Pinochle

Permutations, Formulas, Computations, Odds

09 Apr 07

GAME VARIATIONS

Two versions of pinochle are common - double deck and single deck. Double deck pinochle is almost always played as a partnership game of players on opposite sides of the table and is the game most often played online. A cutthroat version, where each player acts as an individual, is rare. A double pinochle deck consists of 80 cards, consisting of the four suits with four each aces, tens, kings, queens and jacks in order of rank. Single deck pinochle is most commonly played as either a 4-handed partnership or cutthroat game or as a 3-handed cutthroat game. A single pinochle deck consists of 48 cards, consisting of the four suits with two each aces, tens, kings, queens, jacks and nines in order of rank.

Note: For purposes of discussion on this page, the ten of any suit will be abbreviated as "T".

DOUBLE DECK - FOUR HAND

COMBINATIONS

Unique vs. Total Combinations

For purposes of a start of an explanation of the difference between unique and total combinations, let's take one card, say the ace of spades. There are four of these in a double pinochle deck, and let us call them Card AS1, Card AS2, Card AS3 and Card AS4. If a hand were to contain all four of these cards, there would be one unique combination and one total combination. This would also be true if there were no aces of spades held. If a hand were to contain one ace of spades, there would be one unique combination, but four total combinations, either Card AS1, Card AS2, Card AS3 or Card AS4. This would also be true of a holding of three aces of spades, as one of these cards would be missing. If a hand were to contain two aces of spades, there would be one unique combination, but six total combinations, namely AS1-AS2, AS1-AS3, AS1-AS4, AS2-AS3, AS2-AS4 OR AS3-AS4. Therefore a unique combination disregards the fact that there are four cards each of every rank and suit in the deck.

If there were 80 different cards in a pinochle deck, the formula for the number of total combinations for one hand would be (80!/60!)/(20!) = 3,535,316,142,212,174,320. The number of unique combinations for one hand is 35,561,166,195. This number is computer-generated, and I have no idea as to its origin, as its factors are 3, 5, 43, 317 and 173,923.

Given the above, the most common unique hand that will be dealt is the four-suited five-card run - ATKQJ of all four suits. One unique combination - but 1,099,511,627,776 total combinations, computed as 4 to the 20th power (420). The odds of getting this hand dealt to one person in a normal deal is approximately 1::3,215,806.08.

For an example, there is a link to a chart of unique and total distribution possibilities in a 5-card suit in the Links Section below.

Unique Combinations

A holding containing a void has only 1 possibility, as does a holding of all 20 cards in a suit. A holding containing 1 card in a suit has 5 possibilities, either the A, T, K, Q or J, and the same holds true for a holding of 19 cards, as one of these would be missing. A holding containing 2 cards in a suit has 15 possibilities, either AA, AT, AK, AQ, AJ, TT, TK, TQ, TJ, KK, KQ, KJ, QQ, QJ OR JJ, and, again, the opposite is true for a holding of 18 cards. Extrapolating the possibilities throughout the range from 0 to 20 calculates the following:

0 - 1
1 - 5
2 - 15
3 - 35
4 - 70
5 - 121
6 - 185
7 - 255
8 - 320
9 - 365
10 - 381
11 - 365
12 - 320
13 - 255
14 - 185
15 - 121
16 - 70
17 - 35
18 - 15
19 - 5
20 - 1

Distributional Variations

Obviously, the number of cards in each hand will total 20 in all instances. Distribution of suits can vary from 20-0-0-0 (either 20 spades, 20 hearts, 20 diamonds or 20 clubs - 4 permutations) to 5-5-5-5 (5 cards in each suit - 1 permutation). Having a different number of cards in each suit (3-4-6-7, for instance) will result in 24 permutations. Having the same number of cards in two suits (4-4-5-7, for instance) will result in 12 permutations. Having the same number of cards in two suits and the same number of cards in the remaining two suits (4-4-6-6, for instance) has 6 permutations.

Unique Hands

Combining the above two factors will allow the computation of unique hands by distribution.

DistributionPermutationsFormulaPossibilities
0- 0- 0-2041 x 1 x 1 x 14
0- 0- 1-19121 x 1 x 5 x 5300
0- 0- 2-18121 x 1 x 15 x 152,700
0- 0- 3-17121 x 1 x 35 x 3514,700
0- 0- 4-16121 x 1 x 70 x 7058,800
0- 0- 5-15121 x 1 x 121 x 121175,692
0- 0- 6-14121 x 1 x 185 x 185410,700
0- 0- 7-13121 x 1 x 255 x 255780,300
0- 0- 8-12121 x 1 x 320 x 3201,228,800
0- 0- 9-11121 x 1 x 365 x 3651,598,700
0- 0-10-1061 x 1 x 381 x 381870,966
0- 1- 1-18121 x 5 x 5 x 154,500
0- 1- 2-17241 x 5 x 15 x 3563,000
0- 1- 3-16241 x 5 x 35 x 70294,000
0- 1- 4-15241 x 5 x 70 x 1211,016,400
0- 1- 5-14241 x 5 x 121 x 1852,686,200
0- 1- 6-13241 x 5 x 185 x 2555,661,000
0- 1- 7-12241 x 5 x 255 x 3209,792,000
0- 1- 8-11241 x 5 x 320 x 36514,016,000
0- 1- 9-10241 x 5 x 365 x 38116,687,800
0- 2- 2-16121 x 15 x 15 x 70189,000
0- 2- 3-15241 x 15 x 35 x 1211,524,600
0- 2- 4-14241 x 15 x 70 x 1854,662,000
0- 2- 5-13241 x 15 x 121 x 25511,107,800
0- 2- 6-12241 x 15 x 185 x 32021,312,000
0- 2- 7-11241 x 15 x 255 x 36533,507,000
0- 2- 8-10241 x 15 x 320 x 38143,891,200
0- 2- 9- 9121 x 15 x 365 x 36523,980,500
0- 3- 3-14121 x 35 x 35 x 1852,719,500
0- 3- 4-13241 x 35 x 70 x 25514,994,000
0- 3- 5-12241 x 35 x 121 x 32032,524,800
0- 3- 6-11241 x 35 x 185 x 36556,721,000
0- 3- 7-10241 x 35 x 255 x 38181,610,200
0- 3- 8- 9241 x 35 x 320 x 36598,112,000
0- 4- 4-12121 x 70 x 70 x 32018,816,000
0- 4- 5-11241 x 70 x 121 x 36574,197,200
0- 4- 6-10241 x 70 x 185 x 381118,414,800
0- 4- 7- 9241 x 70 x 255 x 365156,366,000
0- 4- 8- 8121 x 70 x 320 x 32086,016,000
0- 5- 5-10121 x 121 x 121 x 38166,938,652
0- 5- 6- 9241 x 121 x 185 x 365196,092,600
0- 5- 7- 8241 x 121 x 255 x 320236,966,400
0- 6- 6- 8121 x 185 x 185 x 320131,424,000
0- 6- 7- 7121 x 185 x 255 x 255144,355,500
1- 1- 1-1745 x 5 x 5 x 3517,500
1- 1- 2-16125 x 5 x 15 x 70315,000
1- 1- 3-15125 x 5 x 35 x 1211,270,500
1- 1- 4-14125 x 5 x 70 x 1853,885,000
1- 1- 5-13125 x 5 x 121 x 2559,256,500
1- 1- 6-12125 x 5 x 185 x 32017,760,000
1- 1- 7-11125 x 5 x 255 x 36527,922,500
1- 1- 8-10125 x 5 x 320 x 38136,576,000
1- 1- 9- 965 x 5 x 365 x 36519,983,750
1- 2- 2-15125 x 15 x 15 x 1211,633,500
1- 2- 3-14245 x 15 x 35 x 18511,655,000
1- 2- 4-13245 x 15 x 70 x 25532,130,000
1- 2- 5-12245 x 15 x 121 x 32069,696,000
1- 2- 6-11245 x 15 x 185 x 365121,545,000
1- 2- 7-10245 x 15 x 255 x 381174,879,000
1- 2- 8- 9245 x 15 x 320 x 365210,240,000
1- 3- 3-13125 x 35 x 35 x 25518,742,500
1- 3- 4-12245 x 35 x 70 x 32094,080,000
1- 3- 5-11245 x 35 x 121 x 365185,493,000
1- 3- 6-10245 x 35 x 185 x 381296,037,000
1- 3- 7- 9245 x 35 x 255 x 365390,915,000
1- 3- 8- 8125 x 35 x 320 x 320215,040,000
1- 4- 4-11125 x 70 x 70 x 365107,310,000
1- 4- 5-10245 x 70 x 121 x 381387,248,400
1- 4- 6- 9245 x 70 x 185 x 365567,210,000
1- 4- 7- 8245 x 70 x 255 x 320685,440,000
1- 5- 5- 9125 x 121 x 121 x 365320,637,900
1- 5- 6- 8245 x 121 x 185 x 320859,584,000
1- 5- 7- 7125 x 121 x 255 x 255472,081,500
1- 6- 6- 7125 x 185 x 185 x 255523,642,500
2- 2- 2-14415 x 15 x 15 x 1852,497,500
2- 2- 3-131215 x 15 x 35 x 25524,097,500
2- 2- 4-121215 x 15 x 70 x 32060,480,000
2- 2- 5-111215 x 15 x 121 x 365119,245,500
2- 2- 6-101215 x 15 x 185 x 381190,309,500
2- 2- 7- 91215 x 15 x 255 x 365251,302,500
2- 2- 8- 8615 x 15 x 320 x 320138,240,000
2- 3- 3-121215 x 35 x 35 x 32070,560,000
2- 3- 4-112415 x 35 x 70 x 365321,930,000
2- 3- 5-102415 x 35 x 121 x 381580,782,600
2- 3- 6- 92415 x 35 x 185 x 365850,815,000
2- 3- 7- 82415 x 35 x 255 x 3201,028,160,000
2- 4- 4-101215 x 70 x 70 x 381336,042,000
2- 4- 5- 92415 x 70 x 121 x 3651,112,958,000
2- 4- 6- 82415 x 70 x 185 x 3201,491,840,000
2- 4- 7- 71215 x 70 x 255 x 255819,315,000
2- 5- 5- 81215 x 121 x 121 x 320843,321,600
2- 5- 6- 72415 x 121 x 185 x 2552,054,943,000
2- 6- 6- 6415 x 185 x 185 x 185379,857,500
3- 3- 3-11435 x 35 x 35 x 36562,597,500
3- 3- 4-101235 x 35 x 70 x 381392,049,000
3- 3- 5- 91235 x 35 x 121 x 365649,225,500
3- 3- 6- 81235 x 35 x 185 x 320870,240,000
3- 3- 7- 7635 x 35 x 255 x 255477,933,750
3- 4- 4- 91235 x 70 x 70 x 365751,170,000
3- 4- 5- 82435 x 70 x 121 x 3202,276,736,000
3- 4- 6- 72435 x 70 x 185 x 2552,773,890,000
3- 5- 5- 71235 x 121 x 121 x 2551,568,051,100
3- 5- 6- 61235 x 121 x 185 x 1851,739,314,500
4- 4- 4- 8470 x 70 x 70 x 320439,040,000
4- 4- 5- 71270 x 70 x 121 x 2551,814,274,000
4- 4- 6- 6670 x 70 x 185 x 1851,006,215,000
4- 5- 5- 61270 x 121 x 121 x 1852,275,211,400
5- 5- 5- 51121 x 121 x 121 x 121214,358,881

Total unique hand possibilities - 35,561,166,195.

Total Combinations

A holding containing a void has only 1 possibility, as does a holding of all 20 cards in a suit. A holding containing 1 card in a suit has 20 possibilities, either A1, A2, A3, A4, T1, T2, T3, T4, K1, K2, K3, K4, Q1, Q2, Q3, Q4, J1, J2, J3 or J4, and the same is true for a holding of 19 cards, as one of these cards would be missing. A holding containing 2 cards in a suit has 190 possibilities, as does a holding of 18 cards in a suit. Calculating the possibilities throughout the range from 0 to 20 comes up with the following:

0 - (20!/20!)/(0!) = 1
1 - (20!/19!)/(1!) = 20
2 - (20!/18!)/(2!) = 190
3 - (20!/17!)/(3!) = 1,140
4 - (20!/16!)/(4!) = 4,845
5 - (20!/15!)/(5!) = 15,504
6 - (20!/14!)/(6!) = 38,760
7 - (20!/13!)/(7!) = 77,520
8 - (20!/12!)/(8!) = 125,970
9 - (20!/11!)/(9!) = 167,960
10 - (20!/10!)/(10!) = 184,756
11 - (20!/9!)/(11!) = 167,960
12 - (20!/8!)/(12!) = 125,970
13 - (20!/7!)/(13!) = 77,520
14 - (20!/6!)/(14!) = 38,760
15 - (20!/5!)/(15!) = 15,504
16 - (20!/4!)/(16!) = 4,845
17 - (20!/3!)/(17!) = 1,140
18 - (20!/2!)/(18!) = 190
19 - (20!/1!)/(19!) = 20
20 - (20!/0!)/(20!) = 1

Distributional Variations

Distributional permutations are as discussed above.

Total Hands

Combining the above factors will allow the computation of total hands by distribution.

DistributionPermutationsFormulaPossibilities
0- 0- 0-2041 x 1 x 1 x 14
0- 0- 1-19121 x 1 x 20 x 204,800
0- 0- 2-18121 x 1 x 190 x 190433,200
0- 0- 3-17121 x 1 x 1,140 x 1,14015,595,200
0- 0- 4-16121 x 1 x 4,845 x 4,845281,688,300
0- 0- 5-15121 x 1 x 15,504 x 15,5042,884,488,192
0- 0- 6-14121 x 1 x 38,760 x 38,76018,028,051,200
0- 0- 7-13121 x 1 x 77,520 x 77,52072,112,204,800
0- 0- 8-12121 x 1 x 125,970 x 125,970190,421,290,800
0- 0- 9-11121 x 1 x 167,960 x 167,960338,526,739,200
0- 0-10-1061 x 1 x 184,756 x 184,756204,808,677,216
0- 1- 1-18121 x 20 x 20 x 190912,000
0- 1- 2-17241 x 20 x 190 x 1,140103,968,000
0- 1- 3-16241 x 20 x 1,140 x 4,8452,651,184,000
0- 1- 4-15241 x 20 x 4,845 x 15,50436,056,102,400
0- 1- 5-14241 x 20 x 15,504 x 38,760288,448,819,200
0- 1- 6-13241 x 20 x 38,760 x 77,5201,442,244,096,000
0- 1- 7-12241 x 20 x 77,520 x 125,9704,687,293,312,000
0- 1- 8-11241 x 20 x 125,970 x 167,96010,155,802,176,000
0- 1- 9-10241 x 20 x 167,960 x 184,75614,895,176,524,800
0- 2- 2-16121 x 190 x 190 x 4,8452,098,854,000
0- 2- 3-15241 x 190 x 1,140 x 15,50480,595,993,600
0- 2- 4-14241 x 190 x 4,845 x 38,760856,332,432,000
0- 2- 5-13241 x 190 x 15,504 x 77,5205,480,527,564,800
0- 2- 6-12241 x 190 x 38,760 x 125,97022,264,643,232,000
0- 2- 7-11241 x 190 x 77,520 x 167,96059,372,381,952,000
0- 2- 8-10241 x 190 x 125,970 x 184,756106,128,132,739,200
0- 2- 9- 9121 x 190 x 167,960 x 167,96064,320,080,448,000
0- 3- 3-14121 x 1,140 x 1,140 x 38,760604,469,952,000
0- 3- 4-13241 x 1,140 x 4,845 x 77,52010,275,989,184,000
0- 3- 5-12241 x 1,140 x 15,504 x 125,97053,435,143,756,800
0- 3- 6-11241 x 1,140 x 38,760 x 167,960178,117,145,856,000
0- 3- 7-10241 x 1,140 x 77,520 x 184,756391,857,720,883,200
0- 3- 8- 9241 x 1,140 x 125,970 x 167,960578,880,724,032,000
0- 4- 4-12121 x 4,845 x 4,845 x 125,97035,484,275,151,000
0- 4- 5-11241 x 4,845 x 15,504 x 167,960302,799,147,955,200
0- 4- 6-10241 x 4,845 x 38,760 x 184,756832,697,656,876,800
0- 4- 7- 9241 x 4,845 x 77,520 x 167,9601,513,995,739,776,000
0- 4- 8- 8121 x 4,845 x 125,970 x 125,970922,591,153,926,000
0- 5- 5-10121 x 15,504 x 15,504 x 184,756532,926,500,401,152
0- 5- 6- 9241 x 15,504 x 38,760 x 167,9602,422,393,183,641,600
0- 5- 7- 8241 x 15,504 x 77,520 x 125,9703,633,589,775,462,400
0- 6- 6- 8121 x 38,760 x 38,760 x 125,9702,270,993,609,664,000
0- 6- 6- 7121 x 38,760 x 77,520 x 77,5202,795,069,058,048,000
1- 1- 1-17420 x 20 x 20 x 1,14036,480,000
1- 1- 2-161220 x 20 x 190 x 4,8454,418,640,000
1- 1- 3-151220 x 20 x 1,140 x 15,50484,837,888,000
1- 1- 4-141220 x 20 x 4,845 x 38,760901,402,560,000
1- 1- 5-131220 x 20 x 15,504 x 77,5205,768,976,384,000
1- 1- 6-121220 x 20 x 38,760 x 125,97023,436,466,560,000
1- 1- 7-111220 x 20 x 77,520 x 167,96062,497,244,160,000
1- 1- 8-101220 x 20 x 125,970 x 184,756111,713,823,936,000
1- 1- 9- 9620 x 20 x 167,960 x 167,96067,705,347,840,000
1- 2- 2-151220 x 190 x 190 x 15,504134,326,656,000
1- 2- 3-142420 x 190 x 1,140 x 38,7604,029,799,680,000
1- 2- 4-132420 x 190 x 4,845 x 77,52034,253,297,280,000
1- 2- 5-122420 x 190 x 15,504 x 125,970178,117,145,856,000
1- 2- 6-112420 x 190 x 38,760 x 167,960593,723,819,520,000
1- 2- 7-102420 x 190 x 77,520 x 184,7561,306,192,402,944,000
1- 2- 8- 92420 x 190 x 125,970 x 167,9601,929,602,413,440,000
1- 3- 3-131220 x 1,140 x 1,140 x 77,52024,178,798,080,000
1- 3- 4-122420 x 1,140 x 4,845 x 125,970333,969,648,480,000
1- 3- 5-112420 x 1,140 x 15,504 x 167,9601,424,937,166,848,000
1- 3- 6-102420 x 1,140 x 38,760 x 184,7563,918,577,208,832,000
1- 3- 7- 92420 x 1,140 x 77,520 x 167,9607,124,685,834,240,000
1- 3- 8- 81220 x 1,140 x 125,970 x 125,9704,341,605,430,240,000
1- 4- 4-111220 x 4,845 x 4,845 x 167,960946,247,337,360,000
1- 4- 5-102420 x 4,845 x 15,504 x 184,7566,661,581,255,014,400
1- 4- 6- 92420 x 4,845 x 38,760 x 167,96015,139,957,397,760,000
1- 4- 7- 82420 x 4,845 x 77,520 x 125,97022,709,936,096,640,000
1- 5- 5- 91220 x 15,504 x 15,504 x 167,9609,689,572,734,566,400
1- 5- 6- 82420 x 15,504 x 38,760 x 125,97036,335,897,754,624,000
1- 5- 7- 71220 x 15,504 x 77,520 x 77,52022,360,552,464,384,000
1- 6- 6- 71220 x 38,760 x 38,760 x 77,52027,950,690,580,480,000
2- 2- 2-144190 x 190 x 190 x 38,7601,063,419,360,000
2- 2- 3-1312190 x 190 x 1,140 x 77,52038,283,096,960,000
2- 2- 4-1212190 x 190 x 4,845 x 125,970264,392,638,380,000
2- 2- 5-1112190 x 190 x 15,504 x 167,9601,128,075,257,088,000
2- 2- 6-1012190 x 190 x 38,760 x 184,7563,102,206,956,992,000
2- 2- 7- 912190 x 190 x 77,520 x 167,9605,640,376,285,440,000
2- 2- 8- 86190 x 190 x 125,970 x 125,9703,437,104,298,940,000
2- 3- 3-1212190 x 1,140 x 1,140 x 125,970373,260,195,360,000
2- 3- 4-1124190 x 1,140 x 4,845 x 167,9604,230,282,214,080,000
2- 3- 5-1024190 x 1,140 x 15,504 x 184,75614,890,593,393,561,600
2- 3- 6- 924190 x 1,140 x 38,760 x 167,96033,842,257,712,640,000
2- 3- 7- 824190 x 1,140 x 77,520 x 125,97050,763,386,568,960,000
2- 4- 4-1012190 x 4,845 x 4,845 x 184,7569,888,284,675,412,000
2- 4- 5- 924190 x 4,845 x 15,504 x 167,96057,531,838,111,488,000
2- 4- 6- 824190 x 4,845 x 38,760 x 125,970107,872,196,459,040,000
2- 4- 7- 712190 x 4,845 x 77,520 x 77,52066,382,890,128,640,000
2- 5- 5- 812190 x 15,504 x 15,504 x 125,97069,038,205,733,785,600
2- 5- 6- 724190 x 15,504 x 38,760 x 77,520212,425,248,411,648,000
2- 6- 6- 64190 x 38,760 x 38,760 x 38,76044,255,260,085,760,000
3- 3- 3-1141,140 x 1,140 x 1,140 x 167,960995,360,520,960,000
3- 3- 4-10121,140 x 1,140 x 4,845 x 184,75613,959,931,306,464,000
3- 3- 5- 9121,140 x 1,140 x 15,504 x 167,96040,610,709,255,168,000
3- 3- 6- 8121,140 x 1,140 x 38,760 x 125,97076,145,079,853,440,000
3- 3- 7- 761,140 x 1,140 x 77,520 x 77,52046,858,510,679,040,000
3- 4- 4- 9121,140 x 4,845 x 4,845 x 167,96053,936,098,229,520,000
3- 4- 5- 8241,140 x 4,845 x 15,504 x 125,970258,893,271,501,696,000
3- 4- 6- 7241,140 x 4,845 x 38,760 x 77,520398,297,340,771,840,000
3- 5- 5- 7121,140 x 15,504 x 15,504 x 77,520254,910,298,093,977,600
3- 5- 6- 6121,140 x 15,504 x 38,760 x 38,760318,637,872,617,472,000
4- 4- 4- 844,845 x 4,845 x 4,845 x 125,97057,307,104,368,865,000
4- 4- 5- 7124,845 x 4,845 x 15,504 x 77,520338,552,739,656,064,000
4- 4- 6- 664,845 x 4,845 x 38,760 x 38,760211,595,462,285,040,000
4- 5- 5- 6124,845 x 15,504 x 15,504 x 38,760541,684,383,449,702,400
5- 5- 5- 5115,504 x 15,504 x 15,504 x 15,50457,779,667,567,968,256

As stated above, the formula for and number of total combinations for one hand is (80!/60!)/(20!) = 3,535,316,142,212,174,320.
Given this, if 20 cards were dealt to the first hand out of an 80-card deck, there will be 60 cards remaining for the other 3 hands. Therefore the formula for and number of total possibilities for the second hand would be (60!/40!)/(20!) = 4,191,844,505,805,495.
The formula for and number of total possibilities for the third hand would be (40!/20!)/(20!) = 137,846,528,820.
The fourth hand is dealt the remaining 20 cards and therefore has only one possibility.

The formula for and number of total possibilities for all 4 hands would be (80!)/((20!)4) = 2,042,816,020,019,820,636,556,288,523,182,573,366,463,688,000.

There is a link to the start of a double deck hand chart below. I have no intention of fully developing this due to size and time limitations. The complete hand chart in this format would be something slightly less than 4 terabytes.

DISTRIBUTIONAL COMBINATIONS OF FOUR HANDS

Disregarding the rank of the cards contained in the four suits, when hands of 20 cards each are dealt to four players there are 1,173,759,851 distributional possibilities in the four hands. This is a computer generated number.

A link to the start of a 4-hand distribution chart can be found below.

PROGRESS

DescriptionTotalPercentage
Possible Distributions1173759851100.000000
Distributions Generated234136801.994759
Distributions Processed210000001.789122
Distributions Posted205000001.746524
Possible Unique Hands35561166195100.000000
Unique Hands Generated733720.000206
Unique Hands Processed733720.000206
Unique Hands Posted700000.000197
Possible Total Hands3535316142212174320100.000000
Total Hands Processed4809312720.000000
Total Hands Posted4668862800.000000

Note: Total Hands Processed in the above table reflect the total number of hands possible from the permuations of processed and posted unique hands. Total hands beyond what is shown in the links below will not be posted due to site storage limitations.

Note: A new, more efficient method of distribution data generation and processing has been initiated. All distribution charts are reproduced with slightly different formatting and will remain posted for about two weeks.

LINKS

Double Deck Total Hand Chart - 000001-010000.
Double Deck Total Hand Chart - 040001-050000 - 635376 planned of 3535316142212174320 possible.

Double Deck Unique Hand Chart - 00000000001 - 00000010000.
Double Deck Unique Hand Chart - 00000010001 - 00000020000.
Double Deck Unique Hand Chart - 00000020001 - 00000030000.
Double Deck Unique Hand Chart - 00000030001 - 00000040000.
Double Deck Unique Hand Chart - 00000040001 - 00000050000.
Double Deck Unique Hand Chart - 00000050001 - 00000060000.
Double Deck Unique Hand Chart - 00000060001 - 00000070000.

Double Deck Distribution Chart - 0000000001-0000010000.
Double Deck Distribution Chart - 0020000001-0020010000.
Double Deck Distribution Chart - 0020010001-0020020000.
Double Deck Distribution Chart - 0020020001-0020030000.
Double Deck Distribution Chart - 0020030001-0020040000.
Double Deck Distribution Chart - 0020040001-0020050000.
Double Deck Distribution Chart - 0020050001-0020060000.
Double Deck Distribution Chart - 0020060001-0020070000.
Double Deck Distribution Chart - 0020070001-0020080000.
Double Deck Distribution Chart - 0020080001-0020090000.
Double Deck Distribution Chart - 0020090001-0020100000.
Double Deck Distribution Chart - 0020100001-0020110000.
Double Deck Distribution Chart - 0020110001-0020120000.
Double Deck Distribution Chart - 0020120001-0020130000.
Double Deck Distribution Chart - 0020130001-0020140000.
Double Deck Distribution Chart - 0020140001-0020150000.
Double Deck Distribution Chart - 0020150001-0020160000.
Double Deck Distribution Chart - 0020160001-0020170000.
Double Deck Distribution Chart - 0020170001-0020180000.
Double Deck Distribution Chart - 0020180001-0020190000.
Double Deck Distribution Chart - 0020190001-0020200000.
Double Deck Distribution Chart - 0020200001-0020210000.
Double Deck Distribution Chart - 0020210001-0020220000.
Double Deck Distribution Chart - 0020220001-0020230000.
Double Deck Distribution Chart - 0020230001-0020240000.
Double Deck Distribution Chart - 0020240001-0020250000.
Double Deck Distribution Chart - 0020250001-0020260000.
Double Deck Distribution Chart - 0020260001-0020270000.
Double Deck Distribution Chart - 0020270001-0020280000.
Double Deck Distribution Chart - 0020280001-0020290000.
Double Deck Distribution Chart - 0020290001-0020300000.
Double Deck Distribution Chart - 0020300001-0020310000.
Double Deck Distribution Chart - 0020310001-0020320000.
Double Deck Distribution Chart - 0020320001-0020330000.
Double Deck Distribution Chart - 0020330001-0020340000.
Double Deck Distribution Chart - 0020340001-0020350000.
Double Deck Distribution Chart - 0020350001-0020360000.
Double Deck Distribution Chart - 0020360001-0020370000.
Double Deck Distribution Chart - 0020370001-0020380000.
Double Deck Distribution Chart - 0020380001-0020390000.
Double Deck Distribution Chart - 0020390001-0020400000.
Double Deck Distribution Chart - 0020400001-0020410000.
Double Deck Distribution Chart - 0020410001-0020420000.
Double Deck Distribution Chart - 0020420001-0020430000.
Double Deck Distribution Chart - 0020430001-0020440000.
Double Deck Distribution Chart - 0020440001-0020450000.
Double Deck Distribution Chart - 0020450001-0020460000.
Double Deck Distribution Chart - 0020460001-0020470000.
Double Deck Distribution Chart - 0020470001-0020480000.
Double Deck Distribution Chart - 0020480001-0020490000.
Double Deck Distribution Chart - 0020490001-0020500000.

Note: Distribution and hand charts between the lowest and highest numbers listed above have been previously posted but have been removed from the site due to site storage limitations. They are available and will be reposted upon request.

Double Deck Unique Suit Content by Distribution.

Unique and Total Content Chart for a Five Card Suit in a Double Deck.

SPECIAL MELD COMBINATIONS

Future

Quadruple Pinochle

Unique Combinations -
Total Combinations -

Triple Pinochle

Unique Combinations -
Total Combinations -

Double Pinochle

Unique Combinations -
Total Combinations -

Quadruple Aces (or Kings, Queens or Jacks)

Unique Combinations - 3,876
Total Combinations - 635,376

Triple Aces (or Kings, Queens or Jacks)

Unique Combinations -
Total Combinations -

Double Aces (or Kings, Queens or Jacks)

Unique Combinations -
Total Combinations -

Quadruple Run

Unique Combinations - 4
Total Combinations - 4

Triple Run

Unique Combinations - 31,004
Total Combinations - 33,039,552

Double Run

Unique Combinations -
Total Combinations -

Single Run

Unique Combinations -
Total Combinations -

SINGLE DECK - 4 HAND

Future

SINGLE DECK - 3 HAND

Future

=*.*=