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Last Updated: October 27, 2017

Wizard Pai Gow Basic Strategy

Introduction



This page introduces my own basic strategy for pai gow. It was devised with the primary focus on simplicity and secondarily on minimizing the cost of errors compared to the optimal strategy. I recommend this strategy for beginning and intermediate players.

The Basic Strategy



If two rules seem to contradict, go with the one listed first.

For purposes of this strategy, count hands of 9 points or less according to its number of points. Count Gongs as 10 points, Wongs as 11 points, and pairs as 12 points.

  1. If there is one way to play a hand that is superior to both alternatives, then play that way.
  2. Pairs

    • Never split 10's or 11's.
    • If the total points by splitting the pair is greater than retaining the pair, then split it.
    • If the total points by splitting or retaining the pair is the same, and that total is less than 15, then split the pair.
    • Otherwise, retain the pair
  3. One High-9, Gong, or Wong Possible

    • Play the best high.
  4. Two or Three Ways to Play High-9, Gong, or Wong

    • With both the 2 and 12 tiles, always play the 12 in the high hand.
    • With 10 or 11 total points, maximize the high
    • With 12 total points, maximize the high, except if it is a High-8 Gong, then balance.
    • With 13 total points, maximize the high, except if it is a High-8 Gong, then play a High-9
    • With 14 or more total points, play High-9 if you can, otherwise Low-8 Gong and 5 in the low if you can, otherwise best low.
  5. All Other

    • With 6 or less total points, balance.
    • With 7 to 9 points, play best high.
    • With 10 to 15 points, if you can get to 5 or more in the low, then balance. Otherwise, play best high.
    • With 16 or more points, play best high.

Analysis



The following table shows how the Wizard Basic Strategy compares to the optimal strategy when the dealer is banking. The bottom row shows the basic strategy has a house edge of 1.98%, compared to 1.66% under optimal strategy. The lower right cell shows the cost to errors using the Basic Strategy, when not banking, is 0.32%.

Dealer Banking Analysis

Decision Type Combinations Probability Return under
Basic Strategy
Return under
Optimal Strategy
Difference
One way 13076 0.363626 0.104995 0.104995 0.000000
One pair 1428 0.039711 0.010435 0.010484 -0.000050
H9/G/W -- one hand 4288 0.119244 0.002473 0.003749 -0.001275
H9/G/W -- 2+ ways 3728 0.103671 0.017431 0.017906 -0.000475
All other 13440 0.373749 -0.155122 -0.153727 -0.001395
Total 35960 1.000000 -0.019788 -0.016593 -0.003195


The following table shows how the Wizard Basic Strategy compares to the optimal strategy when the player is banking. The bottom row shows the basic strategy has a house edge of 0.08%, compared to -0.18% under optimal strategy. The lower right cell shows the cost to errors using the Basic Strategy, when not banking, is 0.26%.

Player Banking Analysis

Decision Type Combinations Probability Return under
Basic Strategy
Return under
Optimal Strategy
Difference
One way 13076 0.363626 0.109506 0.109506 0.000000
One pair 1428 0.039711 0.010748 0.010814 -0.000066
H9/G/W -- one hand 4288 0.119244 0.007517 0.008225 -0.000708
H9/G/W -- 2+ ways 3728 0.103671 0.020564 0.020997 -0.000434
All other 13440 0.373749 -0.149179 -0.147766 -0.001413
Total 35960 1.000000 -0.000844 0.001777 -0.002620


H9/G/W = High-9, Gong, or Wong

Assuming the player banks half the time, the overall house edge under the Basic Strategy is 1.03%, which is 0.29% higher than the 0.74% under optimal strategy.

Acknowledgements



I would like to thank J.B. for a spreadsheet showing the expected value of all three ways to play all 3,620 possible classes of pai gow hands, which made the development of this strategy much easier and effective.


Written by: Michael Shackleford

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