073	8.022716445773
8	425	5100	5,968,963,224	0.939974136577	8.884722400260
9	618	7416	6,267,660,768	0.987012115450	9.329329723255
10	858	10,296	6,288,743,232	0.990332117626	9.360710690623
11	1134	13,608	5,988,505,392	0.943051577634	8.913810657511
12	1431	17,172	5,376,127,896	0.846616235941	8.002294896407
13	1734	20,808	4,629,605,760	0.729056205180	6.891106622145
14	2016	24,192	3,817,654,200	0.601192548141	5.682527520157
15	2250	27,000	2,974,849,200	0.468470185404	4.428023482933
16	2415	28,980	2,231,960,400	0.351482321323	3.322243381001
17	2496	29,952	1,594,443,744	0.251088141331	2.373308314468
18	2479	29,748	1,088,865,180	0.171471169952	1.620761343731
19	2368	28,416	705,038,724	0.111027349470	1.049440767031
20	2177	26,124	439,647,696	0.069234379228	0.654409750284
21	1920	23,040	258,562,800	0.040717681708	0.384867290151
22	1624	19,488	144,483,192	0.022752772727	0.215061310357
23	1316	15,792	76,884,012	0.012107459886	0.114440829672
24	1019	12,228	38,504,268	0.006063534773	0.057313090995
25	750	9000	18,089,424	0.002848667359	0.026925867121
26	524	6288	7,959,168	0.001253385519	0.011847115749
27	346	4152	3,302,208	0.000520021652	0.004915292704
28	213	2556	1,223,244	0.000192632737	0.001820782431
29	122	1464	427,356	0.000067298720	0.000636113724
30	64	768	135,648	0.000021361434	0.000201910245
31	30	360	34,272	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	30,976	371,712	67,182,326,640	10.579668043989	100

5-4-3-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	288,054,144	0.045361888679	0.350807533856
1	4	96	635,548,032	0.100084167085	0.774003923904
2	10	240	1,100,397,312	0.173287214952	1.340121901819
3	23	552	1,996,946,784	0.314473093340	2.431987149389
4	47	1128	3,137,188,320	0.494034855252	3.820633449316
5	85	2040	4,244,734,368	0.668447831362	5.169461458992
6	143	3432	5,370,642,144	0.845752356435	6.540651349764
7	227	5448	6,588,576,288	1.037548913467	8.023915806655
8	337	8088	7,323,861,888	1.153339448785	8.919385402870
9	474	11,376	7,706,183,184	1.213546241257	9.384996447821
10	638	15,312	7,749,400,896	1.220352034826	9.437629257594
11	818	19,632	7,383,262,320	1.162693647778	8.991726382834
12	1003	24,072	6,630,108,768	1.044089321837	8.074496251988
13	1183	28,392	5,702,287,680	0.897978884670	6.944546780612
14	1340	32,160	4,693,321,440	0.739089956277	5.715774462036
15	1457	34,968	3,641,808,816	0.573500953002	4.435186912344
16	1527	36,648	2,719,135,008	0.428201093802	3.311506070114
17	1541	36,984	1,929,268,368	0.303815302655	2.349564803775
18	1494	35,856	1,304,790,336	0.205474405432	1.589042509908
19	1395	33,480	835,879,176	0.131631705081	1.017977760230
20	1253	30,072	513,892,584	0.080926237910	0.625845500976
21	1079	25,896	297,351,000	0.046825929227	0.362129735580
22	891	21,384	162,337,464	0.025564409066	0.197703128334
23	705	16,920	84,834,648	0.013359501812	0.103316110080
24	531	12,744	40,853,664	0.006433510495	0.049753747396
25	380	9120	18,688,320	0.002942979676	0.022759622063
26	258	6192	7,809,120	0.001229756417	0.009510358333
27	164	3936	3,074,976	0.000484237849	0.003744868004
28	97	2328	1,044,864	0.000164541998	0.001272490505
29	53	1272	340,632	0.000053641689	0.000414839621
30	26	624	87,768	0.000013821437	0.000106888501
31	11	264	18,792	0.000002959307	0.000022885889
32	4	96	3240	0.000000510225	0.000003945843
33	1	24	216	0.000000034015	0.000000263056
Totals	19,200	460,800	82,111,732,560	12.930705387098	100

5-4-4-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	24,004,512	0.003780157390	0.304033196008
1	3	36	56,010,528	0.008820367243	0.709410790686
2	6	72	98,685,216	0.015540647047	1.249914250257
3	13	156	181,748,448	0.028621191666	2.301965626920
4	24	288	289,959,264	0.045661901170	3.672527970831
5	39	468	398,805,120	0.062802614837	5.051133520985
6	61	732	511,388,640	0.080531924440	6.477079085031
7	90	1080	633,298,176	0.099729866619	8.021144877910
8	123	1476	711,807,264	0.112093238521	9.015514975513
9	161	1932	754,028,352	0.118742086779	9.550273287767
10	204	2448	763,599,312	0.120249292390	9.671495896152
11	243	2916	728,808,192	0.114770492847	9.230843096949
12	278	3336	655,299,720	0.103194602713	8.299809144838
13	309	3708	561,789,432	0.088468887555	7.115438818114
14	327	3924	459,690,768	0.072390701120	5.822290966406
15	332	3984	352,176,768	0.055459724076	4.460554263087
16	327	3924	258,943,608	0.040777650191	3.279693947795
17	309	3708	179,644,176	0.028289817325	2.275313614939
18	278	3336	117,527,544	0.018507879434	1.488564934015
19	243	2916	72,518,544	0.011419999290	0.918495852038
20	204	2448	42,273,576	0.006657113909	0.535423107872
21	161	1932	22,965,552	0.003616545136	0.290874072868
22	123	1476	11,394,972	0.001794445461	0.144324940061
23	90	1080	5,509,872	0.000867677850	0.069786213265
24	61	732	2,202,156	0.000346788815	0.027891778295
25	39	468	893,664	0.000140731483	0.011318852142
26	24	288	284,940	0.000044871483	0.003608955636
27	13	156	79,200	0.000012472175	0.001003120960
28	6	72	18,900	0.000002976314	0.000239381138
29	3	36	2376	0.000000374165	0.000030093629
30	1	12	108	0.000000017008	0.000001367892
Totals	4096	49,152	7,895,358,900	1.243337056452	100

5-5-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	61,725,888	0.009720404717	0.306260545430
1	4	48	145,741,680	0.022950955581	0.723115176709
2	10	120	253,761,984	0.039961663836	1.259071131211
3	23	276	471,517,200	0.074253091587	2.339490277588
4	47	564	748,331,136	0.117844906567	3.712936489036
5	85	1020	1,026,669,168	0.161676731540	5.093944689261
6	142	1704	1,314,750,528	0.207042906112	6.523295603446
7	223	2676	1,624,967,568	0.255894940105	8.062475402236
8	327	3924	1,816,432,128	0.286046195477	9.012450242226
9	452	5424	1,919,571,696	0.302288300302	9.524189827910
10	596	7152	1,941,202,368	0.305694632603	9.631513053535
11	747	8964	1,842,063,552	0.290082554010	9.139623688389
12	892	10,704	1,655,365,680	0.260681942137	8.213299354111
13	1021	12,252	1,417,246,848	0.223183714202	7.031843635477
14	1120	13,440	1,160,905,392	0.182815842977	5.759974138341
15	1175	14,100	888,961,824	0.139990998706	4.410692853611
16	1183	14,196	660,369,024	0.103992901256	3.276501708247
17	1144	13,728	460,066,608	0.072449887257	2.282676764408
18	1058	12,696	306,517,824	0.048269492732	1.520825686010
19	937	11,244	192,340,656	0.030289220300	0.954321697484
20	795	9540	115,912,080	0.018253481087	0.575111966679
21	643	7716	64,890,828	0.010218809822	0.321963782468
22	494	5928	34,538,616	0.005439035982	0.171367569059
23	361	4332	17,330,544	0.002729161250	0.085987614435
24	249	2988	8,001,288	0.001260018448	0.039699369364
25	160	1920	3,445,200	0.000542539596	0.017093781318
26	96	1152	1,376,352	0.000216743718	0.006828938844
27	53	636	492,480	0.000077554249	0.002443499775
28	26	312	148,392	0.000023368320	0.000736265064
29	11	132	42,768	0.000006734974	0.000212198665
30	4	48	9720	0.000001530676	0.000048226969
31	1	12	972	0.000000153068	0.000004822697
Totals	14,080	168,960	20,154,697,992	3.173900413197	100

5-5-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	16,003,008	0.002520104927	0.281512218526
1	3	36	38,864,448	0.006120254822	0.683672530707
2	6	72	68,584,320	0.010800449685	1.206480936541
3	13	156	128,214,576	0.020190840662	2.255449084145
4	24	288	205,562,448	0.032371347807	3.616091473688
5	39	468	284,815,440	0.044851867443	5.010247222580
6	61	732	367,751,664	0.057912411230	6.469195466212
7	90	1080	457,274,160	0.072010141057	8.044004180735
8	123	1476	515,217,024	0.081134806684	9.063289067201
9	161	1932	547,132,320	0.086160730228	9.624717629999
10	203	2436	555,823,296	0.087529358641	9.777602383598
11	241	2892	529,060,896	0.083314897454	9.306819478466
12	275	3300	475,892,928	0.074942167896	8.371530773604
13	303	3636	407,021,760	0.064096546262	7.160003834658
14	318	3816	332,133,264	0.052303334154	5.842624836219
15	320	3840	252,522,576	0.039766485642	4.442176783123
16	311	3732	185,235,984	0.029170398206	3.258524447825
17	289	3468	127,169,136	0.020026207957	2.237058533210
18	256	3072	82,486,944	0.012989792541	1.451044866371
19	219	2628	50,289,984	0.007919513409	0.884661493982
20	178	2136	28,983,312	0.004564203640	0.509851426767
21	137	1644	15,414,192	0.002427379977	0.271154234673
22	101	1212	7,533,648	0.001186375926	0.132525957750
23	70	840	3,545,964	0.000558407603	0.062377785005
24	45	540	1,376,028	0.000216692696	0.024205992713
25	27	324	530,712	0.000083574908	0.009335864390
26	15	180	167,832	0.000026429672	0.002952367371
27	7	84	40,824	0.000006428839	0.000718143415
28	3	36	8748	0.000001377608	0.000153887875
29	1	12	972	0.000000153068	0.000017098653
Totals	3840	46,080	5,684,658,408	0.895202680645	100

6-3-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	109,734,912	0.017280719497	0.306260545430
1	4	48	266,499,072	0.041967461635	0.743775610329
2	10	120	449,717,184	0.070820091508	1.255121342430
3	24	288	863,890,272	0.136042807109	2.411042220493
4	51	612	1,338,156,288	0.210728773862	3.734677206767
5	96	1152	1,847,667,024	0.290964971703	5.156677125167
6	168	2016	2,350,716,984	0.370183746231	6.560645582607
7	276	3312	2,913,941,520	0.458878629590	8.132556020689
8	425	5100	3,205,597,248	0.504807684740	8.946541658504
9	618	7416	3,408,949,152	0.536830922815	9.514079043810
10	857	10,284	3,424,218,840	0.539235546743	9.556695408011
11	1131	13,572	3,244,906,656	0.510998010506	9.056250779468
12	1425	17,100	2,898,328,752	0.456419978469	8.088982150202
13	1721	20,652	2,499,992,640	0.393691221582	6.977260887552
14	1992	23,904	2,042,896,320	0.321709086226	5.701545021692
15	2211	26,532	1,573,412,976	0.247776280083	4.391258054828
16	2356	28,272	1,170,675,936	0.184354478468	3.267254186897
17	2412	28,944	830,508,048	0.130785876214	2.317875351868
18	2368	28,416	556,662,096	0.087661450308	1.553595241786
19	2231	26,772	354,639,744	0.055847586030	0.989768519872
20	2015	24,180	218,278,656	0.034373857487	0.609196645113
21	1741	20,892	126,158,832	0.019867108362	0.352098270230
22	1437	17,244	68,465,232	0.010781696070	0.191080476697
23	1130	13,560	35,695,728	0.005621254454	0.099623656023
24	844	10,128	17,525,952	0.002759933506	0.048913399764
25	595	7140	7,927,488	0.001248396649	0.022124925919
26	395	4740	3,352,680	0.000527969828	0.009357036760
27	244	2928	1,358,496	0.000213931810	0.003791443565
28	139	1668	483,120	0.000076080265	0.001348345682
29	72	864	154,080	0.000024264049	0.000430023809
30	33	396	48,168	0.000007585350	0.000134432677
31	13	156	11,376	0.000001791458	0.000031749421
32	4	48	2304	0.000000362827	0.000006430263
33	1	12	432	0.000000068030	0.000001205674
Totals	29,040	348,480	35,830,574,208	5.642489623461	100

6-3-3-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	64,012,032	0.010080419706	0.292339611546
1	4	48	157,997,952	0.024881035942	0.721568406277
2	10	120	268,821,504	0.042333191148	1.227693788173
3	23	276	517,466,880	0.081489107150	2.363244252071
4	47	564	807,371,712	0.127142436535	3.687224499602
5	85	1020	1,119,557,376	0.176304483436	5.112960144803
6	143	1716	1,431,860,976	0.225485102539	6.539234397565
7	227	2724	1,779,410,808	0.280216190835	8.126476353576
8	337	4044	1,967,529,312	0.309840519506	8.985603749877
9	474	5688	2,094,792,840	0.329881592028	9.566809644724
10	637	7644	2,110,824,576	0.332406220952	9.640025746888
11	815	9780	2,000,693,520	0.315063117906	9.137062958107
12	997	11,964	1,788,624,288	0.281667101585	8.168553836200
13	1171	14,052	1,539,727,200	0.242471546745	7.031853816726
14	1319	15,828	1,256,282,784	0.197835583982	5.737377952119
15	1425	17,100	962,553,888	0.151580052654	4.395933403746
16	1481	17,772	712,974,672	0.112277078374	3.256118141273
17	1478	17,736	501,522,624	0.078978254309	2.290427666504
18	1415	16,980	332,747,136	0.052400004846	1.519638815425
19	1301	15,612	209,448,144	0.032983255370	0.956538749717
20	1146	13,752	126,998,208	0.019999290736	0.579994192245
21	965	11,580	71,982,576	0.011335596683	0.328740670285
22	776	9312	38,137,392	0.006005760259	0.174171480179
23	594	7128	19,456,992	0.003064027800	0.088859067669
24	430	5160	9,171,936	0.001444368527	0.041887753343
25	294	3528	4,002,336	0.000630275675	0.018278459767
26	188	2256	1,612,800	0.000253978829	0.007365573483
27	111	1332	607,752	0.000095706933	0.002775571686
28	60	720	197,280	0.000031067053	0.000900967471
29	29	348	57,384	0.000009036657	0.000262069735
30	12	144	14,400	0.000002267668	0.000065764049
31	4	48	2304	0.000000362827	0.000010522248
32	1	12	432	0.000000068030	0.000001972921
Totals	18,000	216,000	21,896,462,016	3.448188103226	100

6-4-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	82,301,184	0.012960539622	0.275634490887
1	4	96	208,039,104	0.032761364046	0.696742740852
2	10	240	357,019,488	0.056222340862	1.195692212782
3	23	552	689,925,600	0.108647380764	2.310626436501
4	47	1128	1,086,390,144	0.171081408826	3.638423892489
5	85	2040	1,512,689,472	0.238213727744	5.066140876957
6	142	3408	1,948,375,296	0.306824203443	6.525294129051
7	223	5352	2,426,856,768	0.382174007360	8.127774075554
8	327	7848	2,698,584,336	0.424964836609	9.037815538209
9	452	10,848	2,874,342,240	0.452642655664	9.626445470779
10	596	14,304	2,908,319,904	0.457993354635	9.740239898307
11	747	17,928	2,751,350,112	0.433274230196	9.214533139307
12	892	21,408	2,463,525,792	0.387948533501	8.250582123632
13	1021	24,504	2,113,475,328	0.332823653298	7.078229834881
14	1120	26,880	1,721,571,264	0.271107795727	5.765705860049
15	1175	28,200	1,309,621,536	0.206235208084	4.386047050424
16	1183	28,392	967,753,728	0.152398907609	3.241099254671
17	1144	27,456	673,095,456	0.105997020981	2.254260683938
18	1058	25,392	443,031,264	0.069767213204	1.483753829101
19	937	22,488	275,793,408	0.043431105341	0.923658347418
20	795	19,080	165,054,240	0.025992238670	0.552782344068
21	643	15,432	91,737,216	0.014446497183	0.307236659287
22	494	11,856	47,920,320	0.007546345944	0.160489708220
23	361	8664	23,848,992	0.003755666574	0.079872541908
24	249	5976	10,904,832	0.001717259708	0.036521319262
25	160	3840	4,602,528	0.000724792082	0.015414303907
26	96	2304	1,796,544	0.000282914274	0.006016796682
27	53	1272	635,040	0.000100004164	0.002126809343
28	26	624	187,344	0.000029502362	0.000627432870
29	11	264	50,976	0.000008027545	0.000170723471
30	4	96	11,520	0.000001814134	0.000038581575
31	1	24	864	0.000000136060	0.000002893618
Totals	14,080	337,920	29,858,811,840	4.702074686217	100

6-4-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	21,337,344	0.003360139902	0.253360996674
1	3	72	55,375,488	0.008720363079	0.657532110415
2	6	144	96,526,080	0.015200632891	1.146156889714
3	13	312	187,209,792	0.029481227475	2.222941125577
4	24	576	298,414,368	0.046993385179	3.543391422016
5	39	936	419,126,400	0.066002748077	4.976733863232
6	61	1464	544,737,312	0.085783571668	6.468245921031
7	90	2160	682,311,168	0.107448283219	8.101806746239
8	123	2952	765,761,472	0.120589782757	9.092701029715
9	161	3864	818,893,152	0.128956797791	9.723590019448
10	203	4872	833,066,640	0.131188795484	9.891886928661
11	241	5784	790,398,000	0.124469468100	9.385236749656
12	275	6600	708,825,600	0.111623695161	8.416640819203
13	303	7272	607,037,760	0.095594456342	7.208005452418
14	318	7632	492,804,000	0.077605271974	5.851586430099
15	320	7680	371,841,840	0.058556519680	4.415273952904
16	311	7464	271,408,176	0.042740532371	3.222718159145
17	289	6936	185,666,976	0.029238269513	2.204621629043
18	256	6144	118,867,680	0.018718919967	1.411442486801
19	219	5256	71,718,336	0.011293984973	0.851588139964
20	178	4272	41,009,328	0.006458023987	0.486947401466
21	137	3288	21,532,176	0.003390821452	0.255674444388
22	101	2424	10,289,664	0.001620384926	0.122180132939
23	70	1680	4,778,496	0.000752502986	0.056740169215
24	45	1080	1,835,136	0.000288991624	0.021790523038
25	27	648	671,184	0.000105696011	0.007969682037
26	15	360	214,704	0.000033810932	0.002549409122
27	7	168	46,368	0.000007301891	0.000550576618
28	3	72	10,656	0.000001678074	0.000126530030
29	1	24	864	0.000000136060	0.000010259192
Totals	3840	92,160	8,421,716,160	1.326226193549	100

6-5-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	10,287,648	0.001620067453	0.229695409072
1	4	48	28,005,264	0.004410183622	0.625281946919
2	10	120	49,279,104	0.007760323107	1.100269366914
3	22	264	96,589,584	0.015210633307	2.156584674067
4	43	516	156,219,840	0.024601024283	3.487967322949
5	74	888	220,253,040	0.034684777462	4.917655825919
6	117	1404	289,977,408	0.045664758432	6.474412747430
7	174	2088	363,899,088	0.057305719303	8.124884315558
8	241	2892	411,233,760	0.064759839185	9.181739764766
9	314	3768	439,323,696	0.069183356695	9.808912208879
10	390	4680	449,962,128	0.070858664543	10.046439677755
11	460	5520	423,636,696	0.066713015745	9.458663844810
12	515	6180	381,013,416	0.060000831516	8.507001060897
13	552	6624	323,992,872	0.051021410032	7.233886236245
14	566	6792	262,155,096	0.041283385534	5.853215624805
15	552	6624	195,270,264	0.030750566039	4.359857877051
16	515	6180	142,861,536	0.022497399282	3.189712454412
17	460	5520	95,867,280	0.015096887074	2.140457575555
18	390	4680	61,181,136	0.009634618832	1.366009612792
19	314	3768	36,770,976	0.005790581232	0.820996633468
20	241	2892	20,893,680	0.003290273048	0.466499473410
21	174	2088	10,846,440	0.001708064314	0.242171726013
22	117	1404	5,357,880	0.000843742613	0.119626997187
23	74	888	2,447,928	0.000385492241	0.054655624234
24	43	516	979,560	0.000154258123	0.021870930548
25	22	264	358,344	0.000056430921	0.008000854196
26	10	120	121,824	0.000019184472	0.002720001065
27	4	48	32,400	0.000005102253	0.000723404539
28	1	12	3888	0.000000612270	0.000086808545
Totals	6400	76,800	4,478,821,776	0.705311202933	100

6-5-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	9,144,576	0.001440059958	0.221188171699
1	3	72	25,147,584	0.003960164885	0.608267472173
2	6	144	44,579,808	0.007020292296	1.078292337034
3	13	312	87,508,512	0.013780573765	2.116647920844
4	24	576	142,248,960	0.022400932681	3.440704893099
5	39	936	201,434,688	0.031721320743	4.872283893263
6	60	1440	266,196,672	0.041919840604	6.438740865852
7	87	2088	335,077,344	0.052766958899	8.104820288790
8	117	2808	380,255,904	0.059881540835	9.197595184685
9	149	3576	407,332,800	0.064145527893	9.852528679855
10	183	4392	418,158,720	0.065850360780	10.114385047145
11	211	5064	394,759,008	0.062165445451	9.548394943769
12	232	5568	355,286,736	0.055949472358	8.593643222476
13	246	5904	302,182,272	0.047586743217	7.309157282261
14	248	5952	244,100,304	0.038440171916	5.904275928482
15	238	5712	181,270,656	0.028545950438	4.384558123127
16	219	5256	131,593,248	0.020722903631	3.182965501416
17	193	4632	87,571,584	0.013790506152	2.118173500637
18	160	3840	54,883,872	0.008642944890	1.327526098909
19	127	3048	32,309,280	0.005087966944	0.781493922968
20	96	2304	17,767,296	0.002797939624	0.429753737984
21	67	1608	8,830,080	0.001390534086	0.213581171085
22	44	1056	4,060,368	0.000639414378	0.098211811499
23	27	648	1,753,056	0.000276065916	0.042402758917
24	15	360	592,272	0.000093269189	0.014325821211
25	7	168	186,624	0.000029388979	0.004514044320
26	3	72	57,024	0.000008979966	0.001379291320
27	1	24	7776	0.000001224541	0.000188085180
Totals	2816	67,584	4,134,297,024	0.651056495015	100

6-6-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	762,048	0.000120004997	0.165891128774
1	3	36	2,370,816	0.000373348878	0.516105733965
2	6	72	4,339,440	0.000683361786	0.944657816632
3	12	144	8,784,720	0.001383390932	1.912356067816
4	21	252	14,817,600	0.002333430488	3.225660837280
5	32	384	21,337,344	0.003360139902	4.644951605683
6	46	552	29,211,840	0.004600191533	6.359159936352
7	63	756	37,192,176	0.005856910524	8.096408701573
8	79	948	43,076,880	0.006783615775	9.377456862664
9	94	1128	46,484,928	0.007320304787	10.119358855238
10	108	1296	48,577,536	0.007649842317	10.574901161238
11	116	1392	45,505,152	0.007166012648	9.906070261100
12	118	1416	41,189,904	0.006486460545	8.966678829508
13	116	1392	34,700,400	0.005464513234	7.553971042406
14	108	1296	27,615,168	0.004348752492	6.011578523682
15	94	1128	19,885,824	0.003131558956	4.328968503256
16	79	948	14,164,416	0.002230569062	3.083468441188
17	63	756	8,881,488	0.001398629662	1.933421607978
18	46	552	5,198,256	0.000818605512	1.131614485568
19	32	384	2,915,136	0.000459066733	0.634599397375
20	21	252	1,410,048	0.000222050062	0.306955013787
21	12	144	596,160	0.000093881460	0.129778774211
22	6	72	245,376	0.000038641065	0.053416191125
23	3	36	88,128	0.000013878129	0.019184688362
24	1	12	15,552	0.000002449082	0.003385533240
Totals	1280	15,360	459,366,336	0.072339610557	100

7-2-2-2 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	4	6,718,464	0.001058003234	0.206257102024
1	4	16	20,715,264	0.003262176640	0.635959397908
2	10	40	33,732,288	0.005312057906	1.035582533079
3	24	96	73,868,112	0.011632525146	2.267753866525
4	51	204	112,440,960	0.017706859688	3.451941776930
5	96	384	163,004,400	0.025669436115	5.004241320809
6	167	668	214,137,432	0.033721710153	6.574027360896
7	272	1088	271,247,616	0.042715247871	8.327312196224
8	415	1660	295,621,488	0.046553570948	9.075590999806
9	595	2380	321,580,512	0.050641518931	9.872534030477
10	811	3244	327,180,504	0.051523388604	10.044453999279
11	1049	4196	304,074,048	0.047884654336	9.335084915422
12	1290	5160	269,551,200	0.042448101450	8.275232160075
13	1515	6060	232,895,184	0.036675623769	7.149891065458
14	1699	6796	187,569,264	0.029537836030	5.758383586103
15	1820	7280	139,780,848	0.022012261925	4.291277385269
16	1862	7448	102,354,912	0.016118539589	3.142299717175
17	1823	7292	71,483,424	0.011256991748	2.194543853624
18	1703	6812	46,076,496	0.007255986160	1.414550191291
19	1517	6068	28,131,888	0.004430123983	0.863650038661
20	1288	5152	16,850,496	0.002653564754	0.517310872340
21	1038	4152	9,377,904	0.001476803740	0.287902011844
22	792	3168	4,751,712	0.000748285124	0.145877740325
23	569	2276	2,349,984	0.000370068318	0.072144598772
24	384	1536	1,105,104	0.000174028410	0.033926735110
25	240	960	457,632	0.000072066493	0.014049319921
26	138	552	172,872	0.000027223356	0.005307177019
27	72	288	66,528	0.000010476627	0.002042412147
28	33	132	21,504	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	21,296	85,184	3,257,324,928	0.512953602133	100

7-3-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	23,514,624	0.003703011321	0.196881779205
1	4	96	73,436,544	0.011564563133	0.614864921564
2	10	240	121,056,768	0.019063650873	1.013576567017
3	23	552	264,446,208	0.041644182869	2.214138739152
4	47	1128	406,967,328	0.064087974477	3.407430695675
5	85	2040	591,197,184	0.093099930712	4.949938959125
6	142	3408	781,627,968	0.123088390190	6.544365966305
7	223	5352	992,222,352	0.156252151942	8.307617507663
8	327	7848	1,089,256,896	0.171532856194	9.120062293812
9	452	10,848	1,184,984,208	0.186607701534	9.921561969292
10	595	14,280	1,210,560,768	0.190635420252	10.135707797809
11	744	17,856	1,125,952,128	0.177311509491	9.427301846717
12	886	21,264	999,507,456	0.157399387917	8.368613772677
13	1009	24,216	861,315,264	0.135637302697	7.211566794883
14	1099	26,376	692,336,736	0.109027079112	5.796753900573
15	1143	27,432	512,714,592	0.080740731320	4.292824801163
16	1138	27,312	373,514,688	0.058819954685	3.127340515101
17	1084	26,016	258,083,424	0.040642191036	2.160864817587
18	985	23,640	164,003,328	0.025826744251	1.373156849633
19	854	20,496	98,909,568	0.015575977317	0.828143870309
20	705	16,920	58,073,760	0.009145278730	0.486236360569
21	552	13,248	31,538,304	0.004966555993	0.264061947349
22	408	9792	15,507,072	0.002442006437	0.129836646574
23	284	6816	7,471,296	0.001176556923	0.062555201795
24	184	4416	3,330,432	0.000524466281	0.027884833612
25	110	2640	1,312,416	0.000206675272	0.010988514940
26	60	1440	467,712	0.000073653860	0.003916029902
27	29	696	160,272	0.000025239146	0.001341915419
28	12	288	44,352	0.000006984418	0.000371347663
29	4	96	9072	0.000001428631	0.000075957477
30	1	24	2016	0.000000317474	0.000016879439
Totals	13,200	316,800	11,943,524,736	1.880829874487	100

7-3-3-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	3,048,192	0.000480019986	0.180972140481
1	3	36	9,725,184	0.001531492336	0.577387305345
2	6	72	16,381,440	0.002579699245	0.972571367212
3	13	156	35,665,920	0.005616560381	2.117497153929
4	24	288	55,883,520	0.008800366410	3.317822575488
5	39	468	81,616,896	0.012852780034	4.845621394108
6	61	732	109,049,328	0.017172755818	6.474293714501
7	90	1080	139,132,944	0.021910231978	8.260367682589
8	123	1476	154,681,920	0.024358837329	9.183515394088
9	161	1932	168,623,208	0.026554268874	10.011214151392
10	202	2424	173,449,080	0.027314232488	10.297727725842
11	239	2868	161,955,288	0.025504225154	9.615337594090
12	272	3264	144,129,672	0.022697101475	8.557025032770
13	297	3564	123,826,464	0.019499814158	7.351617036687
14	309	3708	99,195,624	0.015621024544	5.889276135376
15	308	3696	72,718,776	0.011451531215	4.317337144737
16	295	3540	52,284,456	0.008233596781	3.104144987000
17	269	3228	35,383,176	0.005572034717	2.100710551613
18	234	2808	21,724,848	0.003421162851	1.289811220615
19	195	2340	12,636,792	0.001990003490	0.750250409769
20	153	1836	7,041,384	0.001108855692	0.418049235229
21	114	1368	3,557,736	0.000560261422	0.211223931822
22	80	960	1,566,936	0.000246756306	0.093029494834
23	52	624	697,536	0.000109845843	0.041412936909
24	31	372	258,552	0.000040715981	0.015350315487
25	17	204	78,120	0.000012302100	0.004638009553
26	8	96	25,704	0.000004047788	0.001526054756
27	3	36	3528	0.000000555579	0.000209458496
28	1	12	1008	0.000000158737	0.000059845285
Totals	3600	43,200	1,684,343,232	0.265245238710	100

7-4-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	4,408,992	0.000694314623	0.177193601284
1	4	48	14,206,752	0.002237236006	0.570957159694
2	10	120	24,058,944	0.003788729175	0.966908293428
3	22	264	52,289,712	0.008234424480	2.101478609941
4	43	516	82,537,488	0.012997752056	3.317110745422
5	74	888	120,271,824	0.018940040284	4.833621296567
6	117	1404	161,467,776	0.025427453250	6.489251221324
7	174	2088	205,755,120	0.032401689206	8.269121535145
8	241	2892	229,419,648	0.036128306952	9.220178588325
9	314	3768	249,487,560	0.039288540572	10.026690733853
10	390	4680	257,250,384	0.040511006436	10.338671962374
11	460	5520	239,196,024	0.037667860849	9.613082742143
12	515	6180	213,122,880	0.033561941596	8.565225480854
13	552	6624	182,487,096	0.028737511702	7.333999637140
14	566	6792	145,933,056	0.022981092891	5.864924168396
15	552	6624	106,565,544	0.016781617083	4.282777676662
16	515	6180	76,905,216	0.012110799027	3.090754571700
17	460	5520	51,774,120	0.008153230623	2.080757410339
18	390	4680	31,915,728	0.005025991574	1.282665693639
19	314	3768	18,857,160	0.002969568085	0.757853062649
20	241	2892	10,538,640	0.001659592908	0.423538889215
21	174	2088	5,435,640	0.000855988021	0.218453702544
22	117	1404	2,536,128	0.000399381708	0.101924805860
23	74	888	1,146,600	0.000180563073	0.046080869104
24	43	516	444,528	0.000070002915	0.017865198483
25	22	264	159,768	0.000025159778	0.006420938684
26	10	120	48,384	0.000007619365	0.001944511400
27	4	48	12,600	0.000001984210	0.000506383177
28	1	12	1008	0.000000158737	0.000040510654
Totals	6400	76,800	2,488,234,320	0.391839557185	100

7-4-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	3,919,104	0.000617168553	0.170630875311
1	3	72	12,737,088	0.002005797799	0.554550344760
2	6	144	21,772,800	0.003428714186	0.947949307282
3	13	312	47,278,080	0.007445207946	2.058404210099
4	24	576	75,155,040	0.011835186645	3.272117876744
5	39	936	109,873,152	0.017302489111	4.783683234463
6	60	1440	148,119,840	0.023325460970	6.448876567220
7	87	2088	189,294,624	0.029809540464	8.241554034991
8	117	2808	212,209,632	0.033418126084	9.239233063870
9	149	3576	231,222,816	0.036412264353	10.067033558158
10	183	4392	239,084,784	0.037650343112	10.409329777270
11	211	5064	222,994,512	0.035116496117	9.708787715781
12	232	5568	198,910,080	0.031323753169	8.660194028672
13	246	5904	170,249,472	0.026810367972	7.412361710371
14	248	5952	135,959,328	0.021410460603	5.919429324486
15	238	5712	98,897,040	0.015574004445	4.305802678584
16	219	5256	70,805,520	0.011150237492	3.082747447998
17	193	4632	47,185,344	0.007430604164	2.054366648234
18	160	3840	28,496,160	0.004487488427	1.240672542448
19	127	3048	16,428,384	0.002587091843	0.715262861578
20	96	2304	8,873,424	0.001397359767	0.386333229260
21	67	1608	4,347,504	0.000684631680	0.189282655662
22	44	1056	1,862,784	0.000293345547	0.081102329623
23	27	648	794,304	0.000125084573	0.034582595099
24	15	360	262,080	0.000041271560	0.011410500921
25	7	168	73,584	0.000011587784	0.003203717566
26	3	72	23,184	0.000003650946	0.001009390466
27	1	24	2016	0.000000317474	0.000087773084
Totals	2816	67,584	2,296,831,680	0.361698052786	100

7-5-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	979,776	0.000154292138	0.142192396092
1	3	72	3,374,784	0.000531450699	0.489773808763
2	6	144	6,023,808	0.000948610925	0.874219916716
3	12	288	13,009,248	0.002048656726	1.887999037004
4	21	504	21,573,216	0.003397284306	3.130865906552
5	32	768	31,649,184	0.004984017037	4.593165486119
6	46	1104	43,843,680	0.006904369102	6.362921639952
7	63	1512	56,345,760	0.008873158557	8.177316676510
8	79	1896	64,680,768	0.010185730214	9.386955164255
9	94	2256	70,542,144	0.011108761842	10.237601738409
10	108	2592	74,040,480	0.011659669133	10.745306334333
11	116	2784	68,909,184	0.010851608278	10.000614411588
12	118	2832	61,904,736	0.009748569155	8.984076708660
13	116	2784	52,490,160	0.008265990420	7.617763265961
14	108	2592	41,436,576	0.006525305700	6.013584765602
15	94	2256	29,484,000	0.004643050460	4.278937845371
16	79	1896	20,762,784	0.003269659944	3.013249973982
17	63	1512	13,130,208	0.002067705138	1.905553653805
18	46	1104	7,432,992	0.001170524926	1.078731202454
19	32	768	4,161,024	0.000655265378	0.603878817972
20	21	504	1,971,648	0.000310489118	0.286140253865
21	12	288	840,672	0.000132386464	0.122004586771
22	6	144	326,592	0.000051430713	0.047397465364
23	3	72	117,936	0.000018572202	0.017115751381
24	1	24	18,144	0.000002857262	0.002633192520
Totals	1280	30,720	689,049,504	0.108509415836	100

7-6-0-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	36,288	0.000005714524	0.102694508289
1	2	24	139,104	0.000021905674	0.393662281774
2	3	36	266,112	0.000041906507	0.753093060785
3	6	72	574,560	0.000090479958	1.625996381241
4	9	108	1,019,088	0.000160482872	2.884004107780
5	12	144	1,505,952	0.000237152731	4.261822093990
6	16	192	2,186,352	0.000344300049	6.187344124407
7	20	240	2,842,560	0.000447637685	8.044403149298
8	22	264	3,380,832	0.000532403119	9.567705022250
9	24	288	3,719,520	0.000585738673	10.526187099614
10	26	312	3,995,136	0.000629141841	11.306176341141
11	24	288	3,719,520	0.000585738673	10.526187099614
12	22	264	3,380,832	0.000532403119	9.567705022250
13	20	240	2,842,560	0.000447637685	8.044403149298
14	16	192	2,186,352	0.000344300049	6.187344124407
15	12	144	1,505,952	0.000237152731	4.261822093990
16	9	108	1,019,088	0.000160482872	2.884004107780
17	6	72	574,560	0.000090479958	1.625996381241
18	3	36	266,112	0.000041906507	0.753093060785
19	2	24	139,104	0.000021905674	0.393662281774
20	1	12	36,288	0.000005714524	0.102694508289
Totals	256	3072	35,335,872	0.005564585427	100

8-2-2-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	1,259,712	0.000198375606	0.103128551012
1	4	48	5,808,672	0.000914731963	0.475537207444
2	10	120	9,036,684	0.001423069455	0.739804119413
3	23	276	24,695,604	0.003888988452	2.021749302132
4	47	564	36,656,064	0.005772485240	3.000913515251
5	85	1020	56,799,792	0.008944658132	4.650015437453
6	141	1692	80,710,992	0.012710121033	6.607548118700
7	219	2628	104,434,380	0.016446007872	8.549705238372
8	317	3804	113,165,532	0.017820963079	9.264496440191
9	430	5160	126,554,400	0.019929401205	10.360599800745
10	553	6636	135,262,800	0.021300773496	11.073528369842
11	673	8076	118,990,656	0.018738285853	9.741380519715
12	776	9312	104,751,828	0.016495998616	8.575693680382
13	851	10,212	90,612,396	0.014269363958	7.418144070397
14	889	10,668	71,952,336	0.011330834580	5.890505253273
15	882	10,584	49,735,872	0.007832253540	4.071715132252
16	832	9984	35,518,176	0.005593294106	2.907758301477
17	747	8964	24,166,692	0.003805697002	1.978448985732
18	635	7620	14,505,660	0.002284307127	1.187531512975
19	510	6120	8,080,992	0.001272569991	0.661564703440
20	386	4632	4,605,696	0.000725290969	0.377053449425
21	274	3288	2,394,720	0.000377113207	0.196047988492
22	180	2160	1,045,728	0.000164678058	0.085610372365
23	109	1308	460,656	0.000072542703	0.037712418231
24	60	720	197,568	0.000031112407	0.016174253771
25	29	348	67,536	0.000010635363	0.005528954095
26	12	144	18,144	0.000002857262	0.001485390652
27	4	48	6048	0.000000952421	0.000495130217
28	1	12	1512	0.000000238105	0.000123782554
Totals	9680	116,160	1,221,496,848	0.192357600800	100

8-3-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	734,832	0.000115719104	0.098440889602
1	4	48	3,417,552	0.000538185673	0.457828264341
2	10	120	5,409,504	0.000851872203	0.724677730512
3	22	264	14,658,732	0.002308412439	1.963739492187
4	43	516	22,102,308	0.003480604101	2.960909244271
5	74	888	34,225,524	0.005389731209	4.584981369440
6	117	1404	48,950,892	0.007708637282	6.557647673632
7	174	2088	63,536,508	0.010005535636	8.511592268368
8	241	2892	69,490,656	0.010943176716	9.309232580636
9	314	3768	77,698,656	0.012235747540	10.408807479193
10	389	4668	83,309,904	0.013119389774	11.160511603264
11	457	5484	73,648,800	0.011597988560	9.866273366087
12	509	6108	64,854,144	0.010213032938	8.688107798465
13	541	6492	56,016,324	0.008821279979	7.504159817231
14	548	6576	44,245,404	0.006967631373	5.927282604156
15	527	6324	30,400,236	0.004787336513	4.072531239743
16	483	5796	21,488,292	0.003383910733	2.878653325544
17	421	5052	14,467,860	0.002278354498	1.938169553099
18	347	4164	8,408,736	0.001324182118	1.126466256602
19	270	3240	4,671,720	0.000735688227	0.625841379762
20	198	2376	2,556,000	0.000402511090	0.342411481568
21	135	1620	1,292,184	0.000203489198	0.173105883372
22	85	1020	534,240	0.000084130487	0.071568822345
23	49	588	229,320	0.000036112615	0.030720579403
24	25	300	85,680	0.000013492625	0.011478018678
25	11	132	28,728	0.000004523998	0.003848512145
26	4	48	6048	0.000000952421	0.000810213083
27	1	12	1512	0.000000238105	0.000202553271
Totals	6000	72,000	746,470,296	0.117551867155	100

8-3-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	653,184	0.000102861426	0.094794930728
1	3	72	3,055,968	0.000481244527	0.443504854478
2	6	144	4,898,880	0.000771460692	0.710961980462
3	13	312	13,206,240	0.002079678426	1.916587984366
4	24	576	20,123,640	0.003169009495	2.920492632703
5	39	936	31,203,792	0.004913878063	4.528526879253
6	60	1440	44,810,712	0.007056654354	6.503264531774
7	87	2088	58,365,792	0.009191267040	8.470478777095
8	117	2808	64,296,288	0.010125183475	9.331156560850
9	149	3576	71,976,816	0.011334689616	10.445812032687
10	182	4368	77,356,080	0.012181799716	11.226490919874
11	209	5016	68,789,952	0.010832831986	9.983310575027
12	229	5496	60,628,032	0.009547517700	8.798791907990
13	240	5760	52,336,800	0.008241839754	7.595506519659
14	239	5736	41,243,832	0.006494952962	5.985612319663
15	226	5424	28,209,312	0.004442316479	4.093945621649
16	204	4896	19,728,360	0.003106762006	2.863126652799
17	175	4200	13,131,360	0.002067886552	1.905720840632
18	141	3384	7,394,400	0.001164447576	1.073130443760
19	108	2592	3,988,224	0.000628053360	0.578800793970
20	77	1848	2,094,480	0.000329832327	0.303966549260
21	51	1224	992,880	0.000156355716	0.144094146246
22	31	744	356,832	0.000056192816	0.051786119564
23	17	408	147,168	0.000023175568	0.021358117109
24	8	192	48,384	0.000007619365	0.007021846721
25	3	72	9072	0.000001428631	0.001316596260
26	1	24	3024	0.000000476210	0.000438865420
Totals	2640	63,360	689,049,504	0.108509415836	100

8-4-1-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	24	244,944	0.000038573035	0.085315437655
1	3	72	1,170,288	0.000184293387	0.407618202131
2	6	144	1,950,480	0.000307155646	0.679363670219
3	12	288	5,159,376	0.000812482808	1.797041043948
4	21	504	8,150,544	0.001283522828	2.838882473094
5	32	768	12,600,576	0.001984300305	4.388854824573
6	46	1104	18,387,000	0.002895528721	6.404300379556
7	63	1512	24,084,432	0.003792742948	8.388749496872
8	79	1896	27,055,944	0.004260687601	9.423744625466
9	94	2256	30,288,384	0.004769722401	10.549622513044
10	108	2592	32,788,152	0.005163378247	11.420306428375
11	116	2784	29,397,600	0.004629444451	10.239357200089
12	118	2832	25,957,368	0.004087687201	9.041104135241
13	116	2784	22,343,904	0.003518649903	7.782513344644
14	108	2592	17,366,040	0.002734751052	6.048693999205
15	94	2256	11,739,744	0.001848739105	4.089021969603
16	79	1896	8,026,416	0.001263975529	2.795647959715
17	63	1512	5,184,576	0.000816451227	1.805818352349
18	46	1104	2,675,088	0.000421264705	0.931748903777
19	32	768	1,459,584	0.000229850840	0.508381702572
20	21	504	660,240	0.000103972583	0.229965480100
21	12	288	286,272	0.000045081242	0.099710223433
22	6	144	90,720	0.000014286309	0.031598310243
23	3	72	33,264	0.000005238313	0.011586047089
24	1	24	3024	0.000000476210	0.001053277008
Totals	1280	30,720	287,103,960	0.045212256598	100

8-5-0-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	13,608	0.000002142946	0.068463005526
1	2	24	68,040	0.000010714732	0.342315027630
2	3	36	122,472	0.000019286517	0.616167049733
3	6	72	312,984	0.000049287766	1.574649127097
4	9	108	530,712	0.000083574908	2.670057215512
5	12	144	816,480	0.000128576782	4.107780331557
6	16	192	1,231,632	0.000193953654	6.196445357285
7	20	240	1,631,232	0.000256881444	8.206866948126
8	22	264	1,900,800	0.000299332191	9.563086486163
9	24	288	2,137,104	0.000336544625	10.751952010693
10	26	312	2,346,300	0.000369488173	11.804434881358
11	24	288	2,137,104	0.000336544625	10.751952010693
12	22	264	1,900,800	0.000299332191	9.563086486163
13	20	240	1,631,232	0.000256881444	8.206866948126
14	16	192	1,231,632	0.000193953654	6.196445357285
15	12	144	816,480	0.000128576782	4.107780331557
16	9	108	530,712	0.000083574908	2.670057215512
17	6	72	312,984	0.000049287766	1.574649127097
18	3	36	122,472	0.000019286517	0.616167049733
19	2	24	68,040	0.000010714732	0.342315027630
20	1	12	13,608	0.000002142946	0.068463005526
Totals	256	3072	19,876,428	0.003130079303	100

9-2-1-1 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	34,992	0.000005510434	0.030938565304
1	4	48	331,452	0.000052196051	0.293056965793
2	10	120	482,544	0.000075989558	0.426646635113
3	22	264	1,915,812	0.000301696235	1.693886450373
4	43	516	2,714,688	0.000427500793	2.400221535406
5	74	888	4,553,724	0.000717106577	4.026225632962
6	116	1392	7,594,704	0.001195990839	6.714941862871
7	170	2040	9,892,884	0.001557901221	8.746903225738
8	231	2772	10,665,792	0.001679616417	9.430278415258
9	293	3516	12,227,628	0.001925569591	10.811193055162
10	351	4212	14,876,352	0.002342682573	13.153091787593
11	397	4764	11,417,988	0.001798069951	10.095340860020
12	423	5076	10,011,672	0.001576607593	8.851930954799
13	427	5124	8,691,564	0.001368721009	7.684742809913
14	409	4908	6,888,456	0.001084773057	6.090504852453
15	369	4428	4,096,740	0.000645142129	3.622178155633
16	314	3768	2,848,896	0.000448635459	2.518883028669
17	252	3024	1,888,884	0.000297455695	1.670077760201
18	189	2268	1,031,472	0.000162433067	0.911987420863
19	131	1572	482,940	0.000076051919	0.426996762909
20	84	1008	261,216	0.000041135500	0.230957026587
21	49	588	126,216	0.000019876111	0.111595277731
22	25	300	43,272	0.000006814343	0.038259419233
23	11	132	14,616	0.000002301683	0.012922898676
24	4	48	5544	0.000000873052	0.004901789153
25	1	12	1512	0.000000238105	0.001336851587
Totals	4400	52,800	113,101,560	0.017810888963	100

9-2-2-0 Shape

HCP	Ways	Specific	Hands	Percent	Relative
0	1	12	15,552	0.000002449082	0.029792692515
1	3	36	147,744	0.000023266275	0.283030578889
2	6	72	218,700	0.000034440209	0.418959738486
3	13	156	859,140	0.000135294749	1.645839367733
4	24	288	1,235,520	0.000194565924	2.366863905325
5	39	468	2,070,576	0.000326067998	3.966565978400
6	59	708	3,461,088	0.000545041590	6.630345328570
7	84	1008	4,535,484	0.000714234197	8.688546824641
8	111	1332	4,932,420	0.000776742469	9.448950129424
9	137	1644	5,663,808	0.000891919222	10.850057240590
10	162	1944	6,879,264	0.001083325528	13.178484894461
11	179	2148	5,361,840	0.000844366222	10.271582460932
12	187	2244	4,690,860	0.000738702336	8.986197891523
13	186	2232	4,079,724	0.000642462502	7.815455419006
14	175	2100	3,210,168	0.000505527473	6.149662303508
15	155	1860	1,901,520	0.000299445574	3.642708376436
16	129	1548	1,292,976	0.000203613920	2.476931352671
17	102	1224	852,804	0.000134296975	1.633701604116
18	74	888	433,116	0.000068205788	0.829712693618
19	50	600	197,424	0.000031089730	0.378201679977
20	31	372	100,080	0.000015760293	0.191721493497
21	17	204	44,784	0.000007052448	0.085791920111
22	8	96	10,584	0.000001666736	0.020275582406
23	3	36	4032	0.000000634947	0.007724031393
24	1	12	1512	0.000000238105	0.002896511772
Totals	1936	23,232	52,200,720	0.008220410291	100