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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.
- If there is one way to play a hand that is superior to both alternatives, then play that way.
- 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
- One High-9, Gong, or Wong Possible
- Play the best high.
- 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.
- 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.