Illustration for EIS A001400 and A061924 ======================================== Card games with 4 players and 4 suits, n cards per suit (e.g. bridge: 4 * 13 cards). The probability in percent is shown, because it's sometimes erroneous in the older bridge literature. The total number of patterns for n cards is sequence A001400 in EIS: 1,1,2,3,5,6,9,11,15,18,23,27,34,39 etc. The number of combinations for n cards is sequence A061924 in EIS: 1,4,56,1320,43680,1860480,96909120 etc. Pattern | Number of combinations | Percent ------------+------------------------+---------------- 0 0 0 0 | 1 | 100.0000000000 total: 1 | 1 | 100.0000000000 ------------+------------------------+---------------- 1 0 0 0 | 4 | 100.0000000000 total: 1 | 4 | 100.0000000000 ------------+------------------------+---------------- 2 0 0 0 | 8 | 14.2857142857 1 1 0 0 | 48 | 85.7142857143 total: 2 | 56 | 100.0000000000 ------------+------------------------+---------------- 3 0 0 0 | 24 | 1.8181818182 2 1 0 0 | 648 | 49.0909090909 1 1 1 0 | 648 | 49.0909090909 total: 3 | 1320 | 100.0000000000 ------------+------------------------+---------------- 4 0 0 0 | 96 | 0.2197802198 3 1 0 0 | 4608 | 10.5494505495 2 2 0 0 | 5184 | 11.8681318681 2 1 1 0 | 27648 | 63.2967032967 1 1 1 1 | 6144 | 14.0659340659 total: 5 | 43680 | 100.0000000000 ------------+------------------------+---------------- 5 0 0 0 | 480 | 0.0257997936 4 1 0 0 | 36000 | 1.9349845201 3 2 0 0 | 144000 | 7.7399380805 3 1 1 0 | 360000 | 19.3498452012 2 2 1 0 | 720000 | 38.6996904025 2 1 1 1 | 600000 | 32.2497420021 total: 6 | 1860480 | 100.0000000000 ------------+------------------------+---------------- 6 0 0 0 | 2880 | 0.0029718565 5 1 0 0 | 311040 | 0.3209605040 4 2 0 0 | 1944000 | 2.0060031502 4 1 1 0 | 4665600 | 4.8144075604 3 3 0 0 | 1728000 | 1.7831139113 3 2 1 0 | 31104000 | 32.0960504027 3 1 1 1 | 12441600 | 12.8384201611 2 2 2 0 | 9720000 | 10.0300157508 2 2 1 1 | 34992000 | 36.1080567030 total: 9 | 96909120 | 100.0000000000 ------------+------------------------+---------------- 7 0 0 0 | 20160 | 0.0003378264 6 1 0 0 | 2963520 | 0.0496604844 5 2 0 0 | 26671680 | 0.4469443600 5 1 1 0 | 62233920 | 1.0428701733 4 3 0 0 | 74088000 | 1.2415121111 4 2 1 0 | 622339200 | 10.4287017330 4 1 1 1 | 242020800 | 4.0556062295 3 3 1 0 | 518616000 | 8.6905847775 3 2 2 0 | 933508800 | 15.6430525996 3 2 1 1 | 2178187200 | 36.5004560657 2 2 2 1 | 1306912320 | 21.9002736394 total: 11 | 5967561600 | 100.0000000000 ------------+------------------------+---------------- 8 0 0 0 | 161280 | 0.0000380290 7 1 0 0 | 30965760 | 0.0073015601 6 2 0 0 | 379330560 | 0.0894441117 6 1 1 0 | 867041280 | 0.2044436839 5 3 0 0 | 1517322240 | 0.3577764468 5 2 1 0 | 12138577920 | 2.8622115741 5 1 1 1 | 4624220160 | 1.0903663139 4 4 0 0 | 1185408000 | 0.2795128490 4 3 1 0 | 30346444800 | 7.1555289353 4 2 2 0 | 26553139200 | 6.2610878184 4 2 1 1 | 60692889600 | 14.3110578706 3 3 2 0 | 42485022720 | 10.0177405094 3 3 1 1 | 48554311680 | 11.4488462965 3 2 2 1 | 169940090880 | 40.0709620376 2 2 2 2 | 24782929920 | 5.8436819638 total: 15 | 424097856000 | 100.0000000000 ------------+------------------------+---------------- 9 0 0 0 | 1451520 | 0.0000042488 8 1 0 0 | 352719360 | 0.0010324688 7 2 0 0 | 5643509760 | 0.0165195009 7 1 1 0 | 12697896960 | 0.0371688771 6 3 0 0 | 30725775360 | 0.0899395050 6 2 1 0 | 237027409920 | 0.6938190384 6 1 1 1 | 88885278720 | 0.2601821394 5 4 0 0 | 69132994560 | 0.2023638862 5 3 1 0 | 829595934720 | 2.4283666343 5 2 2 0 | 711082229760 | 2.0814571152 5 2 1 1 | 1599935016960 | 4.6832785091 4 4 1 0 | 622196951040 | 1.8212749758 4 3 2 0 | 3318383738880 | 9.7134665374 4 3 1 1 | 3733181706240 | 10.9276498546 4 2 2 1 | 6399740067840 | 18.7331140364 3 3 3 0 | 860321710080 | 2.5183061393 3 3 2 1 | 9955151216640 | 29.1403996122 3 2 2 2 | 5688657838080 | 16.6516569212 total: 18 | 34162713446400 | 100.0000000000 ------------+------------------------+---------------- 10 0 0 0 | 14515200 | 0.0000004719 9 1 0 0 | 4354560000 | 0.0001415661 8 2 0 0 | 88179840000 | 0.0028667136 8 1 1 0 | 195955200000 | 0.0063704748 7 3 0 0 | 627056640000 | 0.0203855192 7 2 1 0 | 4702924800000 | 0.1528913943 7 1 1 1 | 1741824000000 | 0.0566264423 6 4 0 0 | 1920360960000 | 0.0624306527 6 3 1 0 | 21946982400000 | 0.7134931733 6 2 2 0 | 18517766400000 | 0.6020098650 6 2 1 1 | 41150592000000 | 1.3377996999 5 5 0 0 | 1382659891200 | 0.0449500699 5 4 1 0 | 46088663040000 | 1.4983356639 5 3 2 0 | 118513704960000 | 3.8528631358 5 3 1 1 | 131681894400000 | 4.2809590398 5 2 2 1 | 222213196800000 | 7.2241183796 4 4 2 0 | 86416243200000 | 2.8093793699 4 4 1 1 | 96018048000000 | 3.1215326332 4 3 3 0 | 131681894400000 | 4.2809590398 4 3 2 1 | 987614208000000 | 32.1071927983 4 2 2 2 | 277766496000000 | 9.0301479745 3 3 3 1 | 250822656000000 | 8.1542076948 3 3 2 2 | 634894848000000 | 20.6403382275 total: 23 | 3075990524006400 | 100.0000000000 ------------+------------------------+---------------- 11 0 0 0 | 159667200 | 0.0000000522 10 1 0 0 | 57959193600 | 0.0000189325 9 2 0 0 | 1448979840000 | 0.0004733133 9 1 1 0 | 3187755648000 | 0.0010412892 8 3 0 0 | 13040818560000 | 0.0042598194 8 2 1 0 | 95632669440000 | 0.0312386760 8 1 1 1 | 35065312128000 | 0.0114541812 7 4 0 0 | 52163274240000 | 0.0170392778 7 3 1 0 | 573796016640000 | 0.1874320558 7 2 2 0 | 478163347200000 | 0.1561933798 7 2 1 1 | 1051959363840000 | 0.3436254356 6 5 0 0 | 102240017510400 | 0.0333969845 6 4 1 0 | 1606628846592000 | 0.5248097562 6 3 2 0 | 4016572116480000 | 1.3120243905 6 3 1 1 | 4418229328128000 | 1.4432268295 6 2 2 1 | 7363715546880000 | 2.4053780492 5 5 1 0 | 1124640192614400 | 0.3673668293 5 4 2 0 | 8033144232960000 | 2.6240487809 5 4 1 1 | 8836458656256000 | 2.8864536590 5 3 3 0 | 6024858174720000 | 1.9680365857 5 3 2 1 | 44182293281280000 | 14.4322682952 5 2 2 2 | 12272859244800000 | 4.0089634153 4 4 3 0 | 8606940249600000 | 2.8114808367 4 4 2 1 | 31558780915200000 | 10.3087630680 4 3 3 1 | 47338171372800000 | 15.4631446020 4 3 2 2 | 78896952288000000 | 25.7719076700 3 3 3 2 | 39448476144000000 | 12.8859538350 total: 27 | 306135476264217600 | 100.0000000000 ------------+------------------------+---------------- 12 0 0 0 | 1916006400 | 0.0000000057 11 1 0 0 | 827714764800 | 0.0000024803 10 2 0 0 | 25038371635200 | 0.0000750296 10 1 1 0 | 54629174476800 | 0.0001637009 9 3 0 0 | 278204129280000 | 0.0008336619 9 2 1 0 | 2003069730816000 | 0.0060023654 9 1 1 1 | 728388993024000 | 0.0021826783 8 4 0 0 | 1408408404480000 | 0.0042204132 8 3 1 0 | 15023022981120000 | 0.0450177404 8 2 2 0 | 12393993959424000 | 0.0371396358 8 2 1 1 | 27041441366016000 | 0.0810319328 7 5 0 0 | 3605525515468800 | 0.0108042577 7 4 1 0 | 54082882732032000 | 0.1620638655 7 3 2 0 | 132202602233856000 | 0.3961561157 7 3 1 1 | 144221020618752000 | 0.4321703080 7 2 2 1 | 237964684020940800 | 0.7130810082 6 6 0 0 | 2453760420249600 | 0.0073528976 6 5 1 0 | 100954714433126400 | 0.3025192156 6 4 2 0 | 347031830863872000 | 1.0399098037 6 4 1 1 | 378580179124224000 | 1.1344470585 6 3 3 0 | 257060615454720000 | 0.7703035583 6 3 2 1 | 1850836431273984000 | 5.5461856195 6 2 2 2 | 508980018600345600 | 1.5252010454 5 5 2 0 | 237964684020940800 | 0.7130810082 5 5 1 1 | 259597837113753600 | 0.7779065544 5 4 3 0 | 991519516753920000 | 2.9711708676 5 4 2 1 | 3569470260314112000 | 10.6962151234 5 3 3 1 | 2644052044677120000 | 7.9231223136 5 3 2 2 | 4362685873717248000 | 13.0731518175 4 4 4 0 | 232387386739200000 | 0.6963681721 4 4 3 1 | 3718198187827200000 | 11.1418907535 4 4 2 2 | 3067513504957440000 | 9.1920598717 4 3 3 2 | 9088928903577600000 | 27.2357329530 3 3 3 3 | 1122089988096000000 | 3.3624361670 total: 34 | 33371339479827148800 | 100.0000000000 ------------+------------------------+---------------- 13 0 0 0 | 24908083200 | 0.0000000006 12 1 0 0 | 12628398182400 | 0.0000003194 11 2 0 0 | 454622334566400 | 0.0000114971 11 1 1 0 | 985015058227200 | 0.0000249103 10 3 0 0 | 6112144720281600 | 0.0001545718 10 2 1 0 | 43340662561996800 | 0.0010960547 10 1 1 1 | 15650794814054400 | 0.0003957975 9 4 0 0 | 38200904501760000 | 0.0009660739 9 3 1 0 | 397289406818304000 | 0.0100471681 9 2 2 0 | 325054969214976000 | 0.0082204103 9 2 1 1 | 704285766632448000 | 0.0178108890 8 5 0 0 | 123770930585702400 | 0.0031300793 8 4 1 0 | 1787802330682368000 | 0.0452122566 8 3 2 0 | 4290725593637683200 | 0.1085094158 8 3 1 1 | 4648286059774156800 | 0.1175518672 8 2 2 1 | 7606286279630438400 | 0.1923576008 7 6 0 0 | 220037209930137600 | 0.0055645854 7 5 1 0 | 4290725593637683200 | 0.1085094158 7 4 2 0 | 14302418645458944000 | 0.3616980528 7 4 1 1 | 15494286865913856000 | 0.3918395572 7 3 3 0 | 10488440340003225600 | 0.2652452387 7 3 2 1 | 74372576956386508800 | 1.8808298745 7 2 2 2 | 20283430079014502400 | 0.5129536021 6 6 1 0 | 2860483729091788800 | 0.0723396106 6 5 2 0 | 25744353561826099200 | 0.6510564950 6 5 1 1 | 27889716358644940800 | 0.7053112029 6 4 3 0 | 52442201700016128000 | 1.3262261935 6 4 2 1 | 185931442390966272000 | 4.7020746862 6 3 3 1 | 136349724420041932800 | 3.4481881032 6 3 2 2 | 223117730869159526400 | 5.6424896235 5 5 3 0 | 35398486147510886400 | 0.8952026806 5 5 2 1 | 125503723613902233600 | 3.1739004132 5 4 4 0 | 49164564093765120000 | 1.2433370565 5 4 3 1 | 511311466575157248000 | 12.9307053871 5 4 2 2 | 418345745379674112000 | 10.5796680440 5 3 3 2 | 613573759890188697600 | 15.5168464645 4 4 4 1 | 118359135781286400000 | 2.9932188396 4 4 3 2 | 852185777625262080000 | 21.5511756452 4 3 3 3 | 416624157950128128000 | 10.5361303154 total: 39 | 3954242643911239680000 | 100.0000000000 ------------+------------------------+----------------