From LowballWiki
These tables show the probability of being dealt an A-5 hand of the specified strength (5-high, 6-high, etc.) for a variety of different hand sizes and wild card choices. The full list is available at Durago Bill's Lowball Poker Probabilities. Bill Butler wrote the program to generate this data and ran the calculations.
Note that the hands being compared are always 5-card A-5 lowball hands, even if the table is for a deal containing more cards.
Contents
- 1 5 Cards, No Wild Cards
- 2 5 Cards, One Joker
- 3 5 Cards, Two Jokers
- 4 5 Cards, One-Eyed Jacks Wild
- 5 6 Cards, No Wild Cards
- 6 6 Cards, One Joker
- 7 7 Cards, No Wild Cards
- 8 7 Cards, One Joker
- 9 8 Cards, No Wild Cards
- 10 9 Cards, No Wild Cards
- 11 10 Cards, No Wild Cards
|
[edit] 5 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 1,024 | 0.00039400
|
| Six high | 5,120 | 0.00197002
|
| Seven high | 15,360 | 0.00591006
|
| Eight high | 35,840 | 0.01379013
|
| Nine high | 71,680 | 0.02758026
|
| Ten high | 129,024 | 0.04964447
|
| Jack high | 215,040 | 0.04964447
|
| Queen high | 337,920 | 0.13002124
|
| King high | 506,880 | 0.13002124
|
| Pair or worse | 1,281,072 | 0.49291717
|
| Total | 2,598,960 | 1.00000000
|
The median hand is thus a very rough K-high. The median is the "1299480th" hand, while the first pair is hand 1,317,888. Each rank comes in 1024 possibilities due to the suit assignments of the 5 cards. (1024=5^4.) So the median hand is the 18th worst K-high. Counting down from KQJT9 gives us KQJ87 (unless I made an off-by-one error or two or three.)
[edit] 5 Cards, One Joker
| Lowball Hand | Number of Hands | Probability
|
| Five high | 2,304 | 0.00080288
|
| Six high | 7,680 | 0.00267625
|
| Seven high | 20,480 | 0.00713667
|
| Eight high | 44,800 | 0.01561147
|
| Nine high | 86,016 | 0.02997402
|
| Ten high | 150,528 | 0.05245454
|
| Jack high | 245,760 | 0.08564006
|
| Queen high | 380,160 | 0.13247447
|
| King high | 563,200 | 0.19625847
|
| Pair or worse | 1,368,757 | 0.17697117
|
| Total | 2,869,685 | 1.00000000
|
[edit] 5 Cards, Two Jokers
| Lowball Hand | Number of Hands | Probability
|
| Five high | 4,224 | 0.00133565
|
| Six high | 10,880 | 0.00344031
|
| Seven high | 26,560 | 0.00839839
|
| Eight high | 55,104 | 0.01742413
|
| Nine high | 102,144 | 0.03229840
|
| Ten high | 174,336 | 0.05512583
|
| Jack high | 279,360 | 0.08833490
|
| Queen high | 425,920 | 0.13467784
|
| King high | 623,744 | 0.19723068
|
| Pair or worse | 1,460,238 | 0.46173388
|
| Total | 3,162,510 | 1.00000000
|
[edit] 5 Cards, One-Eyed Jacks Wild
| Lowball Hand | Number of Hands | Probability
|
| Five high | 4,224 | 0.00162527
|
| Six high | 10,880 | 0.00418629
|
| Seven high | 26,560 | 0.01021947
|
| Eight high | 55,104 | 0.02120233
|
| Nine high | 102,144 | 0.03930187
|
| Ten high | 174,336 | 0.06707914
|
| Jack high | 139,680 | 0.05374457
|
| Queen high | 352,640 | 0.13568504
|
| King high | 524,832 | 0.20193924
|
| Pair or worse | 1,208,560 | 0.46501678
|
| Total | 2,598,960 | 1.00000000
|
[edit] 6 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 40,448 | 0.00198678
|
| Six high | 181,760 | 0.00892796
|
| Seven high | 483,840 | 0.02376597
|
| Eight high | 985,600 | 0.04841216
|
| Nine high | 1,684,480 | 0.08274079
|
| Ten high | 2,515,968 | 0.12358305
|
| Jack high | 3,333,120 | 0.16372113
|
| Queen high | 3,886,080 | 0.19088224
|
| King high | 3,801,600 | 0.18673263
|
| Pair or worse | 3,445,624 | 0.16924727
|
| Total | 20,358,520 | 1.00000000
|
[edit] 6 Cards, One Joker
| Lowball Hand | Number of Hands | Probability
|
| Five high | 90,112 | 0.00392517
|
| Six high | 268,800 | 0.01170860
|
| Seven high | 637,440 | 0.02776611
|
| Eight high | 1,218,560 | 0.05307900
|
| Nine high | 1,999,872 | 0.08711200
|
| Ten high | 2,903,040 | 0.12645290
|
| Jack high | 3,763,200 | 0.16392043
|
| Queen high | 4,308,480 | 0.18767217
|
| King high | 4,139,520 | 0.18031247
|
| Pair or worse | 3,628,456 | 0.15805114
|
| Total | 22,957,480 | 1.00000000
|
[edit] 7 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 781,824 | 0.00584390
|
| Six high | 3,151,360 | 0.02355548
|
| Seven high | 7,426,560 | 0.05551134
|
| Eight high | 13,171,200 | 0.09845082
|
| Nine high | 19,174,400 | 0.14332297
|
| Ten high | 23,675,904 | 0.17697038
|
| Jack high | 24,837,120 | 0.18565012
|
| Queen high | 21,457,920 | 0.16039160
|
| King high | 13,939,200 | 0.10419140
|
| Pair or worse | 6,169,072 | 0.04611199
|
| Total | 133,784,560 | 1.00000000
|
[edit] 7 Cards, One Joker
| Lowball Hand | Number of Hands | Probability
|
| Five high | 1,725,312 | 0.01119293
|
| Six high | 4,593,920 | 0.02980296
|
| Seven high | 9,666,560 | 0.06271161
|
| Eight high | 16,105,600 | 0.10448474
|
| Nine high | 22,521,856 | 0.14611007
|
| Ten high | 27,019,776 | 0.17529023
|
| Jack high | 27,709,440 | 0.17976441
|
| Queen high | 23,464,320 | 0.15222428
|
| King high | 14,924,800 | 0.09682433
|
| Pair or worse | 6,411,496 | 0.04159445
|
| Total | 154,143,080 | 1.00000000
|
[edit] 8 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 9,856,000 | 0.01309701
|
| Six high | 35,563,520 | 0.04725810
|
| Seven high | 74,019,840 | 0.09836025
|
| Eight high | 113,971,200 | 0.15144907
|
| Nine high | 140,851,200 | 0.18716819
|
| Ten high | 143,216,640 | 0.19031147
|
| Jack high | 118,487,040 | 0.15744988
|
| Queen high | 75,694,080 | 0.10058504
|
| King high | 32,947,200 | 0.04378143
|
| Pair or worse | 7,931,430 | 0.01053957
|
| Total | 752,538,150 | 1.00000000
|
[edit] 9 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 91,126,080 | 0.02476874
|
| Six high | 293,736,000 | 0.07983962
|
| Seven high | 538,618,560 | 0.14640052
|
| Eight high | 717,886,400 | 0.19512685
|
| Nine high | 750,512,000 | 0.20399473
|
| Ten high | 625,806,720 | 0.17009891
|
| Jack high | 406,492,800 | 0.11048776
|
| Queen high | 191,368,320 | 0.05201533
|
| King high | 55,915,200 | 0.01519817
|
| Pair or worse | 7,613,320 | 0.00206936
|
| Total | 3,679,075,400 | 1.00000000
|
[edit] 10 Cards, No Wild Cards
| Lowball Hand | Number of Hands | Probability
|
| Five high | 658,829,280 | 0.04164528
|
| Six high | 1,893,034,080 | 0.11966063
|
| Seven high | 3,050,318,880 | 0.19281379
|
| Eight high | 3,508,367,520 | 0.22176752
|
| Nine high | 3,091,197,760 | 0.19539779
|
| Ten high | 2,104,409,664 | 0.13302190
|
| Jack high | 1,067,774,400 | 0.06749512
|
| Queen high | 368,575,680 | 0.02329805
|
| King high | 71,961,120 | 0.00454874
|
| Pair or worse | 5,555,836 | 0.00035119
|
| Total | 15,820,024,220 | 1.00000000
|
