Pai Gow Tiles Tricky Hands

This post is a collection of hands with a surprising and/or tricky correct play in Pai Gow Tiles. Unless specified, the advice specified assumes the dealer is banking. Some chunks of hands contain similar hands with obvious plays to clarify the ones which aren't obvious.

Paired Teen or Day, 9, high 8. The house plays Gong/Wong, but you should play 7/Pair. There is something special about having a 9 and high 8 in your low hand; it beats over 80.6% of all low hands the house will make. Paired Teen or Day beats over 97.5% of all high hands the house will make. Combined, this 7/Pair is a killer hand. With a 9 and low 8, you should split to make Gong/Wong like the house would.

Paired 6s, Teen or Day, 10. The majority of the time, you should keep the pair together. However, if the pair is of low 6s and the 10 is a high 10, then you should split to make 6/8.

Paired 7s, high 10, low 10. You should always split to make 7/7, with one exception. If you are banking and the pair is of high 7s, keep the pair together and play the zero-point low hand.

Teen, Day, 11, high 8. Play 4/9 but be prepared for funny looks! You have half the tiles the house needs to make a High Nine, and the next best 9-point hand is the one you are playing, so it's almost like playing 5/high 9. This 4/9 is 4.44% better than 3/Gong when the house is banking, and 1.53% better when you are banking.

Teen, Day, high 10, 9. Again, play 4/9, but be prepared to defend yourself if it doesn't work out. This 4/9 is 2.87% better than 2/Wong when the house is banking, and 2.4% better when you are banking.

Teen, Day, 9, 6/Gee. It is ever-so-slightly (0.01%) better to play the high 8 and the low Wong when the house is banking. Play "normal" with the Teen in the high hand when you are banking.

Teen, Day, 11, Gee. Play 4/7.
Teen, Day, 11, high 6. Play 4/7.
Teen, Day, 11, low 6. Play 3/high 8.

Teen, Day, high 10, Gee. Play 4/6.
Teen, Day, high 10, high 6. Play 2/high 8.
Teen, Day, high 10, low 6. Play 2/high 8.

Teen, Day, 10 or 11, 5. Play low 7 (Day+5) in the high hand and high 3 (12+11) or high 2 (12+10) in the low hand. It's a bit of a mystery why, but it is what it is.

Teen, high 8, 7, Gee. Play 4/9.
Teen, high 8, 7, high 6. Play 4/9.
Teen, high 8, 7, low 6. Play 4/9.
Teen, low 8, 7, Gee. Play 3/Gong.
Teen, low 8, 7, high 6. Play 4/9.
Teen, low 8, 7, low 6. Play 3/Gong.

Day, high 8, 7, Gee. Play 5/8.
Day, high 8, 7, high 6. Play 5/8.
Day, high 8, 7, low 6. Play 5/8.
Day, low 8, 7, Gee. Play 5/8 with high 7 and 3/Gong with low 7.
Day, low 8, 7, high 6. Play 3/Gong.
Day, low 8, 7, low 6. Play 3/Gong.

Day, low 10, any 7, high 4. Waste the high 4 to make 6/7.
Day, low 10, low 8, high 4. Waste the high 4 to make 6/8.

Day, low 10, 7, Gee. Play 7/8.
Day, low 10, 7, high 6. Play 6/9.
Day, low 10, 7, low 6. Play 6/9.

Teen, low 10, low 8, Gee. Play 6/Gong.
Teen, low 10, low 8, high 6. Play 6/Gong.
Teen, low 10, low 8, low 6. Play 6/Gong.
Teen, low 10, high 8, Gee. Play 6/Gong.
Teen, low 10, high 8, high 6. Play 6/Gong.
Teen, low 10, high 8, low 6. Play 8/8.

Day, low 10, low 8, Gee. Play 6/Gong.
Day, low 10, low 8, high 6. Play 6/Gong.
Day, low 10, low 8, low 6. Play 8/8.
Day, low 10, high 8, Gee. Play 8/8.
Day, low 10, high 8, high 6. Play 8/8.
Day, low 10, high 8, low 6. Play 8/8.

Teen, 11, high 8, Gee. Play 7/Gong.
Teen, 11, high 8, high 6. Play 7/Gong.
Teen, 11, high 8, low 6. Play 7/Gong.

Day, 11, high 8, Gee. Play 8/9.
Day, 11, high 8, high 6. Play 7/Gong.
Day, 11, high 8, low 6. Play 8/9.

high 8, low 8, 7, high 6. Waste the high 6 by combining it with the high 8 to make high 4/low 5. It looks wrong and it feels wrong, but it isn't wrong. It's 1.5% to 2.9% better than separating the high 6 and high 8.

high 8, high 6, 5, Gee. Again, waste the high 6 by combining it with the high 8 to make 4/8.

11, high 10, high 8, high 4. Play 5/8.
11, high 10, high 8, low 4. Play 4/9.

9, high 8, any 6, any 4 Play 0/7.
9, low 8, low 6, low 4 Play 0/7.
9, low 8, low 6, high 4 Play 3/4.
9, low 8, high 6, low 4 Play 3/4.
9, low 8, high 6, high 4 Play 3/4.

9, high 7, low 6, 5. Play 3/4.
9, low 7, low 6, 5. Play 3/4.
9, low 7, high 6, 5. Play 3/4.
9, high 7, high 6, 5. Play 1/6.

9, high 8, low 8, high 7. Play 5/high 7.
9, high 8, low 8, low 7. Play high 5/7.
You may find it helpful to remember how to set 7-8-8-9 like this: with a high 7, make the high 7; with a low 7, make the low 7.

9, 7, high 6, low 6. Play 3/high 5.

high 8, 7, high 6, low 6. Play 2/5.
low 8, 7, high 6, low 6. Play 3/4.

10, 9, 7, 5. Always play 2/9 instead of 5/6, with no exceptions whatsoever, even when banking.

high 10, low 8, high 7, high 6. Play 5/6.
high 10, low 8, low 7, low 6. Play 4/7.

11, 9, 7, high 6. Play 5/8.
high 10, 9, 7, high 6. Play 5/7.

11, 7, low 6, low 4. Play 0/8.
11, 7, low 6, high 4. Play 0/8.
11, 7, high 6, low 4. Play 0/8.
11, 7, high 6, high 4. Play 1/7.

low 10, 7, low 6, low 4. Play 0/7.
low 10, 7, low 6, high 4. Play 0/7.
low 10, 7, high 6, low 4. Play 0/7.
low 10, 7, high 6, high 4. Play 1/6.

low 8, 7, 6, low 4. Play 2/3.
low 8, 7, 6, high 4. Play 2/3.
high 8, 7, 6, low 4. Play 2/3.
high 8, 7, 6, high 4. Play 1/4.

That's all for now; there are surely more, but these are the ones that stick out in my mind the most.

Wow, after my post in the other thread,
I was going to suggest somehow identifying the noteworthy hands on the combinations strategy page...
This is even better...thanks again!

I have been meaning to ask...
Can you discuss.a little on the value of playing for a push rather than always playing for the highest positive EV.
Especially on some of the hands that could be split to form a gong but that get split to 6/7 or something similar.
I know that the house will always play a high nine, gong, or wong, and most traditionalists (ie chinese) will as well.

It sometimes takes steel nerves to make the optimal play.
Again, yesterday I think I pushed playing something similar to 5/7: yun/tit; teen/ng..
Of course there was a lot of discussion in Cantonese when the dealer flipped 4/Bo...
another black eye for the house way!

First of all, the commission moves the value of a win (from 1.00 to 0.95) closer to the value of a push (0.00). If it didn't, the strategy would be slightly more aggressive (boosting the low hand) than it is.

Secondly, I think some of the reasoning behind playing something like 6/7 instead of 3/Gong is to avoid a copy with the house, who would win the copy. When you're banking, the strategy is more like the house way since you win copies. For example, when you're banking and have Day, 6/Gee, 7, high 8, you play 4/9 like the house would instead of the 5/8 you would play when the house is banking.

Also, hands where the correct play looks like you're playing for a push, like playing 0/Wong instead of 5/6, do have the highest EV (or return). For example, Teen, 9, low 4, low 6: 0/Wong returns 81.69% of your bet, whereas 5/6 only returns 62.25%. (Those percentages are expressed like they would be for a video poker game.)

And now for a couple of pai gow trivia questions. Assume that you are using optimal strategy. No fair cheating please:

1. What is the worst 9/9 hand you can have in terms of expected return?

2. Excluding combinations that have paired Gee Joon, how many 4-tile combinations cannot lose, and what are they?

I am similarly surprised to learn that the lowest returns for 8/8 are even more curious than for 9/9.

PIng eight/foo eight at 0.124254
Ping eight/mooy eight at 0.126110
And only then
Ng eight/ Foo eight at 0.149914
Ng eight/ ping eight At 0.149939

Can you offer any insight into this counterintuitive curiosity?

Quote: WongBo

Can you offer any insight into this counterintuitive curiosity?

The reason the Ng eights are better than the Ping eights is probably because you have a Gee in your hand, reducing the chance of the dealer making a 9-point low or high hand with 6+Gee. I'm not sure why the apparent reversal between Foo and Ping in the high hands when the low hand is Ng eight.

However, there are TONS of situations like that if you look through the strategy chart. It basically boils down to the way that having certain tiles in your hand affects what hands the dealer could have.

jb, any idea, how much playing this entire strategy alters the house edge?

Quote: JB

This post is a collection of hands with a surprising and/or tricky correct play in Pai Gow Tiles.

Would it be time-prohibitive to make a pai gow tiles game that just deals out these hands, and warns of incorrect play? Exactly like the game you have on WOO and WOV now but with just the tricky hands?

I'd like to see you suggest these to the six old men who will be at my table in 12 hours.