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Index > Poker games and rules >
Odds and
probabilities
What is the correct ranking for 3-card poker hands?
Author: Darse Billings
Last updated: 1995
Copyright © 2006 Darse Billings
The official and up-to-date version of this answer is
here.
The standard ranking of poker hands is based on their frequency
of occurrence in a five card hand. In three card hands the relative
frequency of hands is different, so different in fact that three of
a kind beats a straight, and a straight beats a flush.
The following is a break down of all three card poker hands.
They can be used for certain three card games, such as Guts or
3-card-6. They can also be used to analyze starting hands for games
like 7-Card Stud.
Hand Type Kinds Each Total Cuml Rating
--------- ----- ---- ----- ---- ------
straight flush 12 4 48 48 0.9978
trips 13 4 52 100 0.9955
straight 12 60 720 820 0.9629
flush ** 274 4 1096 1916 0.9133
pair *** 156 24 3744 5660 0.7439
Ace high 64 60 3840 9500 0.5701
King high 54 60 3240 12740 0.4235
Queen high 44 60 2640 15380 0.3041
Jack high 35 60 2100 17480 0.2090
Ten high 27 60 1620 19100 0.1357
Nine high 20 60 1200 20300 0.0814
Eight high 14 60 840 21140 0.0434
Seven high 9 60 540 21680 0.0190
Six high 5 60 300 21980 0.0054
Five high 2 60 120 22100 0.0000
** More on Flushes
------------------
High Card Kinds Percent Total Cuml Rating
--------- ----- ------- ----- ---- ------
Ace high 64 23.4 256 1076 0.9513
King high 54 19.7 216 1292 0.9415
Queen high 44 16.1 176 1468 0.9336
Jack high 35 12.8 140 1608 0.9272
Ten high 27 9.9 108 1716 0.9224
Nine high 20 7.3 80 1796 0.9187
Eight high 14 5.1 56 1852 0.9162
Seven high 9 3.3 36 1888 0.9146
Six high 5 1.8 20 1908 0.9137
Five high 2 0.7 8 1916 0.9133
*** More on Pairs
-----------------
Hand Type Kinds Each Total Cuml Rating
--------- ----- ---- ----- ---- ------
AAx 12 24 288 2204 0.9003
KKx 12 24 288 2492 0.8872
QQx 12 24 288 2780 0.8742
JJx 12 24 288 3068 0.8612
TTx 12 24 288 3356 0.8481
99x 12 24 288 3644 0.8351
88x 12 24 288 3932 0.8221
77x 12 24 288 4220 0.8090
66x 12 24 288 4508 0.7960
55x 12 24 288 4796 0.7830
44x 12 24 288 5084 0.7700
33x 12 24 288 5372 0.7569
22x 12 24 288 5660 0.7439
In the preceding tables, "Kinds" refers to the number of card
combinations in each class, while "Each" is the number of
non-distinct hands of each Kind. The product of these two numbers
gives the total number of hands in that class. "Cuml" is the
cumulative total of all hands, and "Rating" is a percentile ranking
of the lowest hand in the class.
Note that "Rating" is only an estimate of the probability of
beating a random hand. To compute the exact probability, a given
hand must be compared to the (49 choose 3) combinations of the
remaining cards in the deck.
Copyright © 2006 Darse Billings.
Unauthorized copying prohibited. Contact
info@rgpfaq.com for
permission to redistribute.