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Pai Gow Poker Power Ratings

Introduction

The following two tables show how often the dealer will make each hand, according to the Trump Plaza house way. This is useful to help determine the probability that any given player hand will beat the dealer. Following are explanations of each column.

  • Hand: Dealer hand
  • Combinations: Number of combinations out of a possible 154,143,080 that the dealer will form this hand.
  • Probability: Probabilty that the dealer will form this hand.
  • Player PR: Player power rating. This is the probability that the player will win against the dealer with this hand, acting as the player (ties lose).
  • Banker PR: Banker power rating. This is the probability that the player will win or tie against the dealer with this hand, acting as the banker (ties win).

To determine the value of any given hand add the power ratings for the 2-card and 5-card hands. Be sure to use the image--rightolumn according to whether you are acting as player or banker. Set the hand according to the way maximizes 0.95*(2 card PR)*(5 card PR) - (1 - 2 card PR)*(1 - 5 card PR).

Two Card Power Ratings

Hand Combinations Probability Player PR Banker PR
3,2 221460 0.001437 0 0.001437
4,2 203436 0.00132 0.001437 0.002757
4,3 188708 0.001224 0.002757 0.003981
5,2 183192 0.001188 0.003981 0.005169
5,3 170756 0.001108 0.005169 0.006277
5,4 163256 0.001059 0.006277 0.007336
6,2 165882 0.001076 0.007336 0.008412
6,3 153212 0.000994 0.008412 0.009406
6,4 147932 0.00096 0.009406 0.010366
6,5 146594 0.000951 0.010366 0.011317
7,2 157212 0.00102 0.011317 0.012337
7,3 153030 0.000993 0.012337 0.01333
7,4 148574 0.000964 0.01333 0.014293
7,5 187184 0.001214 0.014293 0.015508
7,6 272000 0.001765 0.015508 0.017272
8,2 148254 0.000962 0.017272 0.018234
8,3 138024 0.000895 0.018234 0.01913
8,4 142064 0.000922 0.01913 0.020051
8,5 181434 0.001177 0.020051 0.021228
8,6 306278 0.001987 0.021228 0.023215
8,7 842290 0.005464 0.023215 0.02868
9,2 149448 0.00097 0.02868 0.029649
9,3 132726 0.000861 0.029649 0.03051
9,4 130592 0.000847 0.03051 0.031357
9,5 178440 0.001158 0.031357 0.032515
9,6 310056 0.002011 0.032515 0.034527
9,7 955930 0.006202 0.034527 0.040728
9,8 1996404 0.012952 0.040728 0.05368
10,2 177816 0.001154 0.05368 0.054833
10,3 156084 0.001013 0.054833 0.055846
10,4 147530 0.000957 0.055846 0.056803
10,5 189132 0.001227 0.056803 0.05803
10,6 329244 0.002136 0.05803 0.060166
10,7 929162 0.006028 0.060166 0.066194
10,8 2095794 0.013596 0.066194 0.07979
10,9 3779954 0.024522 0.07979 0.104313
J,2 200340 0.0013 0.104313 0.105612
J,3 178596 0.001159 0.105612 0.106771
J,4 165068 0.001071 0.106771 0.107842
J,5 200358 0.0013 0.107842 0.109142
J,6 333972 0.002167 0.109142 0.111308
J,7 880292 0.005711 0.111308 0.117019
J,8 1920682 0.01246 0.117019 0.12948
J,9 3679082 0.023868 0.12948 0.153348
J,10 6013718 0.039014 0.153348 0.192361
Q,2 223086 0.001447 0.192361 0.193809
Q,3 201330 0.001306 0.193809 0.195115
Q,4 187790 0.001218 0.195115 0.196333
Q,5 218142 0.001415 0.196333 0.197748
Q,6 345552 0.002242 0.197748 0.19999
Q,7 822830 0.005338 0.19999 0.205328
Q,8 1716490 0.011136 0.205328 0.216464
Q,9 3209682 0.020823 0.216464 0.237287
Q,10 5476880 0.035531 0.237287 0.272818
Q,J 8204130 0.053224 0.272818 0.326042
K,2 246306 0.001598 0.326042 0.32764
K,3 259354 0.001683 0.32764 0.329322
K,4 280618 0.001821 0.329322 0.331143
K,5 345774 0.002243 0.331143 0.333386
K,6 503098 0.003264 0.333386 0.33665
K,7 981188 0.006365 0.33665 0.343015
K,8 1756866 0.011398 0.343015 0.354413
K,9 2995666 0.019434 0.354413 0.373847
K,10 4830696 0.031339 0.373847 0.405186
K,J 7365056 0.047781 0.405186 0.452967
K,Q 10123398 0.065675 0.452967 0.518642
A,2 297324 0.001929 0.518642 0.520571
A,3 354020 0.002297 0.520571 0.522868
A,4 420652 0.002729 0.522868 0.525597
A,5 497012 0.003224 0.525597 0.528821
A,6 748316 0.004855 0.528821 0.533676
A,7 1257676 0.008159 0.533676 0.541835
A,8 1997086 0.012956 0.541835 0.554791
A,9 3055428 0.019822 0.554791 0.574613
A,10 4510246 0.02926 0.574613 0.603873
A,J 6463634 0.041933 0.603873 0.645806
A,Q 8821842 0.057232 0.645806 0.703037
A,K 11672044 0.075722 0.703037 0.77876
2,2 3437218 0.022299 0.77876 0.801058
3,3 3242090 0.021033 0.801058 0.822091
4,4 3051018 0.019793 0.822091 0.841885
5,5 2868802 0.018611 0.841885 0.860496
6,6 2700550 0.01752 0.860496 0.878016
7,7 3190270 0.020697 0.878016 0.898713
8,8 2960590 0.019207 0.898713 0.91792
9,9 2739766 0.017774 0.91792 0.935694
10,10 2531602 0.016424 0.935694 0.952117
J,J 2210682 0.014342 0.952117 0.966459
Q,Q 1895738 0.012299 0.966459 0.978758
K,K 1589656 0.010313 0.978758 0.989071
A,A 1684694 0.010929 0.989071 1
Total 154143080 1    

Five Card Power Ratings

Hand Combinations Probability Player PR Banker PR
9,5 15540 0.000101 0 0.000101
9,6 15540 0.000101 0.000101 0.000202
10,5 46620 0.000302 0.000202 0.000504
10,6 139860 0.000907 0.000504 0.001411
10,7 62160 0.000403 0.001411 0.001815
J,5 93240 0.000605 0.001815 0.00242
J,6 310800 0.002016 0.00242 0.004436
J,7 404040 0.002621 0.004436 0.007057
J,8 155400 0.001008 0.007057 0.008065
Q,5 155400 0.001008 0.008065 0.009073
Q,6 543900 0.003529 0.009073 0.012602
Q,7 854700 0.005545 0.012602 0.018147
Q,8 854700 0.005545 0.018147 0.023692
Q,9 310800 0.002016 0.023692 0.025708
K,5 233100 0.001512 0.025708 0.02722
K,6 839160 0.005444 0.02722 0.032664
K,7 1460760 0.009477 0.032664 0.042141
K,8 1771560 0.011493 0.042141 0.053634
K,9 1538460 0.009981 0.053634 0.063615
K,10 543900 0.003529 0.063615 0.067143
A,6 1196580 0.007763 0.067143 0.074906
A,7 2451900 0.015907 0.074906 0.090813
A,8 3402900 0.022076 0.090813 0.112889
A,9 3593100 0.02331 0.112889 0.136199
A,10 2794260 0.018128 0.136199 0.154327
A,J 992040 0.006436 0.154327 0.160762
2,2 4954104 0.03214 0.160762 0.192902
3,3 5092848 0.03304 0.192902 0.225942
4,4 5232960 0.033949 0.225942 0.259891
5,5 5373072 0.034858 0.259891 0.294748
6,6 5554764 0.036036 0.294748 0.330785
7,7 5761452 0.037377 0.330785 0.368162
8,8 6037932 0.039171 0.368162 0.407333
9,9 6308940 0.040929 0.407333 0.448262
10,10 6597264 0.0428 0.448262 0.491062
J,J 7863168 0.051012 0.491062 0.542074
Q,Q 8322672 0.053993 0.542074 0.596067
K,K 8783544 0.056983 0.596067 0.65305
A,A 14832140 0.096223 0.65305 0.749273
Two pair, 33 high 315504 0.002047 0.749273 0.75132
Two pair, 44 high 613296 0.003979 0.75132 0.755299
Two pair, 55 high 893376 0.005796 0.755299 0.761095
Two pair, 66 high 1155744 0.007498 0.761095 0.768592
Two pair, 77 high 1400400 0.009085 0.768592 0.777677
Two pair, 88 high 1544400 0.010019 0.777677 0.787697
Two pair, 99 high 1670688 0.010839 0.787697 0.798535
Two pair, 10/10 high 1779264 0.011543 0.798535 0.810078
Two pair, JJ high 937008 0.006079 0.810078 0.816157
Two pair, QQ high 880560 0.005713 0.816157 0.82187
Two pair, KK high 806400 0.005232 0.82187 0.827101
222 825960 0.005358 0.827101 0.83246
333 823016 0.005339 0.83246 0.837799
444 820552 0.005323 0.837799 0.843122
555 818088 0.005307 0.843122 0.848429
666 816636 0.005298 0.848429 0.853727
777 815916 0.005293 0.853727 0.859021
888 815196 0.005289 0.859021 0.864309
999 814476 0.005284 0.864309 0.869593
10,10,10 814488 0.005284 0.869593 0.874877
JJJ 815512 0.005291 0.874877 0.880168
QQQ 816536 0.005297 0.880168 0.885465
KKK 818040 0.005307 0.885465 0.890772
AAA 635504 0.004123 0.890772 0.894895
Straight, 6 high 1407470 0.009131 0.894895 0.904026
Straight, 7 high 1157246 0.007508 0.904026 0.911533
Straight, 8 high 1093070 0.007091 0.911533 0.918625
Straight, 9 high 1082354 0.007022 0.918625 0.925646
Straight, 10 high 1073954 0.006967 0.925646 0.932614
Straight, J high 1064390 0.006905 0.932614 0.939519
Straight, Q high 1055156 0.006845 0.939519 0.946364
Straight, K high 1053224 0.006833 0.946364 0.953197
Straight, A-5 965276 0.006262 0.953197 0.959459
Straight 10-A 1025276 0.006651 0.959459 0.966111
Flush, Q-7 high 1326412 0.008605 0.966111 0.974716
Flush, K high 919220 0.005963 0.974716 0.980679
Flush, A high 2572158 0.016687 0.980679 0.997366
Full house 155346 0.001008 0.997366 0.998374
Four of a kind 174768 0.001134 0.998374 0.999507
Straight flush 75914 0.000492 0.999507 1
Five of a kind 6 0 1 1
Total 154143080 1    

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Written by: Michael Shackleford