Royal poker probabilities

Replay Poker Poker Discussion
1
- AA AK AQ AJ AT KK KQ KJ KT QQ QJ QT JJ JT TT
PRE 45.49 36.33 32.52 29.34 26.98 34.42 28.14 25.35 22.59 26.77 22.02 19.39 20.64 16.80 16.71
AAA 0.00 99.29 99.31 99.28 98.83 33.01 26.81 24.14 23.03 10.55 10.06 8.88 6.90 6.85 6.26
AAK 99.28 94.51 72.97 70.51 68.84 28.30 9.88 9.79 9.79 5.95 4.22 4.26 5.63 4.23 6.81
AAQ 95.36 77.58 91.07 69.73 67.61 12.06 8.82 5.45 5.42 21.44 5.38 5.25 4.56 2.82 4.26
AAJ 95.31 79.42 77.07 83.58 68.74 11.77 6.12 6.33 5.24 7.14 4.78 3.45 18.51 4.57 4.05
AAT 99.24 78.71 76.40 73.67 73.73 11.27 5.62 5.28 6.26 6.41 3.74 3.81 6.02 3.46 16.94
AKK 73.54 94.27 27.43 27.45 27.72 90.79 40.82 38.97 37.04 5.69 3.63 3.68 5.45 3.66 5.23
AKQ 86.66 57.54 46.99 30.77 30.95 60.74 38.71 23.15 23.43 40.76 19.65 19.99 12.61 14.08 12.71
AKJ 90.16 60.53 32.55 44.76 30.83 58.35 25.85 34.40 24.53 15.90 18.57 14.13 37.78 20.73 12.68
AKT 90.55 61.33 32.46 32.37 35.00 57.18 23.82 23.84 35.23 14.49 12.95 18.61 16.88 18.63 35.44
AQQ 73.25 29.94 82.59 26.31 26.35 15.44 38.03 5.05 5.17 90.60 32.72 33.26 5.22 3.32 4.89
AQJ 86.42 35.11 54.85 47.12 32.19 20.80 24.15 19.32 14.11 51.91 33.00 22.97 39.01 20.71 12.50
AQT 86.92 35.42 58.07 33.79 43.29 19.10 23.50 12.73 20.90 40.63 23.77 32.87 16.48 19.50 34.18
AJJ 76.92 29.04 28.66 69.24 25.30 13.96 6.39 33.41 5.77 12.70 31.93 5.90 94.29 29.04 5.70
AJT 90.13 35.38 35.28 55.40 43.47 19.17 12.87 18.08 20.77 19.09 17.86 20.67 49.35 31.30 35.54
ATT 77.39 28.30 26.53 26.55 59.00 14.05 6.30 6.21 30.54 12.61 6.27 29.04 14.17 27.37 93.81
KKK 33.63 99.21 26.60 23.35 22.15 0.00 98.90 98.93 98.98 9.42 8.70 7.46 5.73 5.63 5.24
KKQ 25.28 75.17 11.04 7.64 7.57 98.91 76.20 61.79 59.47 21.88 5.20 5.04 4.16 2.58 3.87
KKJ 27.07 74.56 8.50 8.91 7.53 94.97 65.86 72.11 58.31 7.10 4.94 3.46 18.29 3.66 4.21
KKT 27.26 76.33 8.43 7.96 7.55 95.01 66.98 65.05 65.90 6.98 3.98 3.77 5.20 3.47 16.69
KQQ 25.53 28.83 44.12 6.43 6.64 62.63 76.42 21.34 21.39 90.69 34.34 32.38 4.22 2.46 3.90
KQJ 27.74 33.34 25.44 21.71 13.83 79.00 52.64 42.72 30.66 54.83 34.65 22.96 37.20 19.76 12.70
KQT 27.97 33.65 27.10 14.08 20.33 82.17 55.33 32.02 40.44 52.69 25.40 31.10 15.72 18.37 33.87
KJJ 25.55 27.95 7.96 37.22 7.20 62.12 23.99 65.66 19.89 13.12 32.08 4.01 90.14 26.55 3.92
KJT 27.87 35.10 14.08 27.79 20.55 78.69 34.65 49.37 42.56 20.58 23.99 19.66 46.81 29.14 35.14
KTT 26.59 26.30 7.57 7.59 32.05 65.16 22.46 22.65 53.96 11.83 5.23 27.44 10.97 25.98 93.74
QQQ 30.72 25.87 98.91 22.26 21.80 12.97 98.92 8.69 7.44 0.00 98.57 98.55 5.04 4.99 4.38
QQJ 24.77 10.59 65.98 8.81 7.18 20.06 64.13 7.39 5.75 98.57 59.53 50.53 19.00 3.60 3.52
QQT 26.87 10.84 68.56 7.94 7.78 21.99 63.01 6.57 6.40 94.63 53.98 55.52 5.16 3.49 16.19
QJJ 25.49 9.09 24.47 38.44 7.25 21.36 23.20 37.33 5.05 52.86 59.79 17.86 90.11 27.83 3.71
QJT 27.82 14.24 33.64 27.85 21.46 27.19 33.14 25.40 21.77 71.29 46.88 38.04 49.05 31.25 33.41
QTT 25.45 9.18 23.66 7.78 32.14 21.51 22.36 6.62 30.54 52.49 20.24 50.34 11.94 26.15 89.87
JJJ 28.37 24.45 22.26 98.56 20.67 12.03 8.91 98.55 6.76 9.79 98.53 5.30 0.00 98.07 4.03
JJT 27.59 11.91 11.44 59.33 8.55 19.49 8.57 54.38 6.36 17.70 52.68 6.03 98.12 44.83 16.79
JTT 25.37 9.06 8.86 22.61 33.31 21.15 7.52 20.10 32.10 18.94 19.68 30.61 43.68 45.40 89.83
TTT 25.91 23.32 21.14 19.94 97.80 10.97 8.13 7.26 98.19 9.27 5.72 98.14 8.79 98.12 0.00

+/- 1% accuracy, suited are not considered.

2

Corrected table, making flop cards of different suit, so that the influence of Royal flush is same on all hands.

- AA AK AQ AJ AT KK KQ KJ KT QQ QJ QT JJ JT TT
PRE 44.98 36.27 32.39 29.08 26.38 34.92 28.50 25.12 22.56 26.75 21.93 19.33 20.99 16.73 16.52
AAA 0.00 98.89 98.92 98.87 98.92 33.02 26.92 24.09 22.86 10.47 10.05 8.56 7.02 6.84 6.38
AAK 99.24 98.24 75.23 73.19 70.97 28.45 9.54 9.70 9.71 6.31 4.31 4.39 6.03 4.31 5.65
AAQ 99.28 80.37 90.96 72.03 70.17 11.93 8.64 5.41 5.45 22.14 5.24 5.26 4.68 2.88 4.37
AAJ 99.26 79.33 77.30 83.76 69.30 12.06 6.29 6.49 4.97 7.08 4.99 3.46 19.02 3.75 4.04
AAT 99.24 78.32 76.04 73.76 76.38 11.95 6.07 5.47 5.41 7.02 4.00 3.97 5.22 3.51 16.80
AKK 76.69 94.31 28.00 27.95 28.04 95.01 40.48 38.81 37.35 5.72 3.64 3.64 5.37 3.62 5.15
AKQ 90.17 61.24 49.73 32.43 32.44 60.60 38.93 24.48 24.57 42.84 19.51 19.55 12.68 14.19 12.76
AKJ 90.28 60.90 33.71 47.13 32.05 60.49 25.62 37.05 24.69 16.07 19.70 14.11 39.07 19.51 12.57
AKT 90.15 61.09 33.47 33.94 44.76 60.61 25.70 25.61 34.95 15.87 14.17 19.87 15.67 19.54 35.39
AQQ 76.84 30.58 82.57 26.66 26.35 15.53 39.68 5.11 5.15 94.49 33.83 32.36 5.16 3.45 4.93
AQJ 90.38 35.23 58.15 47.43 32.42 20.91 25.70 20.63 14.06 54.61 34.84 24.23 39.01 19.63 12.65
AQT 90.36 35.53 58.03 33.77 44.86 21.03 25.63 14.02 20.51 54.44 25.47 33.00 15.95 19.54 35.02
AJJ 76.85 28.92 28.69 71.50 24.74 15.31 6.67 34.73 4.86 14.23 33.38 4.93 94.12 27.76 4.75
AJT 90.09 35.26 35.10 55.37 44.84 21.09 14.00 25.45 20.60 20.68 25.31 20.46 48.90 31.07 35.40
ATT 76.99 26.77 26.65 26.95 61.37 15.43 6.40 6.58 30.34 14.18 6.65 28.64 13.12 27.19 93.81
KKK 33.50 99.28 26.51 23.35 22.40 0.00 98.44 98.50 98.51 9.30 8.80 7.48 5.71 5.71 5.13
KKQ 27.33 78.47 11.19 7.81 7.80 98.91 79.04 63.57 61.70 22.22 5.23 5.14 4.58 2.86 4.43
KKJ 27.10 77.47 8.57 9.05 7.41 98.89 67.99 72.68 60.46 7.04 5.02 3.47 19.02 3.50 4.01
KKT 27.29 76.20 8.52 7.87 7.93 98.92 67.20 64.91 65.94 7.05 4.07 3.94 5.22 3.50 16.86
KQQ 25.87 29.39 44.02 6.57 6.60 65.37 76.18 21.76 21.81 94.51 34.02 32.13 4.36 2.51 3.90
KQJ 27.59 35.05 26.52 21.73 14.16 82.22 55.36 44.92 31.85 54.66 34.67 24.35 39.06 19.39 12.68
KQT 27.81 34.74 26.98 13.93 21.64 82.13 55.41 33.50 42.49 54.63 25.32 32.73 15.86 19.57 35.15
KJJ 25.53 28.06 7.87 38.83 6.34 65.33 24.23 65.61 20.15 13.27 33.31 3.89 94.23 27.57 3.73
KJT 27.82 35.14 14.16 26.76 21.79 82.10 34.75 52.39 42.49 20.68 25.15 20.67 49.11 30.93 35.18
KTT 25.15 26.31 8.10 7.94 33.64 65.05 22.59 22.70 55.73 13.09 5.60 28.67 12.13 27.45 93.85
QQQ 30.69 26.06 98.83 21.89 21.01 12.82 98.86 8.87 7.63 0.00 98.19 98.25 5.06 4.88 4.50
QQJ 26.90 11.28 68.29 8.98 7.37 21.71 66.46 7.21 6.06 98.60 61.67 51.74 18.90 3.67 4.02
QQT 26.81 10.96 67.41 8.03 7.87 21.76 65.62 6.56 6.53 98.54 55.79 56.15 5.21 3.45 16.83
QJJ 25.72 9.30 24.87 38.87 6.31 21.38 23.70 37.13 5.01 55.25 59.88 17.77 94.20 27.52 3.76
QJT 27.75 13.99 34.70 26.74 21.75 27.19 34.56 26.63 21.87 74.04 49.54 40.36 48.87 30.99 35.25
QTT 25.33 9.07 23.74 7.94 33.56 21.11 22.05 6.52 32.01 55.38 20.15 50.36 12.00 27.29 93.78
JJJ 27.99 24.66 22.35 98.50 19.54 11.88 9.05 98.51 6.76 9.61 98.53 5.24 0.00 97.80 4.01
JJT 26.29 10.80 10.56 58.12 7.80 21.62 8.99 56.25 6.24 19.20 54.65 6.03 98.13 46.27 16.85
JTT 25.05 9.18 8.95 21.78 33.49 21.19 7.35 20.49 32.09 19.17 20.07 30.51 45.64 44.83 93.75
TTT 25.76 23.03 20.76 20.24 98.16 10.84 8.12 7.32 98.19 9.18 5.94 98.13 9.00 98.19 0.00