Pai Gow Tiles Optimal Strategy when not Banking

Introduction

Following is the optimal strategy, when not banking, for Pai Gow Tiles. This strategy is optimal against the "standard house way," which the Trump Plaza uses. However, it should be very near optimal against any casino house way. We believe this is the first time a pai gow optimal strategy has been put in writing, other than a very long list of hands.

To use the strategy, follow the first rule that applies.

1. Pairs

   With tile combinations containing at least one pair, follow the first rule that applies:

   1. Play a pair in the low hand if possible.
   2. Split Gee Joon to make 7/9 or better if it improves the low hand.
   3. Split Teens and Days to make 6/8 or better if it improves the low hand, except with 9 and H8. Also split with 9 and 11.
   4. Split 9s to make 9/9 or better.
   5. Split 8s to make 8/8 or better. Also split with 9 and 11.
   6. Split 7s to make 7/7 or better.
   7. Split 6s to make 7/8 or better. Also split L6s with H10 and Teen/Day.
   8. Split 5s to make 7/7.
   9. Play a pair in the high hand.

2. Only One Way

   Counting a Wong as 11 points and a Gong as 10 points, add the number of points in the low and high hands for the three possible splits, then follow the first rule that applies:

   1. If only one split has the highest point total, set the tiles that way and disregard all other rules. Example

      0/2 2 points invalid

      1/1 2 points invalid

      3/9 12 points only way to play

   2. If two splits have the highest point total, the same number of points in their respective low and high hands, and the same high tile rank in their respective low and high hands, set the tiles one of those ways and disregard all other rules. Example

      1/4 5 points invalid

      7/8 15 points only way to play

      7/8 15 points only way to play

   3. If two splits have the highest point total, the same number of points in their low hands, and the same high tile ranks in their high hands, but one of the low hands has a better high tile rank than the other, play the split that has the stronger low hand and disregard all other rules. Example

      2/9 11 points invalid

      low 6/8 14 points invalid

      high 6/8 14 points only way to play

   4. If two splits have the highest point total, the same number of points in their high hands, and the same high tile rank in their low hands, but one of the high hands has a better high tile rank than the other, play the split that has the stronger high hand and disregard all other rules. Example

      0/1 1 point invalid

      4/low 7 11 points invalid

      4/high 7 11 points only way to play

3. Teen and Day

   Follow the first rule that applies:

   1. Play Teen and Day in the same hand with the following combinations:

      1. 11 and H8 - play 4/9
      2. 11 and H6 - play 4/7
      3. 11 and Gee - play 4/7
      4. 11 and 4 - play 4/5
      5. H10 and 9 - play 4/9
      6. H10 and Gee - play 4/6
      7. H10 and 4 - play 4/4
      8. L10 and H4 - play 4/4

   2. Play Teen in the low hand and Day in the high hand with the following combinations:

      1. 11 and 10 - play high 2/3
      2. 11 and 5 - play high 3/7
      3. 10 and 5 - play high 2/7
      4. 9 and 6 - play high 8/Wong
      5. 9 and Gee - play high 8/Wong
      6. 5 and 4 - play high 6/7

   3. Play the best high hand which separates Teen and Day.

4. Teen only

   1. If Wong, Gong, and High Nine can be made, play High Nine.

   2. If Wong and Gong can be made, but not High Nine, follow the first rule that applies:

      1. Play Wong with H8 and L10.
      2. Play 9 and H8 in the same hand if the fourth tile is a Gee, 4, 5, or 6.
      3. Play 9 and L8 in the low hand if the fourth tile is a 5.
      4. Play Gong.

   3. If Wong and High Nine can be made, but not Gong, follow the first rule that applies:

      1. Play Wong if the fourth tile is a 4 or 5.
      2. Play High Nine.

   4. If Gong and High Nine can be made, but not Wong, follow the first rule that applies:

      1. Play H8 Gong if the fourth tile is a 4.
      2. Play L8 Gong if the fourth tile is a Gee, 4, 5, L6, H10, or 11.
      3. Play H8 and 7 in the low hand if the fourth tile is a 5.
      4. Play High Nine.

   5. If Wong can be made, but not Gong or High Nine, follow the first rule that applies:

      1. Play the best low hand if the third tile is a 10 and the fourth tile is a 4 or 5, except with L10 and H4.
      2. Play Wong.

   6. If Gong can be made, but not Wong or High Nine, follow the first rule that applies:

      1. Play H8 and L8 in the low hand if the fourth tile is a Gee, 4, 5, or 6.
      2. With H8, play the best low hand if the third tile is a 10 or 11 and the fourth tile is a 4 or 5.
      3. With H8, play the best low hand if the third tile is a L10 and the fourth tile is a L6.
      4. With L8, play the best low hand if the third tile is a 10 and the fourth tile is a L4.
      5. With L8, play the best low hand if the third tile is a L10 and the fourth tile is a 5.
      6. Play Gong.

   7. If High Nine can be made, but not Wong or Gong, follow the first rule that applies:

      1. Play the best low hand if the third tile is a H10 and the fourth tile is a 5.
      2. Play the best low hand if the third tile is a 10 and the fourth tile is a 4, except with L10 and H4.
      3. Play High Nine.

   8. If no Wong, Gong, or High Nine can be made, follow the first rule that applies:

      1. Play 11 and 10 in the low hand if the fourth tile is a Gee, 5, or 6.
      2. Play 11 and H10 in the low hand if the fourth tile is a 4.
      3. Play 11 and H4 in the low hand if the fourth tile is a 5.
      4. Play 10 and 10 in the low hand if the fourth tile is a Gee, 4, 5, or 6.
      5. Play H6 and 5 in the low hand if the fourth tile is a L6.
      6. Play 6 and 4 in the low hand if the fourth tile is a 6.
      7. Play 6 and Gee in the high hand if the fourth tile is a 5.
      8. Play 5 and H4 in the high hand if the fourth tile is a L10.
      9. Play 4 and 4 in the high hand if the fourth tile is a 10.
      10. Play the best low hand.

5. Day only

   1. If Wong, Gong, and High Nine can be made, play High Nine.

   2. If Wong and Gong can be made, but not High Nine, follow the first rule that applies:

      1. Play Wong with H8 and 10.
      2. Play Wong with L8 and 4.
      3. Play Gong with L8 and H6.
      4. Play the best low hand.

   3. If Wong and High Nine can be made, but not Gong, follow the first rule that applies:

      1. Play Wong if the fourth tile is a 4, 5, or H10.
      2. Play High Nine.

   4. If Gong and High Nine can be made, but not Wong, follow the first rule that applies:

      1. Play H8 and 7 in the low hand if the fourth tile is a Gee, 5, or 6.
      2. Play L8 and H7 in the low hand if the fourth tile is a Gee.
      3. Play H8 Gong if the fourth tile is a 4 or H10.
      4. Play L8 Gong if the fourth tile is a Gee, 4, 5, 6, H10, or 11.
      5. Play High Nine.

   5. If Wong can be made, but not Gong or High Nine, follow the first rule that applies:

      1. Play the best low hand if the third tile is a 10 and the fourth tile is a 4 or 5, except with L10 and H4.
      2. Play Wong.

   6. If Gong can be made, but not Wong or High Nine, follow the first rule that applies:

      1. Play H8 and L8 in the low hand if the fourth tile is a Gee, 4, 5, or 6.
      2. Play the best low hand if the third tile is a 10 and the fourth tile is a 4 or 5.
      3. With H8, play the best low hand if the third tile is an 11 and the fourth tile is a Gee, 4, 5, or L6.
      4. With H8, play the best low hand if the third tile is a L10 and the fourth tile is a Gee or 6.
      5. With L8, play the best low hand if the third tile is an 11 and the fourth tile is a L4 or 5.
      6. With L8, play the best low hand if the third tile is a L10 and the fourth tile is a 6.
      7. Play Gong.

   7. If High Nine can be made, but not Wong or Gong, follow the first rule that applies:

      1. Play the best low hand if the third tile is an 11 and the fourth tile is a L4 or 5.
      2. Play the best low hand if the third tile is a 10 and the fourth tile is a Gee, 4, or 5.
      3. Play the best low hand if the third tile is a H10 and the fourth tile is a 6.
      4. Play High Nine.

   8. If no Wong, Gong, or High Nine can be made, follow the first rule that applies:

      1. Play 11 and 10 in the low hand if the fourth tile is a Gee, 5, or 6.
      2. Play 11 and H10 in the low hand if the fourth tile is a 4.
      3. Play 11 and H4 in the low hand if the fourth tile is a 5.
      4. Play 10 and 10 in the low hand if the fourth tile is a Gee, L4, 5, or 6.
      5. Play H6 and 5 in the low hand if the fourth tile is a L6.
      6. Play 6 and 4 in the low hand if the fourth tile is a 6.
      7. Play 6 and Gee in the high hand if the fourth tile is a 5.
      8. Play 5 and H4 in the high hand if the fourth tile is a L10.
      9. Play 4 and 4 in the high hand if the fourth tile is a 10.
      10. Play the best low hand.

6. No Teen or Day

   1. With H10 and L10, play as follows:

      1. 11 with a 7 - play 1/high 7
      2. 11 with a Gee or 6 - play high 1/6
      3. H6 with a 7, L8, or 9 - play the H10 in the high hand
      4. L6 with a 9 - play the H10 in the high hand
      5. 5 with a 7 or 9 - play the H10 in the high hand
      6. L4 with a H4 or H6 - play the best low hand

   2. With H8 and L8, play as follows:

      1. 9 with H7 - play 5/high 7
      2. 9 with L7 - play high 5/7
      3. H6 with L6 - play 4/4
      4. L4 with 11 - play 2/high 9
      5. L4 with H10 - play 4/6

   3. With H7 and L7, play as follows:

      1. 11 with Gee - play 4/7
      2. L10 with Gee, L4, 5, or 6 - play both 7s in the low hand
      3. 8 with 4 - play 1/5

   4. With H6 and L6, play as follows:

      1. 9 with L8 - play high 4/5
      2. 9 with 7 - play 3/high 5
      3. H8 with 7, L10, or 11 - play the best high hand
      4. 5 with 9, L10, or 11 - play the higher 1 in the low hand
      5. Gee with L10 or 11 - play the higher 9 in the high hand

   5. With H4 and L4, play as follows:

      1. 11 with L10 - play high 4/5
      2. 5 with Gee - play high 7/9

   6. Play H8 and 11 in the high hand with the following combinations:

      1. H10 with a Gee, L4, 5, or 6
      2. L10 with a 5
      3. 7 with a 4
      4. 6 with a 4 or 5

   7. Play H10 and 9 in the high hand if the third tile is a 5 and the fourth tile is a L6 or 7.

   8. Play H6 and Gee in the high hand if the third tile is a 5 and the fourth tile is a H10.

   9. Play 11 and L8 in the high hand with the following combinations:

      1. 7 with a 4
      2. 5 with a L7 or H10

   10. Play L10 and 9 in the high hand if the third tile is a 5 and the fourth tile is a 7.

   11. Play the following combinations as specified:

       1. 11, 9, 7, H6 - play 5/8
       2. H10, 9, 7, H6 - play 5/7
       3. L10, 9, H8, 4 - play 4/7
       4. H10, L8, L7, H6 - play 4/7
       5. L8, L6, H4, Gee - play 4/7
       6. 9, L8, 6, H4 - play 3/4
       7. 9, L8, H6, L4 - play 3/4
       8. 10, H8, H6, 5 - play 1/8
       9. 11, 7, H6, H4 - play 1/7
       10. 10, 7, H6, H4 - play 1/6
       11. 9, H7, H6, 5 - play 1/6
       12. H8, 7, 6, H4 - play 1/4

   12. Play all other combinations as follows:

       1. Play the best low hand if the best high hand ranks lower than 6-with-H6.
       2. Play the best low hand if it is at least 4-with-H8 but no higher than 8-with-L10.
       3. Play the best high hand.

Written by: Michael Shackleford