Question re: pai gow tiles strategy

Hi All,

I recently began trying to learn pai gow tiles (a slow process, by the way), and as I've been practicing I've noticed some apparent discrepancies between the JB's recommended strategy and the suggested play on the Wizard of Odds practice game. These inconsistencies seem to predominantly surround the play of eight point and 15 point hands, and I'm not sure if it's either a glitch in the software or a mistake on my interpretation of the strategy guide. A few of the deals in question are:

1)
High 4
High 6
High 7
High 8

2)
Five
Low 7
Low 8
11

3)
2
12
Low 4
High 10

4)
Low 6
High 8
High 10
11

I have a few others as well, but I thought I'd post these first. If anyone can steer me in the right direction on these hands it would be much appreciated.

Thanks much!

There are quite a few "house ways", and the hands you posted could be plausibly played in differing fashions:
I learned the "Chinatown house way" in San Francisco, and it might not be mathematically perfect:

1. The standard rule seems to be that if the Low hand is Low 3 or worse, then it should be sacrificed to make High 7 or better (i.e., 0-7 rather than 3-4, if the 3 would be Low and the 7 High).

2. The other times when low hands are sacrificed is, again, (prospective) Low 3 in front, vs. maximization of High hand, with Gong, Wong, or Pair.

So:

Hand 1: Play 2-3. The sacrifice of the Low hand (to make 0-5) isn't worth it as you don't make a back hand of at least High 7.

Hand 2: I would play the 5-6 because the Low 9 that you would have if you set 2-9 is weak. Obviously, you would never play 3-8.

Hand 3: First, I would throw up. Then, I play 4-4, because a) the front 4 (High 10-Low 4) is too big to be sacrificed (to make 2-6), and b) the resultant high hand from making the sacrifice would only be a High 6.

Hand 4: I actually have differed from other people (vehemently) on this, but the house way that I have learned generally splits two high cards, and, of course, equalizes the two hands, and only violates those rules to make a High 9 or better in back. Playing 6-9 follows one rule, breaks the other, and the tiebreaker is that you are making that High 9 in back. I play, therefore, 6-9.

Quote: KTBaslow

I recently began trying to learn pai gow tiles (a slow process, by the way), and as I've been practicing I've noticed some apparent discrepancies between the JB's recommended strategy and the suggested play on the Wizard of Odds practice game. These inconsistencies seem to predominantly surround the play of eight point and 15 point hands, and I'm not sure if it's either a glitch in the software or a mistake on my interpretation of the strategy guide.

The strategies, in order to keep them simple, necessarily omit some exceptions -- because there are so many. Looking at the strategy data and trying to put it into words is a far more difficult task than it is for something like video poker, despite there being many more combinations in video poker than there are in Pai Gow.

Quote: KTBaslow

High 4
High 6
High 7
High 8

The best play is 1/4 instead of 2/3. The reason why is because it separates the two high tiles; playing the best low hand (2/3) would put them both in the same hand, wasting the high 4. If the dealer is banking, the best play is 1/4. If you are banking, the best play is actually 0/5.

Quote: KTBaslow

Five
Low 7
Low 8
11

The best play here is 2/9, which again is an exception to making the best low hand because it is worth 5 points. I speculate that the reason why is because it is the lowest 5-point hand possible, making it almost a 4-point hand.

Quote: KTBaslow

2
12
Low 4
High 10

With 2,12,10,4 - always play 4/4 except with Low 10 + Low 4, in which case play 2/high 6.

Quote: KTBaslow

Low 6
High 8
High 10
11

Playing 7/8 would waste the strength of the High 10. Therefore, it is better to play high 6/high 9 instead of low 7/high 8.
In fact, any time you have a High 8, High 10, and 11 together, always play the High 8 and 11 in the high hand, except when the last tile is a High 4 and the dealer is banking.

Quote: JB

The best play is 1/4 instead of 2/3. The reason why is because it separates the two high tiles; playing the best low hand (2/3) would put them both in the same hand, wasting the high 4. If the dealer is banking, the best play is 1/4. If you are banking, the best play is actually 0/5.
The best play here is 2/9, which again is an exception to making the best low hand because it is worth 5 points. I speculate that the reason why is because it is the lowest 5-point hand possible, making it almost a 4-point hand.

The "split high cards" rule would only apply if by doing so, you create a front hand that is worth anything. 1-4 will push quite a bit less often than 2-3, even if the 1 is high and the 2 is low. That's because the opposing hands will contain a fair amount of 1-Gong, 1-Wong, and 1-Bo sets. The increase of the back hand from 3 to 4 (by playing 1-4 rather than 2-3) doesn't count for much--playing 1-4 is only correct if you expect to be up against 3-4, 2-4, or 2-3. The "1-big" hands will be more common against you.

The 9 that you make is a very lousy 9, and low 9s suffer more from being low than other back hands, because so many people set a high 9 in back. You are also, by setting 2-9, pretty much abandoning any hope of winning the hand. And as far as tying potential goes (for this is, of course, a hand you would be happy to push with), the 5 in front, even though it's a low 5, will accomplish that more often than a low 9 in back will.

Quote: mkl654321

The "split high cards" rule would only apply if by doing so, you create a front hand that is worth anything. 1-4 will push quite a bit less often than 2-3, even if the 1 is high and the 2 is low. That's because the opposing hands will contain a fair amount of 1-Gong, 1-Wong, and 1-Bo sets. The increase of the back hand from 3 to 4 (by playing 1-4 rather than 2-3) doesn't count for much--playing 1-4 is only correct if you expect to be up against 3-4, 2-4, or 2-3. The "1-big" hands will be more common against you.

The 9 that you make is a very lousy 9, and low 9s suffer more from being low than other back hands, because so many people set a high 9 in back. You are also, by setting 2-9, pretty much abandoning any hope of winning the hand. And as far as tying potential goes (for this is, of course, a hand you would be happy to push with), the 5 in front, even though it's a low 5, will accomplish that more often than a low 9 in back will.

I am only stating what the math indicates is the best play, and attempting to explain why the math works out the way it does. Obviously 2/3 is pretty bad, as are 1/4 and 0/5. But I stand by the math which says that 1/4 is the better play for that particular combination. It may or may not be because of separating the high tiles, but that appears to be the most logical explanation.

I think another reason why the best play for many combinations seems to defy logic is because of the possibility that the house could get the exact same combination -- and if they do, and you both set the hands the same way, then you would lose (if the house is banking). These situations won't happen often, but could be just frequent enough to tip the scale in favor of the seemingly "strange" play.

Here is the math on the two combinations in question, when the house is banking:

Combination	Way 1	Way 2	Way 3
H8,H4,H6,7	2/3: -0.868161	1/4: -0.861587	0/5: -0.901685
5,L7,L8,11	2/9: -0.443873	3/8: -0.510740	5/6: -0.467512

Here is the math on the same combinations when the player is banking:

Combination	Way 1	Way 2	Way 3
H8,H4,H6,7	2/3: -0.859504	1/4: -0.853314	0/5: -0.848400
5,L7,L8,11	2/9: -0.441558	3/8: -0.503258	5/6: -0.460510

With the 4-6-7-8 combination, all of the options are pretty dismal, but the best one is to play 1/4 when the house is banking, and 0/5 when you are banking. With the 5-L7-L8-11 combination, you save about 2% of your bet every time you set it correctly as 2/9 instead of the seemingly "obvious" choice of 5/6.

Note: the above figures are when the house uses the Traditional Way, so they may differ from the figures against the Foxwoods house way.