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Thread: pai gow poker... side bet, copies push

  1. #1


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    pai gow poker... side bet, copies push

    Hello, everyone.

    1. A bet that the dealer's hand will push versus the player's hand pays 1:1. If there is a push and if either the dealer's hand or the player's hand has 33 on the top and a better pair on the bottom, the bet pays 2:1. For purposes of determining the 2:1 payout, you have to go the house way. That is, if either the dealer's hand or the player's hand has two pairs (33 to 88) with a K kicker or lower, the house way is K high on the top and two pairs on the bottom. (This is set after paying your main pai gow bet.)

    wizardofodds shows probability of the dealer's hand pushing versus the player's hand is 41.5%. Using odds calculator, the payoff on the push bet has to be 1.4:1 to make it a break-even play.

    wizardofodds also shows probability of two pairs is 23.1%.

    Does the 2:1 payoff make the push bet a plus ev play?

    2. Copies push in this game. What is the house edge now?

    Thank you for your time.

    PS. I also posted these questions on bj21.

  2. #2


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    Sorry but. Pai Gow?

  3. #3


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    Quote Originally Posted by DatabaseGuy View Post
    Sorry but. Pai Gow?
    Math is not my strength. That's why I posted the question.

    As an advantage player, don't limit yourself to just blackjack.

  4. #4


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    True, I also play video poker and low stakes. I also lure people into bets where I have the edge. And I also put everything on the AMEX and then pay off immediately so I can get free stuff.

    Pai Gow will offer a much better edge when playing bank against just the dealer. But you're still a loser. It's just a game where you enjoy a ton of pushes and get a lot of mileage for your money. It's fun and cute.

    I am not sure the effort of counting to beat the side bet is worth it.

  5. #5


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    Sorry, I forgot to add: IMHO.

  6. #6
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    I cannot recall from where I copied this:


    Pai Gow Poker Power Ratings
    Last Update: Feb 03, 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
    0.001437
    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
    0.000101
    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
    1
    1
    Total
    154143080
    1



  7. #7
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    Silver Dollar Casino House Way


    The following house way is for the Silver Dollar casino in Seatac, Washington. Note that it does not cover some situations, like a hand that contains a straight, flush, and a pair. The Silver Dollar treats the A2345 straight as the second highest straight.

    • No pair: Place the second and third highest cards in the low hand.
    • One pair: Place the two highest singletons in the low hand.
    • Two pair: Use the following groups to determine how to play a two pair:
    • 2 through 6: Low pair
    • 7 through 10: Medium pairs
    • Jack through king: High pairs

      • Low pair and low pair or low pair and medium pair: Split pairs unless holding a king singleton or better.
      • Low pair and high pair or medium pair and medium pair: Split pairs unless holding an ace singleton.
      • Medium pair and high pair or high pair and high pair: Always split.
      • Pair of aces and any other pair: Always split.

    • Three pair: Play highest pair in front.
    • Three of a kind: Play three of a kind in back unless they are aces, then play a pair of aces in back and one ace in front.
    • Three of a kind twice: Play a pair from the higher three of a kind in front.
    • Straights, flushes, straight flushes, and royal flush:

      • With no pair: Play the highest hand possible in front while maintaining at least a straight in the back.
      • With six or seven card: Play the lower straight or flush in the high hand.
      • With two pair: Use two pair rule unless you can keep one pair in the low hand and play the straight or higher in the high hand.
      • With three pair: Use three pair rule.
      • With three of a kind: Play pair in the low hand.
      • With full house: Use full house rule.

    • Full house: Always split unless the pair is 2's and you can play an ace and king in the low hand.
    • Full house with three of a kind and two pairs: Play the highest pair in front.
    • Four of a kind: Play according to the rank of the four of a kind:
    • 2 through 6: Always keep together.
    • 7 through 10: Split unless a king or better can be played in front.
    • J through K: Split unless an ace can be played in front.
    • Aces: Always split.
    • Four of a kind and a pair: Play pair in front.
    • Four of a kind and three of a kind: Play pair in front from the three of a kind.
    • Five aces: Play pair of aces in front unless a pair of kings can be played in front.

  8. #8
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    Please pardon the bad formatting


    Silver Dollar Casino House Way



    The following house way is for the Silver Dollar casino in Seatac, Washington.
    Note that it does not cover some situations, like a hand that contains a straight, flush, and a pair.
    The Silver Dollar treats the A2345 straight as the second highest straight.


    • No pair: Place the second and third highest cards in the low hand.
    • One pair: Place the two highest singletons in the low hand.
    • Two pair: Use the following groups to determine how to play a two pair:
    • 2 through 6: Low pair
    • 7 through 10: Medium pairs
    • Jack through king: High pairs
      • Low pair and low pair or low pair and medium pair: Split pairs unless holding a king singleton or better.
      • Low pair and high pair or medium pair and medium pair: Split pairs unless holding an ace singleton.
      • Medium pair and high pair or high pair and high pair: Always split.
      • Pair of aces and any other pair: Always split.

    • Three pair: Play highest pair in front.
    • Three of a kind: Play three of a kind in back unless they are aces, then play a pair of aces in back and one ace in front.
    • Three of a kind twice: Play a pair from the higher three of a kind in front.
    • Straights, flushes, straight flushes, and royal flush:

      • With no pair: Play the highest hand possible in front while maintaining at least a straight in the back.
      • With six or seven card: Play the lower straight or flush in the high hand.
      • With two pair: Use two pair rule unless you can keep one pair in the low hand and play the straight or higher in the high hand.
      • With three pair: Use three pair rule.
      • With three of a kind: Play pair in the low hand.
      • With full house: Use full house rule.

    • Full house: Always split unless the pair is 2's and you can play an ace and king in the low hand.
    • Full house with three of a kind and two pairs: Play the highest pair in front.
    • Four of a kind: Play according to the rank of the four of a kind:
    • 2 through 6: Always keep together.
    • 7 through 10: Split unless a king or better can be played in front.
    • J through K: Split unless an ace can be played in front.
    • Aces: Always split.
    • Four of a kind and a pair: Play pair in front.
    • Four of a kind and three of a kind: Play pair in front from the three of a kind.
    • Five aces: Play pair of aces in front unless a pair of kings can be played in front.

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BJTF is an advantage player site based on the principles of comity. That is, civil and considerate behavior for the mutual benefit of all involved. The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage. To maximize our success, it is important to understand that we are all on the same side. Personal conflicts simply get in the way of our goals.