Pai Gow Poker Appendix 1

Last update: February 23, 2007

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 right column 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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