non-flush example flush example



distribution of hand types
distinct combinations probability odds
royal flush 0 0 impossible impossible
straight flush 0 0 impossible impossible
four of a kind 1 4 0.02% 1 : 6260
full house 2 48 0.19% 1 : 521
flush 0 0 impossible impossible
straight 0 0 impossible impossible
three of a kind 11 704 2.81% 1 : 34.6
two pairs 22 3,168 12.65% 1 : 6.91
one pair 55 21,120 84.33% 5.38 : 1
high card 0 0 impossible impossible
total 91 25,044 100 %



note: in the table below, a flush (or straight flush or royal flush) can by definition only occur if all five cards are of the same suit.
therefore, the "s" next to hole cards means that the hole cards are suited AND all three flop cards are of that suit, too.


ranking of all 91 distinct hole cards
hole cards hand category combinations probability odds equity
nuts 77 77773 four of a kind 4 0.02% 1 : 6260 100.00%
 
2 73 77733 full house 24 0.10% 1 : 1043 99.98%
3 33 77333 full house 24 0.10% 1 : 1043 99.89%
 
4 A7 A7773 three of a kind 64 0.26% 1 : 390 99.79%
5 K7 K7773 three of a kind 64 0.26% 1 : 390 99.54%
6 Q7 Q7773 three of a kind 64 0.26% 1 : 390 99.28%
7 J7 J7773 three of a kind 64 0.26% 1 : 390 99.03%
8 T7 T7773 three of a kind 64 0.26% 1 : 390 98.77%
9 97 97773 three of a kind 64 0.26% 1 : 390 98.51%
10 87 87773 three of a kind 64 0.26% 1 : 390 98.26%
11 76 77763 three of a kind 64 0.26% 1 : 390 98.00%
12 75 77753 three of a kind 64 0.26% 1 : 390 97.75%
13 74 77743 three of a kind 64 0.26% 1 : 390 97.49%
14 72 77732 three of a kind 64 0.26% 1 : 390 97.24%
 
15 AA AA773 two pairs 144 0.57% 1 : 173 96.98%
16 KK KK773 two pairs 144 0.57% 1 : 173 96.41%
17 QQ QQ773 two pairs 144 0.57% 1 : 173 95.83%
18 JJ JJ773 two pairs 144 0.57% 1 : 173 95.26%
19 TT TT773 two pairs 144 0.57% 1 : 173 94.68%
20 99 99773 two pairs 144 0.57% 1 : 173 94.11%
21 88 88773 two pairs 144 0.57% 1 : 173 93.53%
22 66 77663 two pairs 144 0.57% 1 : 173 92.96%
23 55 77553 two pairs 144 0.57% 1 : 173 92.38%
24 44 77443 two pairs 144 0.57% 1 : 173 91.81%
25 A3 A7733 two pairs 144 0.57% 1 : 173 91.23%
26 K3 K7733 two pairs 144 0.57% 1 : 173 90.66%
27 Q3 Q7733 two pairs 144 0.57% 1 : 173 90.08%
28 J3 J7733 two pairs 144 0.57% 1 : 173 89.51%
29 T3 T7733 two pairs 144 0.57% 1 : 173 88.93%
30 93 97733 two pairs 144 0.57% 1 : 173 88.36%
31 83 87733 two pairs 144 0.57% 1 : 173 87.78%
32 63 77633 two pairs 144 0.57% 1 : 173 87.21%
33 53 77533 two pairs 144 0.57% 1 : 173 86.63%
34 43 77433 two pairs 144 0.57% 1 : 173 86.06%
35 32 77332 two pairs 144 0.57% 1 : 173 85.48%
36 22 77322 two pairs 144 0.57% 1 : 173 84.91%
 
37 AK AK773 one pair 384 1.53% 1 : 64.2 84.33%
38 AQ AQ773 one pair 384 1.53% 1 : 64.2 82.80%
39 AJ AJ773 one pair 384 1.53% 1 : 64.2 81.26%
40 AT AT773 one pair 384 1.53% 1 : 64.2 79.73%
41 A9 A9773 one pair 384 1.53% 1 : 64.2 78.20%
42 A8 A8773 one pair 384 1.53% 1 : 64.2 76.67%
43 A6 A7763 one pair 384 1.53% 1 : 64.2 75.13%
44 A5 A7753 one pair 384 1.53% 1 : 64.2 73.60%
45 A4 A7743 one pair 384 1.53% 1 : 64.2 72.07%
46 A2 A7732 one pair 384 1.53% 1 : 64.2 70.53%
47 KQ KQ773 one pair 384 1.53% 1 : 64.2 69.00%
48 KJ KJ773 one pair 384 1.53% 1 : 64.2 67.47%
49 KT KT773 one pair 384 1.53% 1 : 64.2 65.93%
50 K9 K9773 one pair 384 1.53% 1 : 64.2 64.40%
51 K8 K8773 one pair 384 1.53% 1 : 64.2 62.87%
52 K6 K7763 one pair 384 1.53% 1 : 64.2 61.33%
53 K5 K7753 one pair 384 1.53% 1 : 64.2 59.80%
54 K4 K7743 one pair 384 1.53% 1 : 64.2 58.27%
55 K2 K7732 one pair 384 1.53% 1 : 64.2 56.73%
56 QJ QJ773 one pair 384 1.53% 1 : 64.2 55.20%
57 QT QT773 one pair 384 1.53% 1 : 64.2 53.67%
58 Q9 Q9773 one pair 384 1.53% 1 : 64.2 52.13%
59 Q8 Q8773 one pair 384 1.53% 1 : 64.2 50.60%
60 Q6 Q7763 one pair 384 1.53% 1 : 64.2 49.07%
61 Q5 Q7753 one pair 384 1.53% 1 : 64.2 47.53%
62 Q4 Q7743 one pair 384 1.53% 1 : 64.2 46.00%
63 Q2 Q7732 one pair 384 1.53% 1 : 64.2 44.47%
64 JT JT773 one pair 384 1.53% 1 : 64.2 42.93%
65 J9 J9773 one pair 384 1.53% 1 : 64.2 41.40%
66 J8 J8773 one pair 384 1.53% 1 : 64.2 39.87%
67 J6 J7763 one pair 384 1.53% 1 : 64.2 38.33%
68 J5 J7753 one pair 384 1.53% 1 : 64.2 36.80%
69 J4 J7743 one pair 384 1.53% 1 : 64.2 35.27%
70 J2 J7732 one pair 384 1.53% 1 : 64.2 33.73%
71 T9 T9773 one pair 384 1.53% 1 : 64.2 32.20%
72 T8 T8773 one pair 384 1.53% 1 : 64.2 30.67%
73 T6 T7763 one pair 384 1.53% 1 : 64.2 29.13%
74 T5 T7753 one pair 384 1.53% 1 : 64.2 27.60%
75 T4 T7743 one pair 384 1.53% 1 : 64.2 26.07%
76 T2 T7732 one pair 384 1.53% 1 : 64.2 24.53%
77 98 98773 one pair 384 1.53% 1 : 64.2 23.00%
78 96 97763 one pair 384 1.53% 1 : 64.2 21.47%
79 95 97753 one pair 384 1.53% 1 : 64.2 19.93%
80 94 97743 one pair 384 1.53% 1 : 64.2 18.40%
81 92 97732 one pair 384 1.53% 1 : 64.2 16.87%
82 86 87763 one pair 384 1.53% 1 : 64.2 15.33%
83 85 87753 one pair 384 1.53% 1 : 64.2 13.80%
84 84 87743 one pair 384 1.53% 1 : 64.2 12.27%
85 82 87732 one pair 384 1.53% 1 : 64.2 10.73%
86 65 77653 one pair 384 1.53% 1 : 64.2 9.20%
87 64 77643 one pair 384 1.53% 1 : 64.2 7.67%
88 62 77632 one pair 384 1.53% 1 : 64.2 6.13%
89 54 77543 one pair 384 1.53% 1 : 64.2 4.60%
90 52 77532 one pair 384 1.53% 1 : 64.2 3.07%
91 42 77432 one pair 384 1.53% 1 : 64.2 1.53%