The subsequent two tables illustrate how frequently the dealer achieves specific hands, based on the house rules of Trump Plaza. This information is crucial for evaluating the likelihood of a player's hand defeating the dealer. Each column is further explained below.
- Hand: Dealer hand
- Combinations: This represents the total number of ways, from a grand total of 154,143,080, in which the dealer can create this specific hand.
- Probability: This indicates the likelihood that the dealer will be able to achieve this hand.
- Player PR: Refers to the player power rating, which is the chance of the player winning against the dealer with this particular hand (note that ties result in losses).
- Banker PR: This is the banker power rating. It signifies the probability that the player will either win or tie with the dealer while acting as the banker (in this case, ties are advantageous).
To evaluate the worth of any hand, sum the power ratings from both the 2-card and 5-card formations. Remember to refer to the right column based on whether you are playing as the player or banker. Configure the hand to optimize the formula 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 |
|
|