Durango Bill's
Poker Probabilities
6 Card Poker
Probabilities
for various wild card specifications
Including a “Pai Gow” (“Bug”) Joker
for various wild card specifications
Including a “Pai Gow” (“Bug”) Joker
The tables below show the probabilities of being dealt various poker hands with different wild card specifications. Each Poker hand consists of selecting the 5 best cards from a random 6 card deal.
While the results on the main Poker Probabilities page can be calculated via direct combinatorics, the introduction of wild cards greatly complicates the combinatoric calculations. Thus, to produce the results shown here, the author wrote a computer program that would generate all possible poker hands. Each of these poker hands was evaluated for matched ranks (pairs, 3 of a kind, etc.), straights, and flushes. Wild cards introduce multiple evaluations for a given hand, and the best standard evaluation for any given hand is used in the tables.
Data from this page may be freely used provided it includes an acknowledgement to the author.
6 card poker probabilities if there are no wild cards
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 0 0.00000000
Royal straight flush 188 0.00000923
Other straight flush 1,656 0.00008134
4 of a kind 14,664 0.00072029
Full House 165,984 0.00815305
Flush 205,792 0.01010840
Ace high straight 39,780 0.00195397
Other straights 321,840 0.01580861
3 of a kind 732,160 0.03596332
2 pairs 2,532,816 0.12441062
One pair >= Jacks 3,000,756 0.14739559
One pair <= Tens 6,729,984 0.33057334
Ace high 3,095,400 0.15204445
King high 1,804,980 0.08865969
Queen high 968,820 0.04758794
Jack high 470,340 0.02310286
Ten high 196,980 0.00967556
Nine high 64,320 0.00315937
Eight high 12,060 0.00059238
Subtotals high card only 6,612,900 0.32482224
Total = 20,358,520 1.00000000
= COMBIN(52,6)
6 card poker probabilities if one “Pai Gow” (“Bug”) Joker is added to the deck
A “Pai Gow” (“Bug”) Joker is partially wild. If you are using it to complete a straight and/or a flush, it is an ordinary wild card. If you are using it for pairs, 3-of-a-kind, etc., it is forced to be an Ace.
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 Aces 48 0.00000209
Royal straight flush 1,132 0.00004931
Other straight flush 8,248 0.00035927
4 of a kind 19,752 0.00086037
Full House 196,896 0.00857655
Flush 314,944 0.01371858
Ace high straight 86,580 0.00377132
Other straights 609,648 0.02655553
3 of a kind 853,264 0.03716715
2 pairs 2,873,952 0.12518587
One pair >= Jacks 3,177,084 0.13838993
One pair <= Tens 7,632,792 0.33247517
Ace high 3,665,640 0.15967083
King high 1,804,980 0.07862274
Queen high 968,820 0.04220062
Jack high 470,340 0.02048744
Ten high 196,980 0.00858021
Nine high 64,320 0.00280170
Eight high 12,060 0.00052532
Subtotals high card only 7,183,140 0.31288887
Total = 22,957,480 1.00000000
= COMBIN(53,6)
6 card poker probabilities if one ordinary Joker is added to the deck
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 624 0.00002718
Royal straight flush 1,132 0.00004931
Other straight flush 8,248 0.00035927
4 of a kind 73,320 0.00319373
Full House 289,536 0.01261184
Flush 314,944 0.01371858
Ace high straight 86,580 0.00377132
Other straights 609,648 0.02655553
3 of a kind 1,735,072 0.07557763
2 pairs 2,532,816 0.11032639
One pair >= Jacks 3,905,076 0.17010038
One pair <= Tens 6,787,584 0.29565893
Ace high 3,095,400 0.13483187
King high 1,804,980 0.07862274
Queen high 968,820 0.04220062
Jack high 470,340 0.02048744
Ten high 196,980 0.00858021
Nine high 64,320 0.00280170
Eight high 12,060 0.00052532
Subtotals high card only 6,612,900 0.28804991
Total = 22,957,480 1.00000000
= COMBIN(53,6)
6 card poker probabilities if two Jokers are added to the deck
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 3,757 0.00014547
Royal straight flush 3,976 0.00015395
Other straight flush 24,652 0.00095450
4 of a kind 214,848 0.00831868
Full House 413,088 0.01599432
Flush 451,868 0.01749584
Ace high straight 150,720 0.00583572
Other straights 968,244 0.03748936
3 of a kind 2,795,716 0.10824711
2 pairs 2,532,816 0.09806791
One pair >= Jacks 4,809,396 0.18621463
One pair <= Tens 6,845,184 0.26503815
Ace high 3,095,400 0.11985055
King high 1,804,980 0.06988688
Queen high 968,820 0.03751167
Jack high 470,340 0.01821106
Ten high 196,980 0.00762685
Nine high 64,320 0.00249040
Eight high 12,060 0.00046695
Subtotals high card only 6,612,900 0.25604436
Total = 25,827,165 1.00000000
= COMBIN(54,6)
6 card poker probabilities with One-eyed Jacks wild
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 3,324 0.00016327
Royal straight flush 2,458 0.00012074
Other straight flush 21,022 0.00103259
4 of a kind 183,006 0.00898916
Full House 342,144 0.01680594
Flush 360,040 0.01768498
Ace high straight 86,394 0.00424363
Other straights 802,038 0.03939569
3 of a kind 2,286,996 0.11233606
2 pairs 2,014,056 0.09892939
One pair >= Jacks 3,446,488 0.16928971
One pair <= Tens 5,721,234 0.28102406
Ace high 2,454,210 0.12054953
King high 1,398,960 0.06871619
Queen high 727,620 0.03574032
Jack high 235,170 0.01155143
Ten high 196,980 0.00967556
Nine high 64,320 0.00315937
Eight high 12,060 0.00059238
Subtotals high card only 5,089,320 0.24998477
Total = 20,358,520 1.00000000
= COMBIN(52,6)
6 card poker probabilities with Deuces (2’s) wild
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 28,848 0.00141700
Royal straight flush 20,148 0.00098966
Other straight flush 82,456 0.00405020
4 of a kind 608,656 0.02989687
Full House 507,936 0.02494955
Flush 502,436 0.02467940
Ace high straight 295,560 0.01451775
Other straights 1,341,012 0.06586982
3 of a kind 3,463,728 0.17013653
2 pairs 1,758,240 0.08636384
One pair >= Jacks 4,185,240 0.20557683
One pair <= Tens 4,046,760 0.19877476
Ace high 1,804,980 0.08865969
King high 968,820 0.04758794
Queen high 470,340 0.02310286
Jack high 196,980 0.00967556
Ten high 64,320 0.00315937
Nine high 12,060 0.00059238
Eight high 0 0.00000000
Subtotals high card only 3,517,500 0.17277779
Total = 20,358,520 1.00000000
= COMBIN(52,6)
6 card poker probabilities with 2 Jokers,
One-eyed Jacks, and Deuces (2’s) wild
(8 out of 54 cards are wild)
(Computer program and data by Bill Butler)
Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 290,962 0.01126574
Royal straight flush 102,610 0.00397295
Other straight flush 429,922 0.01664612
4 of a kind 2,233,119 0.08646396
Full House 726,000 0.02810994
Flush 960,852 0.03720315
Ace high straight 511,260 0.01979544
Other straights 2,710,872 0.10496204
3 of a kind 5,676,056 0.21977077
2 pairs 1,368,180 0.05297446
One pair >= Jacks 4,780,192 0.18508388
One pair <= Tens 3,391,980 0.13133381
Ace high 1,400,970 0.05424405
King high 729,630 0.02825049
Queen high 339,690 0.01315243
Jack high 98,490 0.00381343
Ten high 64,320 0.00249040
Nine high 12,060 0.00046695
Eight high 0 0.00000000
Subtotals high card only 2,645,160 0.10241775
Total = 25,827,165 1.00000000
= COMBIN(54,6)
Also please see 5 card Poker probabilities
Also please see 7 card Poker probabilities
Also please see 8 card, 9 card, and 10 card Poker probabilities
Return to the main Poker probabilities page
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