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

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.

HCPWaysSpecificHandsPercent
01123107896000.363896103487
11450067108000.788441557556
221086115425761.356119478996
3324156363429602.462363633597
4551244190551363.845438379518
5596329330310405.186193356366
68170416193991846.554096137761
79284509794419688.028087148267
812445564666081288.892189351605
913664594133138729.356227591333
1016952597237548169.405114885046
11171304567999335208.944680418443
12211716509716820808.026865144755
13212184439069447526.914331841931
14242680361533742245.693323186165
15253176280909627244.423679195401
16283650210247817563.310918552550
17274064149970828482.361694899468
18304380101925040201.605084468814
1929458465798384401.036172903795
2031465840865384040.643535613094
2129458423995078440.377867182161
2230438013338000360.210042764574
232740647106036280.111903693592
242836503549938640.055903351769
252531761678198920.026427765118
26242680740952480.011668293831
27212184311579400.004906657430
28211716117907600.001856772950
2917130442365880.000667164966
301695213960680.000219848534
31136643881960.000061131923
32114391091560.000017189554
338268223600.000003521185
34614844840.000000706127
353646240.000000098266
36225600.000000009449
371440.000000000630
Totals61065399635013559600100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

## HCP by Range

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

2-Point Ranges
RangeWaysSpecificHandsPercent
0-12573175004001.152337661043
1-2314136182533762.144561036551
2-3534242478855363.818483112593
3-4875400553980966.307802013115
4-510147573520861769.031631735884
5-6132667455243022411.740289494127
6-7174549259884115214.582183286028
7-82172910744605009616.920276499872
8-925110911587992200018.248416942938
9-1029161611913706868818.761342476379
10-1133225611652368833618.349795303489
11-1238302010777161560016.971545563198
12-134239009487862683214.941196986686
13-144548648006031897612.607655028096
14-154958566424433694810.117002381566
15-16536826491157444807.734597747950
16-17557714360218646045.672613452017
17-18578444251895868683.966779368281
18-19598964167723424602.641257372609
19-20609242106663768441.679708516889
20-2160924264860462481.021402795255
21-2259896437333078800.587909946734
22-2357844420444036640.321946458165
23-2455771410655974920.167807045360
24-255368265228137560.082331116887
25-264958562419151400.038096058949
26-274548641052531880.016574951260
27-28423900429487000.006763430379
28-29383020160273480.002523937916
29-3033225656326560.000887013500
30-3129161617842640.000280980457
31-322411034973520.000078321477
32-33197071315160.000020710739
33-3414416268440.000004227311
34-35921251080.000000804392
35-365896840.000000107714
36-37329640.000000010079

3-Point Ranges
RangeWaysSpecificHandsPercent
0-2415159290429762.508457140039
1-3638292545963364.606924670148
2-41085486669406727.663921492110
3-5131717298842913611.493995369481
4-6183179897148536015.585727873645
5-72255012553187219219.768376642394
6-82989914906544928023.474372637633
7-934139316685936396826.276504091205
8-1041206117560367681627.653531827984
9-1146292017593700220827.706022894822
10-1254397216749537041626.376660448244
11-1359520415167856035223.885877405129
12-1466658013103200105620.634520172851
13-1570804010815128170017.031334223497
14-167795068526911870413.427920934115
15-1780108906411282732810.096292647418
16-188512094462143686247.277697920830
17-198613028317694253085.002952272076
18-209013622208588808643.284792985702
19-218913826130658846882.057575699050
20-22901362278198462841.231445559828
21-23861302844439115080.699813640326
22-24851209423993975280.377849809933
23-25801089012334173840.194234810478
24-267795065969090040.093999410717
25-277080402730730800.043002716379
26-286665801170439480.018431724210
27-29595204471852880.007430595345
28-30543972174234160.002743786449
29-3146292060208520.000948145423
30-3240205518934200.000298170011
31-333213715197120.000081842662
32-34258551360000.000021416866
33-3517480274680.000004325577
34-361123751680.000000813841
35-376936880.000000108344

4-Point Ranges
RangeWaysSpecificHandsPercent
0-3739315653859364.970820773636
1-41189536736514728.452363049666
2-5151818159997171212.850114848477
3-62134111460782832018.048091507242
4-72760114995092732823.613815021912
5-83499518199848032028.660565993999
6-942156320847876315232.830600228966
7-1050234522658311878435.681618976251
8-1158336523240361033636.598212246427
9-1267463622690868428835.732888039577
10-1375615621140231516833.290992290175
11-1483788418783193457629.579200591294
12-1591975615912296378025.058199368252
13-16981169012917606345620.342252776046
14-171041357010026620155215.789615833583
15-18110152707430533134811.701377116231
16-1911416678527942070648.313870824625
17-2011717686358559637125.646487885170
18-2111918206232583887083.662660167863
19-2211918206143996847242.267618463623
20-231171768685304499121.343349253420
21-241141667847989053720.755716992094
22-251101527025672174200.404277575052
23-261041357013075126320.205903104309
24-2798116906280669440.098906068147
25-289197562848638400.044859489328
26-298378841212805360.019098889176
27-30756156485813560.007650443879
28-31674636178116120.002804918372
29-3257335961300080.000965334977
30-3348232319157800.000301691196
31-343815195241960.000082548788
32-35289191366240.000021515131
33-3619505275280.000004335026
34-371224151720.000000814471

5-Point Ranges
RangeWaysSpecificHandsPercent
0-41290559844410728.816259153153
1-5161858660668251213.638556406032
2-62335112321937089619.404210986237
3-73062516558727028826.076178655509
4-839104620641753545632.506004373517
5-947165924141179419238.016793585332
6-1058251526820251796842.235715114012
7-1167364928338305230444.626299394694
8-1279508128337529241644.625077391182
9-1388682027081562904042.647219881508
10-1499883624755568939238.984315476340
11-151081106021592289730034.002879786695
12-161191340618014774553628.369117920801
13-171251575414417314630422.703947675514
14-181341795011045870557217.394700302397
15-19139198548088516978812.737550020026
16-2014521336568807454688.957406437719
17-2114622270382554715566.024355067331
18-2214922586245921887443.872702932437
19-2314622270151102883522.379522157215
20-241452133688854437761.399252605188
21-251391985449667252640.782144757213
22-261341795026413126680.415945868883
23-271251575413386705720.210809761739
24-28119134066398577040.100762841096
25-29108110602891004280.045526654294
26-309988361226766040.019318737710
27-31886820489695520.007711575802
28-32785075179207680.002822107927
29-3365362761523680.000968856162
30-3454247119202640.000302397322
31-354115835248200.000082647054
32-36309441366840.000021524580
33-3720509275320.000004335655

 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
HCPWaysSpecificHandsPercentRelative
0142987228160.0470419586300.446482315816
14165832207360.0918438239910.871703568975
2104010038712320.1580865820621.500423564717
3249617391386880.2738742601172.599381859551
45120426980128000.4248748328624.032551042390
59638435391686400.5573374909085.289774084254
617068044035721280.6934611177086.581743932055
7284113653119851840.8365152371467.939492129503
8445178058636120320.9233837519468.763974289452
9664265660987109680.9604064158639.115361969833
10949379660942440880.9597029852159.108685603583
111295518058208978160.9166572473938.700132021448
121698679252362722160.8245921897007.826328690089
132145858045251127360.7126009622306.763403079662
1426081043237623093840.5924770151955.623288602724
1530591223629765682360.4687408939544.448890436260
1634671386822549378320.3551007372853.370314590411
1737941517616416135000.2585162907442.453617058683
1840111604411457161280.1804238839751.712430262099
194101164047610916720.1198543968861.137556135863
204049161964863173520.0765837744170.726868139669
213861154442967918960.0467378832330.443596290421
223555142201722564240.0271264166560.257460906842
23315512620955668000.0150495684000.142837720769
24269610784503631120.0079310293830.075274594618
2522168864251793600.0039651688720.037634015085
2617476988118206480.0018614796210.017667583495
271317526853074560.0008358019950.007932722641
28948379221833920.0003438339180.003263379509
2964725888469600.0001333766790.001265898157
3041716683084480.0000485734510.000461017940
312521008956320.0000150598360.000142935171
32141564307200.0000048376920.000045915263
337228869600.0000010960400.000010402677
343313218400.0000002897580.000002750133
3513522760.0000000434640.000000412520
36416480.0000000075590.000000071743
371440.0000000006300.000000005979
Totals540002160006690585616010.536130315413100.000000000000

4-4-3-2 Shape
HCPWaysSpecificHandsPercentRelative
01125761082880.0907237773570.420969040627
144811590750080.1825275996830.846949617452
21012019980898560.3146531008341.460027545666
32428835000864640.5511829489442.557553973015
45161254474184800.8578428598333.980492173407
596115272019886401.1341472211305.262577038966
6169202889950785121.4165175492736.572808707034
72803360108966850561.7159767521927.962334772102
84355220120486009601.8973769579968.804053148821
96417692125663244481.9789064749929.182359735609
1090410848125743531681.9801708133489.188226414888
11121614592120036250081.8902942821518.771188696496
12156718804107924676481.6995649124097.886181897414
1319442332893148077601.4668675367926.806438595016
1423192782877257467361.2166270498015.645293184153
1526633195660840447840.9580968299064.445682433668
1629513541245935282520.7233748291763.356544631653
1731563787233236218080.5233938327392.428609192167
1832543904823032330560.3627061219691.682999238373
1932403888015172915680.2389384517961.108702632885
203114373689612836640.1513800216500.702421177118
212884346085795703360.0912689701250.423498799451
222575309003319884000.0522805214130.242587793230
232214265681817412480.0286200578320.132800448121
24182921948939781440.0147993916950.068670925143
25144917388460843200.0072572182600.033674349740
26110013200211215600.0033261588950.015433770065
27796955292440800.0014557295450.006754756996
28547656436597600.0005763278510.002674229287
29356427213766880.0002167966300.001005961967
3021726044731360.0000745080150.000345725990
3112314761391520.0000219132330.000101679988
3264768409920.0000064552950.000029953332
333036085920.0000013530420.000006278275
341214417760.0000002796790.000001297744
354482400.0000000377940.000000175371
36112120.0000000018900.000000008769
Totals4224050688013685288760021.551175645163100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

4-4-4-1 Shape
HCPWaysSpecificHandsPercentRelative
014720135360.0113404721700.378872136564
14161520285760.0239409968030.799841177191
210402640496320.0415817312891.389197834069
323924698025920.0739830803452.471689652824
4471887373661120.1161181680063.879374487090
5853409879528960.1555798110245.197742609561
614357212440463840.1959086330046.545082184148
722790815180056640.2390509054577.986415904314
8337134816876490400.2657658272788.878930727071
9474189617686632960.2785237054029.305156766893
10639255617762220000.2797140270709.344924045286
11821328416954289280.2669909803298.919861681896
121009403615240452400.2400019994798.018190862054
131195478013120192080.2066127861636.902695634169
141361544410834966080.1706257435965.700409917839
15148959568457480000.1331858174074.449585030166
16157362926333398640.0997364315183.332079505789
17160464164523558400.0712356190132.379900128611
18157362923082973400.0485497254881.621990508880
19148959561992967200.0313846400581.048524740080
20136154441234310400.0194375439920.649385996587
2111954780723630240.0113955084750.380710836240
2210094036399783960.0062956759580.210331295341
238213284212125680.0033404905580.111601948836
246392556103509360.0016300338540.054457556948
25474189648558240.0007646803640.025547091781
26337134820605320.0003244862990.010840714186
272279088379360.0001319556070.004408485130
281435722930400.0000461470460.001541719753
29853401002240.0000157829700.000527290883
3047188266040.0000041895170.000139966941
31239265920.0000010380880.000034681329
32104011920.0000001877130.000006271260
334161120.0000000176370.000000589246
341440.0000000006300.000000021044
Totals2048081920190073455002.993218839606100.000000000000

5-3-3-2 Shape
HCPWaysSpecificHandsPercentRelative
01123840721920.0604825182380.389786148729
14488092949760.1274453062880.821335099107
21012013873628160.2184776679221.408003027040
32428824849296640.3913191500302.521898704898
45161238630390400.6083396144223.920510625747
596115251642904320.8132567177395.241121123410
6169202864732530241.0193881573306.569557542898
7280336078898412881.2424681597308.007220813659
8435522087100246081.3716281292468.839606245912
9641769291294082641.4376713892149.265229197838
109031083691374985441.4389454218519.273439839351
1112131455687120178561.3719420198668.841629148058
1215611873278186288961.2312538492767.934948973631
1319312317267476732481.0626030178406.848060398544
1422952754055749258720.8779223353145.657865709514
1526243148843690078080.6880180339384.434006842249
1628913469232869510560.5176190344773.335852008723
1730693682823669389080.3727383253822.402152565175
1831373764416274740680.2562896560861.651686485861
1930913709210640300760.1675602134651.079859969283
202932351846696020520.1054468903660.679563921748
212675321003996344160.0629332098440.405579896584
222346281522261716920.0356168287400.229536515823
231974236881224389160.0192813073280.124260476328
24159019080625784760.0098546676770.063509474681
25122314676301161960.0047426067590.030564243644
2689610752135744480.0021376626990.013776399118
27621745258384440.0009194203670.005925304275
28406487222587480.0003557007510.002292352069
2924829768211960.0001293194430.000833413178
3014016802770200.0000436242650.000281141309
3172864779040.0000122680840.000079063001
3233396216360.0000034071710.000021957885
331315644280.0000006973080.000004493877
344487560.0000001190530.000000767247
351121080.0000000170080.000000109607
Totals396004752009853407907215.516846464518100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

5-4-2-2 Shape
HCPWaysSpecificHandsPercentRelative
01122469035520.0388816188670.367512654516
14485349576960.0842435075460.796277418117
2101209207444960.1449960370261.370515940798
32428816634147040.2619494779052.475970671444
45161225996723200.4093884737893.869577685111
596115234981269120.5508743646685.206915400154
6168201644069780160.6939974665706.559728185085
7276331253898475680.8487767680738.022716445773
8425510059689632240.9399741365778.884722400260
9618741662676607680.9870121154509.329329723255
108581029662887432320.9903321176269.360710690623
1111341360859885053920.9430515776348.913810657511
1214311717253761278960.8466162359418.002294896407
1317342080846296057600.7290562051806.891106622145
1420162419238176542000.6011925481415.682527520157
1522502700029748492000.4684701854044.428023482933
1624152898022319604000.3514823213233.322243381001
1724962995215944437440.2510881413312.373308314468
1824792974810888651800.1714711699521.620761343731
192368284167050387240.1110273494701.049440767031
202177261244396476960.0692343792280.654409750284
211920230402585628000.0407176817080.384867290151
221624194881444831920.0227527727270.215061310357
23131615792768840120.0121074598860.114440829672
24101912228385042680.0060635347730.057313090995
257509000180894240.0028486673590.026925867121
26524628879591680.0012533855190.011847115749
27346415233022080.0005200216520.004915292704
28213255612232440.0001926327370.001820782431
2912214644273560.0000672987200.000636113724
30647681356480.0000213614340.000201910245
3130360342720.0000053970500.000051013416
321214486400.0000013606010.000012860525
3344816200.0000002551130.000002411348
341121080.0000000170080.000000160757
Totals309763717126718232664010.579668043989100.000000000000

5-4-3-1 Shape
HCPWaysSpecificHandsPercentRelative
01242880541440.0453618886790.350807533856
14966355480320.1000841670850.774003923904
21024011003973120.1732872149521.340121901819
32355219969467840.3144730933402.431987149389
447112831371883200.4940348552523.820633449316
585204042447343680.6684478313625.169461458992
6143343253706421440.8457523564356.540651349764
7227544865885762881.0375489134678.023915806655
8337808873238618881.1533394487858.919385402870
94741137677061831841.2135462412579.384996447821
106381531277494008961.2203520348269.437629257594
118181963273832623201.1626936477788.991726382834
1210032407266301087681.0440893218378.074496251988
1311832839257022876800.8979788846706.944546780612
1413403216046933214400.7390899562775.715774462036
1514573496836418088160.5735009530024.435186912344
1615273664827191350080.4282010938023.311506070114
1715413698419292683680.3038153026552.349564803775
1814943585613047903360.2054744054321.589042509908
191395334808358791760.1316317050811.017977760230
201253300725138925840.0809262379100.625845500976
211079258962973510000.0468259292270.362129735580
22891213841623374640.0255644090660.197703128334
2370516920848346480.0133595018120.103316110080
2453112744408536640.0064335104950.049753747396
253809120186883200.0029429796760.022759622063
26258619278091200.0012297564170.009510358333
27164393630749760.0004842378490.003744868004
2897232810448640.0001645419980.001272490505
295312723406320.0000536416890.000414839621
3026624877680.0000138214370.000106888501
3111264187920.0000029593070.000022885889
3249632400.0000005102250.000003945843
331242160.0000000340150.000000263056
Totals192004608008211173256012.930705387098100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

5-4-4-0 Shape
HCPWaysSpecificHandsPercentRelative
0112240045120.0037801573900.304033196008
1336560105280.0088203672430.709410790686
2672986852160.0155406470471.249914250257
3131561817484480.0286211916662.301965626920
4242882899592640.0456619011703.672527970831
5394683988051200.0628026148375.051133520985
6617325113886400.0805319244406.477079085031
79010806332981760.0997298666198.021144877910
812314767118072640.1120932385219.015514975513
916119327540283520.1187420867799.550273287767
1020424487635993120.1202492923909.671495896152
1124329167288081920.1147704928479.230843096949
1227833366552997200.1031946027138.299809144838
1330937085617894320.0884688875557.115438818114
1432739244596907680.0723907011205.822290966406
1533239843521767680.0554597240764.460554263087
1632739242589436080.0407776501913.279693947795
1730937081796441760.0282898173252.275313614939
1827833361175275440.0185078794341.488564934015
192432916725185440.0114199992900.918495852038
202042448422735760.0066571139090.535423107872
211611932229655520.0036165451360.290874072868
221231476113949720.0017944454610.144324940061
2390108055098720.0008676778500.069786213265
246173222021560.0003467888150.027891778295
25394688936640.0001407314830.011318852142
26242882849400.0000448714830.003608955636
2713156792000.0000124721750.001003120960
28672189000.0000029763140.000239381138
2933623760.0000003741650.000030093629
301121080.0000000170080.000001367892
Totals40964915278953589001.243337056452100.000000000000

5-5-2-1 Shape
HCPWaysSpecificHandsPercentRelative
0112617258880.0097204047170.306260545430
14481457416800.0229509555810.723115176709
2101202537619840.0399616638361.259071131211
3232764715172000.0742530915872.339490277588
4475647483311360.1178449065673.712936489036
585102010266691680.1616767315405.093944689261
6142170413147505280.2070429061126.523295603446
7223267616249675680.2558949401058.062475402236
8327392418164321280.2860461954779.012450242226
9452542419195716960.3022883003029.524189827910
10596715219412023680.3056946326039.631513053535
11747896418420635520.2900825540109.139623688389
128921070416553656800.2606819421378.213299354111
1310211225214172468480.2231837142027.031843635477
1411201344011609053920.1828158429775.759974138341
151175141008889618240.1399909987064.410692853611
161183141966603690240.1039929012563.276501708247
171144137284600666080.0724498872572.282676764408
181058126963065178240.0482694927321.520825686010
19937112441923406560.0302892203000.954321697484
2079595401159120800.0182534810870.575111966679
216437716648908280.0102188098220.321963782468
224945928345386160.0054390359820.171367569059
233614332173305440.0027291612500.085987614435
24249298880012880.0012600184480.039699369364
25160192034452000.0005425395960.017093781318
2696115213763520.0002167437180.006828938844
27536364924800.0000775542490.002443499775
28263121483920.0000233683200.000736265064
2911132427680.0000067349740.000212198665
3044897200.0000015306760.000048226969
311129720.0000001530680.000004822697
Totals14080168960201546979923.173900413197100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

5-5-3-0 Shape
HCPWaysSpecificHandsPercentRelative
0112160030080.0025201049270.281512218526
1336388644480.0061202548220.683672530707
2672685843200.0108004496851.206480936541
3131561282145760.0201908406622.255449084145
4242882055624480.0323713478073.616091473688
5394682848154400.0448518674435.010247222580
6617323677516640.0579124112306.469195466212
79010804572741600.0720101410578.044004180735
812314765152170240.0811348066849.063289067201
916119325471323200.0861607302289.624717629999
1020324365558232960.0875293586419.777602383598
1124128925290608960.0833148974549.306819478466
1227533004758929280.0749421678968.371530773604
1330336364070217600.0640965462627.160003834658
1431838163321332640.0523033341545.842624836219
1532038402525225760.0397664856424.442176783123
1631137321852359840.0291703982063.258524447825
1728934681271691360.0200262079572.237058533210
182563072824869440.0129897925411.451044866371
192192628502899840.0079195134090.884661493982
201782136289833120.0045642036400.509851426767
211371644154141920.0024273799770.271154234673
22101121275336480.0011863759260.132525957750
237084035459640.0005584076030.062377785005
244554013760280.0002166926960.024205992713
25273245307120.0000835749080.009335864390
26151801678320.0000264296720.002952367371
27784408240.0000064288390.000718143415
2833687480.0000013776080.000153887875
291129720.0000001530680.000017098653
Totals38404608056846584080.895202680645100.000000000000

6-3-2-2 Shape
HCPWaysSpecificHandsPercentRelative
01121097349120.0172807194970.306260545430
14482664990720.0419674616350.743775610329
2101204497171840.0708200915081.255121342430
3242888638902720.1360428071092.411042220493
45161213381562880.2107287738623.734677206767
596115218476670240.2909649717035.156677125167
6168201623507169840.3701837462316.560645582607
7276331229139415200.4588786295908.132556020689
8425510032055972480.5048076847408.946541658504
9618741634089491520.5368309228159.514079043810
108571028434242188400.5392355467439.556695408011
1111311357232449066560.5109980105069.056250779468
1214251710028983287520.4564199784698.088982150202
1317212065224999926400.3936912215826.977260887552
1419922390420428963200.3217090862265.701545021692
1522112653215734129760.2477762800834.391258054828
1623562827211706759360.1843544784683.267254186897
172412289448305080480.1307858762142.317875351868
182368284165566620960.0876614503081.553595241786
192231267723546397440.0558475860300.989768519872
202015241802182786560.0343738574870.609196645113
211741208921261588320.0198671083620.352098270230
22143717244684652320.0107816960700.191080476697
23113013560356957280.0056212544540.099623656023
2484410128175259520.0027599335060.048913399764
25595714079274880.0012483966490.022124925919
26395474033526800.0005279698280.009357036760
27244292813584960.0002139318100.003791443565
2813916684831200.0000760802650.001348345682
29728641540800.0000242640490.000430023809
3033396481680.0000075853500.000134432677
3113156113760.0000017914580.000031749421
3244823040.0000003628270.000006430263
331124320.0000000680300.000001205674
Totals29040348480358305742085.642489623461100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

6-3-3-1 Shape
HCPWaysSpecificHandsPercentRelative
0112640120320.0100804197060.292339611546
14481579979520.0248810359420.721568406277
2101202688215040.0423331911481.227693788173
3232765174668800.0814891071502.363244252071
4475648073717120.1271424365353.687224499602
585102011195573760.1763044834365.112960144803
6143171614318609760.2254851025396.539234397565
7227272417794108080.2802161908358.126476353576
8337404419675293120.3098405195068.985603749877
9474568820947928400.3298815920289.566809644724
10637764421108245760.3324062209529.640025746888
11815978020006935200.3150631179069.137062958107
129971196417886242880.2816671015858.168553836200
1311711405215397272000.2424715467457.031853816726
1413191582812562827840.1978355839825.737377952119
151425171009625538880.1515800526544.395933403746
161481177727129746720.1122770783743.256118141273
171478177365015226240.0789782543092.290427666504
181415169803327471360.0524000048461.519638815425
191301156122094481440.0329832553700.956538749717
201146137521269982080.0199992907360.579994192245
2196511580719825760.0113355966830.328740670285
227769312381373920.0060057602590.174171480179
235947128194569920.0030640278000.088859067669
24430516091719360.0014443685270.041887753343
25294352840023360.0006302756750.018278459767
26188225616128000.0002539788290.007365573483
2711113326077520.0000957069330.002775571686
28607201972800.0000310670530.000900967471
2929348573840.0000090366570.000262069735
3012144144000.0000022676680.000065764049
3144823040.0000003628270.000010522248
321124320.0000000680300.000001972921
Totals18000216000218964620163.448188103226100.000000000000

6-4-2-1 Shape
HCPWaysSpecificHandsPercentRelative
0124823011840.0129605396220.275634490887
14962080391040.0327613640460.696742740852
2102403570194880.0562223408621.195692212782
3235526899256000.1086473807642.310626436501
447112810863901440.1710814088263.638423892489
585204015126894720.2382137277445.066140876957
6142340819483752960.3068242034436.525294129051
7223535224268567680.3821740073608.127774075554
8327784826985843360.4249648366099.037815538209
94521084828743422400.4526426556649.626445470779
105961430429083199040.4579933546359.740239898307
117471792827513501120.4332742301969.214533139307
128922140824635257920.3879485335018.250582123632
1310212450421134753280.3328236532987.078229834881
1411202688017215712640.2711077957275.765705860049
1511752820013096215360.2062352080844.386047050424
161183283929677537280.1523989076093.241099254671
171144274566730954560.1059970209812.254260683938
181058253924430312640.0697672132041.483753829101
19937224882757934080.0434311053410.923658347418
20795190801650542400.0259922386700.552782344068
2164315432917372160.0144464971830.307236659287
2249411856479203200.0075463459440.160489708220
233618664238489920.0037556665740.079872541908
242495976109048320.0017172597080.036521319262
25160384046025280.0007247920820.015414303907
2696230417965440.0002829142740.006016796682
275312726350400.0001000041640.002126809343
28266241873440.0000295023620.000627432870
2911264509760.0000080275450.000170723471
30496115200.0000018141340.000038581575
311248640.0000001360600.000002893618
Totals14080337920298588118404.702074686217100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

6-4-3-0 Shape
HCPWaysSpecificHandsPercentRelative
0124213373440.0033601399020.253360996674
1372553754880.0087203630790.657532110415
26144965260800.0152006328911.146156889714
3133121872097920.0294812274752.222941125577
4245762984143680.0469933851793.543391422016
5399364191264000.0660027480774.976733863232
66114645447373120.0857835716686.468245921031
79021606823111680.1074482832198.101806746239
812329527657614720.1205897827579.092701029715
916138648188931520.1289567977919.723590019448
1020348728330666400.1311887954849.891886928661
1124157847903980000.1244694681009.385236749656
1227566007088256000.1116236951618.416640819203
1330372726070377600.0955944563427.208005452418
1431876324928040000.0776052719745.851586430099
1532076803718418400.0585565196804.415273952904
1631174642714081760.0427405323713.222718159145
1728969361856669760.0292382695132.204621629043
1825661441188676800.0187189199671.411442486801
192195256717183360.0112939849730.851588139964
201784272410093280.0064580239870.486947401466
211373288215321760.0033908214520.255674444388
221012424102896640.0016203849260.122180132939
2370168047784960.0007525029860.056740169215
2445108018351360.0002889916240.021790523038
25276486711840.0001056960110.007969682037
26153602147040.0000338109320.002549409122
277168463680.0000073018910.000550576618
28372106560.0000016780740.000126530030
291248640.0000001360600.000010259192
Totals38409216084217161601.326226193549100.000000000000

6-5-1-1 Shape
HCPWaysSpecificHandsPercentRelative
0112102876480.0016200674530.229695409072
1448280052640.0044101836220.625281946919
210120492791040.0077603231071.100269366914
322264965895840.0152106333072.156584674067
4435161562198400.0246010242833.487967322949
5748882202530400.0346847774624.917655825919
611714042899774080.0456647584326.474412747430
717420883638990880.0573057193038.124884315558
824128924112337600.0647598391859.181739764766
931437684393236960.0691833566959.808912208879
1039046804499621280.07085866454310.046439677755
1146055204236366960.0667130157459.458663844810
1251561803810134160.0600008315168.507001060897
1355266243239928720.0510214100327.233886236245
1456667922621550960.0412833855345.853215624805
1555266241952702640.0307505660394.359857877051
1651561801428615360.0224973992823.189712454412
174605520958672800.0150968870742.140457575555
183904680611811360.0096346188321.366009612792
193143768367709760.0057905812320.820996633468
202412892208936800.0032902730480.466499473410
211742088108464400.0017080643140.242171726013
22117140453578800.0008437426130.119626997187
237488824479280.0003854922410.054655624234
24435169795600.0001542581230.021870930548
25222643583440.0000564309210.008000854196
26101201218240.0000191844720.002720001065
27448324000.0000051022530.000723404539
2811238880.0000006122700.000086808545
Totals64007680044788217760.705311202933100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

6-5-2-0 Shape
HCPWaysSpecificHandsPercentRelative
012491445760.0014400599580.221188171699
1372251475840.0039601648850.608267472173
26144445798080.0070202922961.078292337034
313312875085120.0137805737652.116647920844
4245761422489600.0224009326813.440704893099
5399362014346880.0317213207434.872283893263
66014402661966720.0419198406046.438740865852
78720883350773440.0527669588998.104820288790
811728083802559040.0598815408359.197595184685
914935764073328000.0641455278939.852528679855
1018343924181587200.06585036078010.114385047145
1121150643947590080.0621654454519.548394943769
1223255683552867360.0559494723588.593643222476
1324659043021822720.0475867432177.309157282261
1424859522441003040.0384401719165.904275928482
1523857121812706560.0285459504384.384558123127
1621952561315932480.0207229036313.182965501416
171934632875715840.0137905061522.118173500637
181603840548838720.0086429448901.327526098909
191273048323092800.0050879669440.781493922968
20962304177672960.0027979396240.429753737984
2167160888300800.0013905340860.213581171085
2244105640603680.0006394143780.098211811499
232764817530560.0002760659160.042402758917
24153605922720.0000932691890.014325821211
2571681866240.0000293889790.004514044320
26372570240.0000089799660.001379291320
2712477760.0000012245410.000188085180
Totals28166758441342970240.651056495015100.000000000000

6-6-1-0 Shape
HCPWaysSpecificHandsPercentRelative
01127620480.0001200049970.165891128774
133623708160.0003733488780.516105733965
267243394400.0006833617860.944657816632
31214487847200.0013833909321.912356067816
421252148176000.0023334304883.225660837280
532384213373440.0033601399024.644951605683
646552292118400.0046001915336.359159936352
763756371921760.0058569105248.096408701573
879948430768800.0067836157759.377456862664
9941128464849280.00732030478710.119358855238
101081296485775360.00764984231710.574901161238
111161392455051520.0071660126489.906070261100
121181416411899040.0064864605458.966678829508
131161392347004000.0054645132347.553971042406
141081296276151680.0043487524926.011578523682
15941128198858240.0031315589564.328968503256
1679948141644160.0022305690623.083468441188
176375688814880.0013986296621.933421607978
184655251982560.0008186055121.131614485568
193238429151360.0004590667330.634599397375
202125214100480.0002220500620.306955013787
21121445961600.0000938814600.129778774211
226722453760.0000386410650.053416191125
23336881280.0000138781290.019184688362
24112155520.0000024490820.003385533240
Totals1280153604593663360.072339610557100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

7-2-2-2 Shape
HCPWaysSpecificHandsPercentRelative
01467184640.0010580032340.206257102024
1416207152640.0032621766400.635959397908
21040337322880.0053120579061.035582533079
32496738681120.0116325251462.267753866525
4512041124409600.0177068596883.451941776930
5963841630044000.0256694361155.004241320809
61676682141374320.0337217101536.574027360896
727210882712476160.0427152478718.327312196224
841516602956214880.0465535709489.075590999806
959523803215805120.0506415189319.872534030477
1081132443271805040.05152338860410.044453999279
11104941963040740480.0478846543369.335084915422
12129051602695512000.0424481014508.275232160075
13151560602328951840.0366756237697.149891065458
14169967961875692640.0295378360305.758383586103
15182072801397808480.0220122619254.291277385269
16186274481023549120.0161185395893.142299717175
1718237292714834240.0112569917482.194543853624
1817036812460764960.0072559861601.414550191291
1915176068281318880.0044301239830.863650038661
2012885152168504960.0026535647540.517310872340
211038415293779040.0014768037400.287902011844
22792316847517120.0007482851240.145877740325
23569227623499840.0003700683180.072144598772
24384153611051040.0001740284100.033926735110
252409604576320.0000720664930.014049319921
261385521728720.0000272233560.005307177019
2772288665280.0000104766270.002042412147
2833132215040.0000033863840.000660173623
29135250400.0000007936840.000154728193
3041615120.0000002381050.000046418458
31143360.0000000529120.000010315213
Totals212968518432573249280.512953602133100.000000000000

7-3-2-1 Shape
HCPWaysSpecificHandsPercentRelative
0124235146240.0037030113210.196881779205
1496734365440.0115645631330.614864921564
2102401210567680.0190636508731.013576567017
3235522644462080.0416441828692.214138739152
44711284069673280.0640879744773.407430695675
58520405911971840.0930999307124.949938959125
614234087816279680.1230883901906.544365966305
722353529922223520.1562521519428.307617507663
8327784810892568960.1715328561949.120062293812
94521084811849842080.1866077015349.921561969292
105951428012105607680.19063542025210.135707797809
117441785611259521280.1773115094919.427301846717
12886212649995074560.1573993879178.368613772677
131009242168613152640.1356373026977.211566794883
141099263766923367360.1090270791125.796753900573
151143274325127145920.0807407313204.292824801163
161138273123735146880.0588199546853.127340515101
171084260162580834240.0406421910362.160864817587
18985236401640033280.0258267442511.373156849633
1985420496989095680.0155759773170.828143870309
2070516920580737600.0091452787300.486236360569
2155213248315383040.0049665559930.264061947349
224089792155070720.0024420064370.129836646574
23284681674712960.0011765569230.062555201795
24184441633304320.0005244662810.027884833612
25110264013124160.0002066752720.010988514940
266014404677120.0000736538600.003916029902
27296961602720.0000252391460.001341915419
2812288443520.0000069844180.000371347663
2949690720.0000014286310.000075957477
3012420160.0000003174740.000016879439
Totals13200316800119435247361.880829874487100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

7-3-3-0 Shape
HCPWaysSpecificHandsPercentRelative
011230481920.0004800199860.180972140481
133697251840.0015314923360.577387305345
2672163814400.0025796992450.972571367212
313156356659200.0056165603812.117497153929
424288558835200.0088003664103.317822575488
539468816168960.0128527800344.845621394108
6617321090493280.0171727558186.474293714501
79010801391329440.0219102319788.260367682589
812314761546819200.0243588373299.183515394088
916119321686232080.02655426887410.011214151392
1020224241734490800.02731423248810.297727725842
1123928681619552880.0255042251549.615337594090
1227232641441296720.0226971014758.557025032770
1329735641238264640.0194998141587.351617036687
143093708991956240.0156210245445.889276135376
153083696727187760.0114515312154.317337144737
162953540522844560.0082335967813.104144987000
172693228353831760.0055720347172.100710551613
182342808217248480.0034211628511.289811220615
191952340126367920.0019900034900.750250409769
20153183670413840.0011088556920.418049235229
21114136835577360.0005602614220.211223931822
228096015669360.0002467563060.093029494834
23526246975360.0001098458430.041412936909
24313722585520.0000407159810.015350315487
2517204781200.0000123021000.004638009553
26896257040.0000040477880.001526054756
2733635280.0000005555790.000209458496
2811210080.0000001587370.000059845285
Totals36004320016843432320.265245238710100.000000000000

7-4-1-1 Shape
HCPWaysSpecificHandsPercentRelative
011244089920.0006943146230.177193601284
1448142067520.0022372360060.570957159694
210120240589440.0037887291750.966908293428
322264522897120.0082344244802.101478609941
443516825374880.0129977520563.317110745422
5748881202718240.0189400402844.833621296567
611714041614677760.0254274532506.489251221324
717420882057551200.0324016892068.269121535145
824128922294196480.0361283069529.220178588325
931437682494875600.03928854057210.026690733853
1039046802572503840.04051100643610.338671962374
1146055202391960240.0376678608499.613082742143
1251561802131228800.0335619415968.565225480854
1355266241824870960.0287375117027.333999637140
1456667921459330560.0229810928915.864924168396
1555266241065655440.0167816170834.282777676662
165156180769052160.0121107990273.090754571700
174605520517741200.0081532306232.080757410339
183904680319157280.0050259915741.282665693639
193143768188571600.0029695680850.757853062649
202412892105386400.0016595929080.423538889215
21174208854356400.0008559880210.218453702544
22117140425361280.0003993817080.101924805860
237488811466000.0001805630730.046080869104
24435164445280.0000700029150.017865198483
25222641597680.0000251597780.006420938684
2610120483840.0000076193650.001944511400
27448126000.0000019842100.000506383177
2811210080.0000001587370.000040510654
Totals64007680024882343200.391839557185100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

7-4-2-0 Shape
HCPWaysSpecificHandsPercentRelative
012439191040.0006171685530.170630875311
1372127370880.0020057977990.554550344760
26144217728000.0034287141860.947949307282
313312472780800.0074452079462.058404210099
424576751550400.0118351866453.272117876744
5399361098731520.0173024891114.783683234463
66014401481198400.0233254609706.448876567220
78720881892946240.0298095404648.241554034991
811728082122096320.0334181260849.239233063870
914935762312228160.03641226435310.067033558158
1018343922390847840.03765034311210.409329777270
1121150642229945120.0351164961179.708787715781
1223255681989100800.0313237531698.660194028672
1324659041702494720.0268103679727.412361710371
1424859521359593280.0214104606035.919429324486
152385712988970400.0155740044454.305802678584
162195256708055200.0111502374923.082747447998
171934632471853440.0074306041642.054366648234
181603840284961600.0044874884271.240672542448
191273048164283840.0025870918430.715262861578
2096230488734240.0013973597670.386333229260
2167160843475040.0006846316800.189282655662
2244105618627840.0002933455470.081102329623
23276487943040.0001250845730.034582595099
24153602620800.0000412715600.011410500921
257168735840.0000115877840.003203717566
26372231840.0000036509460.001009390466
2712420160.0000003174740.000087773084
Totals28166758422968316800.361698052786100.000000000000

7-5-1-0 Shape
HCPWaysSpecificHandsPercentRelative
01249797760.0001542921380.142192396092
137233747840.0005314506990.489773808763
2614460238080.0009486109250.874219916716
312288130092480.0020486567261.887999037004
421504215732160.0033972843063.130865906552
532768316491840.0049840170374.593165486119
6461104438436800.0069043691026.362921639952
7631512563457600.0088731585578.177316676510
8791896646807680.0101857302149.386955164255
9942256705421440.01110876184210.237601738409
101082592740404800.01165966913310.745306334333
111162784689091840.01085160827810.000614411588
121182832619047360.0097485691558.984076708660
131162784524901600.0082659904207.617763265961
141082592414365760.0065253057006.013584765602
15942256294840000.0046430504604.278937845371
16791896207627840.0032696599443.013249973982
17631512131302080.0020677051381.905553653805
1846110474329920.0011705249261.078731202454
193276841610240.0006552653780.603878817972
202150419716480.0003104891180.286140253865
21122888406720.0001323864640.122004586771
2261443265920.0000514307130.047397465364
233721179360.0000185722020.017115751381
24124181440.0000028572620.002633192520
Totals1280307206890495040.108509415836100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

7-6-0-0 Shape
HCPWaysSpecificHandsPercentRelative
0112362880.0000057145240.102694508289
12241391040.0000219056740.393662281774
23362661120.0000419065070.753093060785
36725745600.0000904799581.625996381241
4910810190880.0001604828722.884004107780
51214415059520.0002371527314.261822093990
61619221863520.0003443000496.187344124407
72024028425600.0004476376858.044403149298
82226433808320.0005324031199.567705022250
92428837195200.00058573867310.526187099614
102631239951360.00062914184111.306176341141
112428837195200.00058573867310.526187099614
122226433808320.0005324031199.567705022250
132024028425600.0004476376858.044403149298
141619221863520.0003443000496.187344124407
151214415059520.0002371527314.261822093990
16910810190880.0001604828722.884004107780
176725745600.0000904799581.625996381241
183362661120.0000419065070.753093060785
192241391040.0000219056740.393662281774
20112362880.0000057145240.102694508289
Totals2563072353358720.005564585427100.000000000000

8-2-2-1 Shape
HCPWaysSpecificHandsPercentRelative
011212597120.0001983756060.103128551012
144858086720.0009147319630.475537207444
21012090366840.0014230694550.739804119413
323276246956040.0038889884522.021749302132
447564366560640.0057724852403.000913515251
5851020567997920.0089446581324.650015437453
61411692807109920.0127101210336.607548118700
721926281044343800.0164460078728.549705238372
831738041131655320.0178209630799.264496440191
943051601265544000.01992940120510.360599800745
1055366361352628000.02130077349611.073528369842
1167380761189906560.0187382858539.741380519715
1277693121047518280.0164959986168.575693680382
1385110212906123960.0142693639587.418144070397
1488910668719523360.0113308345805.890505253273
1588210584497358720.0078322535404.071715132252
168329984355181760.0055932941062.907758301477
177478964241666920.0038056970021.978448985732
186357620145056600.0022843071271.187531512975
19510612080809920.0012725699910.661564703440
20386463246056960.0007252909690.377053449425
21274328823947200.0003771132070.196047988492
22180216010457280.0001646780580.085610372365
2310913084606560.0000725427030.037712418231
24607201975680.0000311124070.016174253771
2529348675360.0000106353630.005528954095
2612144181440.0000028572620.001485390652
2744860480.0000009524210.000495130217
2811215120.0000002381050.000123782554
Totals968011616012214968480.192357600800100.000000000000

8-3-1-1 Shape
HCPWaysSpecificHandsPercentRelative
01127348320.0001157191040.098440889602
144834175520.0005381856730.457828264341
21012054095040.0008518722030.724677730512
322264146587320.0023084124391.963739492187
443516221023080.0034806041012.960909244271
574888342255240.0053897312094.584981369440
61171404489508920.0077086372826.557647673632
71742088635365080.0100055356368.511592268368
82412892694906560.0109431767169.309232580636
93143768776986560.01223574754010.408807479193
103894668833099040.01311938977411.160511603264
114575484736488000.0115979885609.866273366087
125096108648541440.0102130329388.688107798465
135416492560163240.0088212799797.504159817231
145486576442454040.0069676313735.927282604156
155276324304002360.0047873365134.072531239743
164835796214882920.0033839107332.878653325544
174215052144678600.0022783544981.938169553099
18347416484087360.0013241821181.126466256602
19270324046717200.0007356882270.625841379762
20198237625560000.0004025110900.342411481568
21135162012921840.0002034891980.173105883372
228510205342400.0000841304870.071568822345
23495882293200.0000361126150.030720579403
2425300856800.0000134926250.011478018678
2511132287280.0000045239980.003848512145
2644860480.0000009524210.000810213083
2711215120.0000002381050.000202553271
Totals6000720007464702960.117551867155100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

8-3-2-0 Shape
HCPWaysSpecificHandsPercentRelative
01246531840.0001028614260.094794930728
137230559680.0004812445270.443504854478
2614448988800.0007714606920.710961980462
313312132062400.0020796784261.916587984366
424576201236400.0031690094952.920492632703
539936312037920.0049138780634.528526879253
6601440448107120.0070566543546.503264531774
7872088583657920.0091912670408.470478777095
81172808642962880.0101251834759.331156560850
91493576719768160.01133468961610.445812032687
101824368773560800.01218179971611.226490919874
112095016687899520.0108328319869.983310575027
122295496606280320.0095475177008.798791907990
132405760523368000.0082418397547.595506519659
142395736412438320.0064949529625.985612319663
152265424282093120.0044423164794.093945621649
162044896197283600.0031067620062.863126652799
171754200131313600.0020678865521.905720840632
18141338473944000.0011644475761.073130443760
19108259239882240.0006280533600.578800793970
2077184820944800.0003298323270.303966549260
215112249928800.0001563557160.144094146246
22317443568320.0000561928160.051786119564
23174081471680.0000231755680.021358117109
248192483840.0000076193650.007021846721
2537290720.0000014286310.001316596260
2612430240.0000004762100.000438865420
Totals2640633606890495040.108509415836100.000000000000

8-4-1-0 Shape
HCPWaysSpecificHandsPercentRelative
01242449440.0000385730350.085315437655
137211702880.0001842933870.407618202131
2614419504800.0003071556460.679363670219
31228851593760.0008124828081.797041043948
42150481505440.0012835228282.838882473094
532768126005760.0019843003054.388854824573
6461104183870000.0028955287216.404300379556
7631512240844320.0037927429488.388749496872
8791896270559440.0042606876019.423744625466
9942256302883840.00476972240110.549622513044
101082592327881520.00516337824711.420306428375
111162784293976000.00462944445110.239357200089
121182832259573680.0040876872019.041104135241
131162784223439040.0035186499037.782513344644
141082592173660400.0027347510526.048693999205
15942256117397440.0018487391054.089021969603
1679189680264160.0012639755292.795647959715
1763151251845760.0008164512271.805818352349
1846110426750880.0004212647050.931748903777
193276814595840.0002298508400.508381702572
20215046602400.0001039725830.229965480100
21122882862720.0000450812420.099710223433
226144907200.0000142863090.031598310243
23372332640.0000052383130.011586047089
2412430240.0000004762100.001053277008
Totals1280307202871039600.045212256598100.000000000000

8-5-0-0 Shape
HCPWaysSpecificHandsPercentRelative
0112136080.0000021429460.068463005526
1224680400.0000107147320.342315027630
23361224720.0000192865170.616167049733
36723129840.0000492877661.574649127097
491085307120.0000835749082.670057215512
5121448164800.0001285767824.107780331557
61619212316320.0001939536546.196445357285
72024016312320.0002568814448.206866948126
82226419008000.0002993321919.563086486163
92428821371040.00033654462510.751952010693
102631223463000.00036948817311.804434881358
112428821371040.00033654462510.751952010693
122226419008000.0002993321919.563086486163
132024016312320.0002568814448.206866948126
141619212316320.0001939536546.196445357285
15121448164800.0001285767824.107780331557
1691085307120.0000835749082.670057215512
176723129840.0000492877661.574649127097
183361224720.0000192865170.616167049733
19224680400.0000107147320.342315027630
20112136080.0000021429460.068463005526
Totals2563072198764280.003130079303100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

9-2-1-1 Shape
HCPWaysSpecificHandsPercentRelative
0112349920.0000055104340.030938565304
14483314520.0000521960510.293056965793
2101204825440.0000759895580.426646635113
32226419158120.0003016962351.693886450373
44351627146880.0004275007932.400221535406
57488845537240.0007171065774.026225632962
6116139275947040.0011959908396.714941862871
7170204098928840.0015579012218.746903225738
82312772106657920.0016796164179.430278415258
92933516122276280.00192556959110.811193055162
103514212148763520.00234268257313.153091787593
113974764114179880.00179806995110.095340860020
124235076100116720.0015766075938.851930954799
13427512486915640.0013687210097.684742809913
14409490868884560.0010847730576.090504852453
15369442840967400.0006451421293.622178155633
16314376828488960.0004486354592.518883028669
17252302418888840.0002974556951.670077760201
18189226810314720.0001624330670.911987420863
1913115724829400.0000760519190.426996762909
208410082612160.0000411355000.230957026587
21495881262160.0000198761110.111595277731
2225300432720.0000068143430.038259419233
2311132146160.0000023016830.012922898676
2444855440.0000008730520.004901789153
2511215120.0000002381050.001336851587
Totals4400528001131015600.017810888963100.000000000000

9-2-2-0 Shape
HCPWaysSpecificHandsPercentRelative
0112155520.0000024490820.029792692515
13361477440.0000232662750.283030578889
26722187000.0000344402090.418959738486
3131568591400.0001352947491.645839367733
42428812355200.0001945659242.366863905325
53946820705760.0003260679983.966565978400
65970834610880.0005450415906.630345328570
784100845354840.0007142341978.688546824641
8111133249324200.0007767424699.448950129424
9137164456638080.00089191922210.850057240590
10162194468792640.00108332552813.178484894461
11179214853618400.00084436622210.271582460932
12187224446908600.0007387023368.986197891523
13186223240797240.0006424625027.815455419006
14175210032101680.0005055274736.149662303508
15155186019015200.0002994455743.642708376436
16129154812929760.0002036139202.476931352671
1710212248528040.0001342969751.633701604116
18748884331160.0000682057880.829712693618
19506001974240.0000310897300.378201679977
20313721000800.0000157602930.191721493497
2117204447840.0000070524480.085791920111
22896105840.0000016667360.020275582406
2333640320.0000006349470.007724031393
2411215120.0000002381050.002896511772
Totals193623232522007200.008220410291100.000000000000

9-3-1-0 Shape
HCPWaysSpecificHandsPercentRelative
0124181440.0000028572620.028438479218
13721730880.0000272573710.271294063656
261442620800.0000412715600.410778033156
31228810139760.0001596778501.589282154102
42150414887440.0002344428682.333422360319
53276824863760.0003915469153.897087312902
646110441742000.0006573402946.542542986868
763151255054320.0008669786528.629084739897
879189660493440.0009526322569.481599626839
994225669567840.00109553314210.903899758122
10107256884327360.00132796156413.217272238251
11114273666820320.00105226603410.473259929957
12115276058203840.0009165763339.122733103368
13111266450819280.0008002865337.965294522583
14101242439417840.0006207401316.178259610212
1586206423274000.0003665118593.647912066417
1670168015379920.0002421982932.410612518197
1753127210136880.0001596324971.588830749670
18378884613760.0000726560860.723149900127
19245762223360.0000350127960.348484221534
2014336976320.0000153747900.153026102461
217168423360.0000066669440.066356451510
2237280640.0000012698940.012639324097
2312430240.0000004762100.004739746536
Totals120028800638008800.010047168133100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

9-4-0-0 Shape
HCPWaysSpecificHandsPercentRelative
011215120.0000002381050.024646681989
1224146160.0000023016830.238251259230
2336236880.0000037303140.386131351166
3672876240.0000137987601.428333903858
491081368720.0000215541852.231111545797
5121442263680.0000356477433.689960389261
6161923854520.0000606998066.283143429997
7202405177520.0000815340078.439728104064
8222645861160.0000922997619.554110225439
9242886782400.00010680716811.055797349504
10263128182200.00012885079213.337571519390
11242886782400.00010680716811.055797349504
12222645861160.0000922997619.554110225439
13202405177520.0000815340078.439728104064
14161923854520.0000606998066.283143429997
15121442263680.0000356477433.689960389261
1691081368720.0000215541852.231111545797
17672876240.0000137987601.428333903858
18336236880.0000037303140.386131351166
19224146160.0000023016830.238251259230
2011215120.0000002381050.024646681989
Totals256307261347000.000966073859100.000000000000

10-1-1-1 Shape
HCPWaysSpecificHandsPercentRelative
11429160.0000004592030.116019619889
241638880.0000006122700.154692826518
31144312120.0000049151711.241839635103
42496411520.0000064804921.637324896314
545180755080.0000118907703.004255644219
6732921732000.0000272750086.891151633983
71074282202200.0000346795748.761948111061
81425682370400.0000373283379.431169649649
91736922743720.00004320726610.916507252420
101957804460000.00007023472117.745113330002
112058202536360.00003994182410.091478844324
122008002243680.0000353327898.926985622479
131837321953560.0000307640677.772677936538
141576281593760.0000250980476.341132695252
15125500703240.0000110744092.797998542195
1692368488320.0000076899151.942890973387
1763252309240.0000048698171.230380907213
1839156161280.0000025397880.641688761853
19218448360.0000007615590.192411139157
20104025920.0000004081800.103128551012
2141611520.0000001814130.045834911561
22143360.0000000529120.013368515872
Totals1875750025133680.000395797533100.000000000000

10-2-1-0 Shape
HCPWaysSpecificHandsPercentRelative
112477760.0000012245410.111722596930
2372105840.0000016667360.152066868043
37168835920.0000131638131.201017916994
4143361123200.0000176878111.613770844540
5245762054400.0000323520652.951683425056
6378884703040.0000740620416.757148177267
75212486045360.0000952004878.685742265624
86716086567120.0001034170049.435387098109
97918967632960.00012020152810.966745286272
1088211212268800.00019320532317.627343071130
119021607244160.00011407882410.408132301623
128620646333840.0000997433829.100219307320
137718485570160.0000877171828.002993062165
146515604455360.0000701616516.401291016676
155012001956480.0000308100512.810995710404
16368641272960.0000200461861.828940290479
1724576833040.0000131184601.196880043034
1814336344880.0000054310650.495510406753
197168106560.0000016780740.153101336533
2037248960.0000007710070.070343857326
2112420160.0000003174740.028965117723
Totals8251980069600960.001096054705100.000000000000

 Study 7Z76   Main Top   High Card Expectancy

10-3-0-0 Shape
HCPWaysSpecificHandsPercentRelative
111210080.0000001587370.102694508289
222414400.0000002267670.146706440413
3448109440.0000017234281.114968947137
4784153720.0000024207361.566091251406
510120278640.0000043879382.838769621986
614168636120.0000100174246.480757005233
718216837120.0000131827118.528534402660
821252926880.0000145962249.443004547900
9232761087920.00001713223311.083671573182
10253001706880.00002687942617.389603403589
11232761087920.00001713223311.083671573182
1221252926880.0000145962249.443004547900
1318216837120.0000131827118.528534402660
1414168636120.0000100174246.480757005233
1510120278640.0000043879382.838769621986
16784153720.0000024207361.566091251406
17448109440.0000017234281.114968947137
1822414400.0000002267670.146706440413
1911210080.0000001587370.102694508289
Totals22527009815520.000154571817100.000000000000

11-1-1-0 Shape
HCPWaysSpecificHandsPercentRelative
31129720.0000001530680.614474283113
433611880.0000001870830.751024123805
578423880.0000003760551.509634349871
613156106200.0000016724056.713700500683
721252128280.0000020201148.109543316644
828336139680.0000021996388.830223031406
934408159600.00000251333210.089516006676
1037444440640.00000693906427.856167501138
1136432150960.0000023772729.543316643908
1231372135360.0000021316088.557123350023
1325300119640.0000018840547.563343953876
1418216101880.0000016043756.440600819299
151113223880.0000003760551.509634349871
1667216200.0000002551131.024123805189
173369720.0000001530680.614474283113
181124320.0000000680300.273099681384
Totals27533001581840.000024910334100.000000000000

11-2-0-0 Shape
HCPWaysSpecificHandsPercentRelative
31124320.0000000680300.591715976331
42245400.0000000850380.739644970414
544810800.0000001700751.479289940828
678447640.0000007502206.525312294543
71012058560.0000009221858.021038790270
81315664320.0000010128928.809993425378
91518074160.00000116784910.157790927022
1017204199680.00000314450027.350427350427
111518074160.00000116784910.157790927022
121315664320.0000010128928.809993425378
131012058560.0000009221858.021038790270
1478447640.0000007502206.525312294543
1544810800.0000001700751.479289940828
162245400.0000000850380.739644970414
171124320.0000000680300.591715976331
Totals1211452730080.000011497077100.000000000000

12-1-0-0 Shape
HCPWaysSpecificHandsPercentRelative
61121080.0000000170085.325443786982
72241200.0000000188975.917159763314
83361320.0000000207876.508875739645
94481440.0000000226777.100591715976
1056010200.00000016062650.295857988166
114481440.0000000226777.100591715976
123361320.0000000207876.508875739645
132241200.0000000188975.917159763314
141121080.0000000170085.325443786982
Totals2530020280.000000319363100.000000000000

13-0-0-0 Shape
HCPWaysSpecificHandsPercentRelative
101440.000000000630100.000000000000

Check Totals
ShapesWaysSpecificHandsPercentsRelative Percents
393838114582640635013559600100.0000000000003900.000000000000

 Study 7Z76   Main Top   High Card Expectancy

© 2003 Richard Pavlicek