The AK/AQ rule for Pai Gow strategy

When I was developing a Commission-free pai gow game (EZ Pai Gow), I did some PGP strategy work, I came up with a stronger and less volitile strategy that's a little bit counter intutive, only because it is not how we're always used to playing the game.
Basically, a stronger and less volitile strategy was at first desired for the commission-free version, and it used the AK/AQ. The way it works is as follows:
1. It's the same as your standard House way strategy, except
a) Don't split any two pairs with an AK/AQ for the top, otherwise play as per standard two-pair rules;
b) A straight or a flush with two pairs, ignore the two pairs if you can play the flush or straight with an AK/AQ top.
c) Keep a full house togeher, if the pair part is 5's or less, and (you guessed it), you have an AK/AQ for the top.
It makes the strategy slightly stronger and less volitile, and no real complexity, and takes advantage of the slight copy effect the dealer or banker has.
The only other area affected is four of a kinds, but they're rare enough that the above covers it. The Full strategy is below, FYI:
Nine out of ten houses just maintain their existing strategy when installing EZ Pai Gow, to avoid any retraining issues; the effect is about 0.35% effect. Houses adopting Pai Gow poker as a new game can select this strategy.
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EZ Pai Gow: Commission-free Pai Gow Poker House rules set
Uses the “AK/AQ” Rule.

1. Pai Gow: Highest card in five card hand, 2nd and 3rd strongest on two card side.
All Hands push on Dealer’s Queen-only Pai Gow, except Bonus bets

2. One pair: Always play pair in five card side, with next two strongest cards up

3. Two pairs:
a. Always split Ace-high two pairs.
b. Split faces and 7’s or better, except with an AK/AQ for the top.
c. (Optional: Keep 8’s and 4’s or lower with a KJ or better top, else split).
d. Keep two pairs 6’s and less with a Q-x or better top, else split.
e. All other two pairs split without an ace, but keep together with an ace.

4. Three pairs: always play the highest pair in the two-card side

5. Three of a kind, simple (NO flush or straight with it): Split Three Aces 2-and-1, (with joker on 5-card side if joker is an ace.) All other three of a kinds (Kings and less) never break up.

6. Two three of a kinds: split off a pair from the higher group for the top.

7. Straights and/or flushes:
a. Straight or flush with AK/AQ or better top and two pairs: Play as straight/flush with AK/AQ or better top; ignore all two pairs present.
b. Straight or Flush with KJ to AJ top and two pairs: Play as straight/flush, - except if two pairs Queens with 6’s or better can be split:
c. Straight or flush K-low or lower top and two pairs: Play as two pairs if:
i. Seven-high two pairs can be split, (9887655 = 55/88976) OR
ii. Two pairs with any ace top can be played. (A233455= A4 / 55332)
d. Straight with Flush: Play the one with the higher top –if at least one of them has a queen top, else just play the flush on the five-card side.
e. Straight or flush with three pairs: Always play as a three pair hand.
f. Straight or flush with three of a kind: always play as straight or flush with pair or the ace up. (9888765 = 88 / 98765, and AA*QJ105=A5 / A*QJ10)
g. Straight or flush with full house: Play as flush or straight if it has a pair of 10’s or better for the top, else treat as full house, below.

8. Straight flush or Royal Flush: Always handle as straight and/or flush, above.

9. Full house:
a. If you have a full house with an extra pair, then play the higher pair up;
b. If your full house’s pair part is 5’s or less, keep with AK/AQ, else split.

10. Four of a kind:
a. Always keep four Aces together with pair of 4’s or better, else split.
b. Keep four King’s and less with an Ace-Jack or better for the top.
c. Split four K’s or Q’s 3 & 1 with an Ace-low for the top, else split 2&2.
d. Keep four 10’s or J’s together with any Ace or better top, else split 2 & 2.
e. Keep 7’s through 9’s together with any King or better top, else split 2 & 2.
f. Keep 6’s and lower with any Queen or better top, else split 2 & 2.

11. For four of a kind with a three of a kind, split a pair from the higher group.

12. Five aces: Always play a pair of aces up.

That's really strong for the house, because so many copies are the result of AK/AQ in front (and of course, the house wants copies). If I were playing against this strategy, I'd be forced to split my own two pair MUCH more often as a defensive measure. AK in front for the dealer is like a pair of "ones"--it takes a pair to beat it.

Which brings up another point. I think that the player should be able to see the house way a particular casino is using; in fact, the house should either put it on a sign on the table, or print up a bunch of little cards. How I play my hand is often HEAVILY dependent on the particular house way the casino uses.

MKL,
I totally agree that the house should post its house way.
The interesting thing is that pai gow players unintentionally adaopt the same strategy of the house or area they play at most frequently. When I deal to a guy from the East coast, I see that he keeps two middle pair, or middle and low pair, together with a K top. "You've played a lot in Atlantic City," I say.
I have come up with a composite Vegas house way, and play against it. I also have developed an anti-banker/house strategy way that subtracts out the copy effect of AK/AQ/AJ/KQ and KJ, - the group of 2-card hands that effectively copy the most by far. Basically, it turns the AK/AQ rule to the "pair top" rule slightly, with splitting two pairs more easily.

The optimal banker/house way is above, and the anti-banker strategy is below. It frequently split good two pairs with Ace-low (A-10 or less), but keeps middle two pairs together with King-face. This is because a single pairs of nines or less actually loses more often than it wins on the five-card side. It also keeps four of a kind together with decent tops. This might sound counter-intuitive, but when you're banking, you try for the win ONLY when you solidly have it, else you can get creamed. Here it is:
Warning: heavy duty Pai Gow sh*t below:

Anti-Banker Strategy: optimal play

1. Pai Gow: Highest card in five card hand, 2nd and 3rd strongest on two card side.

2. One pair: Always play pair in five card side, with next two strongest cards up

3. Two pairs: when the two pair hand has a two-card top that is listed in the left column, perform the split or keep action to its right:
Top: Two Pair Split action to take
AK: split no two pairs with AK for the top, except Q’s with 8+’s.
AQ: split King’s with 5’s or better only.
AJ: split K’s with 3’s and better, and Q’s with 6’s and better, keep lower
A-low: split all K’s, Q’s w 4’s+, J’s w 6’s+, 10’s or 9’s w 8’s+, keep lower
KQ: split all two pair jacks and better, 10’s w 3’s+, 9’s w 4’s +, 8’s w/ 6’s
KJ: split all two pair 9’s and higher, 8’s w 3’s+, 7’s with 5’s+
K-low: split all two pair 9’s and better, 8’s w 3’s+, 7’s w 4’s+, keep all lower
QJ-: split 7’s with 2’s or better, and 6’s w/ 4’s+, keep all lower two pairs

4. Three pairs: always play the highest pair in two-card side

5. Three of a kind, simple (no flush or straight with it):
a. Three aces always split 2-and-1, with a pair of aces for the five-card side.
b. All other three of a kinds (kings and less) never break up.

6. Two three of a kinds: split off a pair from the higher group for the top.

7. Straights and/or flushes:
a. Straight or Flush with two pairs: when the straight or flush has a two-card top that is listed in the left column, perform the action to its right:
Pair: Always play the straight or the flush if a pair can be played on top.
AK: keep all straights and flushes with AK top, ignore all two pairs
AQ: if straight only split A’s & 5’s+ or K’s w/ 7’s+, else keep str/flsh.
AJ: if straight only, split two pairs K’s with 5’s+ or Aces with 3’s+
A-x: split all two pairs Aces and King w/3’s, else play straight or flush
KQ: split all two pairs queens+, else play straight or flush w/ KQ
KJ: split all two pairs jacks+, or play two pairs with ace-face top
K-x: split eight-high two pairs or play two pairs with ace up
Q-x-: split seven-high two pairs or play two pairs with King or Ace up (e.g.: Kd-9d-8d-5d-5c-4h-4d play as 5’s and 4’s with K-9 up, ignore flush)
b. Straight or flush with one pair:
If straight or flush has a two-card side of:
Kx+: always play as straight or flush.
Q-10+: if straight then play face card pair with ace-face up, keep flush.
Q9-: play face card pair with ace-face up.
c. Straight with Flush: if you cannot produce a good hand with a), or b) above with either the straight or the flush, then play the one with the higher top. Except: if the tops are adjacent or essentially the same with both the straight and flush, then always play the stronger flush with essentially the same top. (“Same tops” are A-9 vs. A-6 [both ace-low], K-Q vs. K-J [both King-face], K-10 vs. K-5 [both King-low], adjacent ace-face [AQ vs. AJ, but not AK vs. AJ], or both tops are Q-10 or lower)
d. Straight or flush with three pairs: Automatic: Always play as a three pair.
e. Straight or flush with three of a kind: Automatic: always play as straight or flush with pair or ace up. (e.g., Play 9888765 as 98765/88, and play AA*2459 as A2*45/A9)
f. Straight or flush with full house:
i. Play as flush or straight if a pair 9’s/better can be put on top, else:
ii. Play Split-up full house if split full house has jacks+ for top;
iii. Play as straight/flush if a pair can be played on top;
iv. Else treat as full house, as listed below in #9.
g. 6 or 7 card long straight or flush: play the straight/flush which gives the best two card side, unless straight and flush with Q- top, then play flush.

8. Straight flush or Royal Flush: Always (just) handle as straight or flush, above.

9. Full house:
a. If your full house’s pair is 4’s or less, and your hand has an AK (or AQ with 3’s or less), then keep the full house together, else split.
b. If you have a full house with an extra pair, then play the higher pair up;
c. Full house with straight for flush: Play as flush or straight with pair 9’s or better top; else Play Split-up full house if it has jacks+ on top; else play as straight or flush if it has a pair top; Else treat as full house “a.” above
d. If your full house consists of two three-of-a-kinds or a four-of-a-kind with a three of a kind, then split off a pair from the higher group, - unless they are adjacent, then split up the lower group for a pair for the top.

10. Four of a kind, with no pair or three of a kind with it:
Four Aces: always split into two pairs of aces.
Four Kings: split into two pairs only without an AQ or better top – else split
Four Queens: keep together with Ace-Jack or better top, else split 2 & 2.
Jacks: keep together with any Ace top else split into two pairs.
10’s: keep together with KQ or better, else split into two pairs
9’s: keep together with any King-jack or better top, else split.
8’s: keep together with a King or better top, else split.
7’s: keep together with a Q-10 or better top, else split
6’s: keep together with a J-10 or better top, else split.
5’s or less: always keep together.

11. Four or a kind - with a pair: Always play a four of a kind with a pair as an unsplit four of a kind down with the pair up on the two-card hand, Except: Four Aces or Kings with a pair of 5’s or less, then split off a high pair from the four of a kind, to play two very strong pairs down with a top pair up.

12. For four of a kind with a three of a kind, split off pair from the higher group for the top, unless the groups are adjacent, then keep the four of a kind together.

13. Five aces: Play a pair of aces in the two-card side in ALL cases.

Heh. That's heavy-duty, all right. I can see the reason for many of the rules, though--especially, of course, two-pair hands.

One thing you mentioned made me curious--you said that a pair of nines in the back lost more often than it won. Many years ago, I mused to myself just what was the "median" hand--what hand would lose just about as often as it won? My unscientific guess was a pair of 10s with AJ in front. Maybe I wasn't that far off...

Have you figured out what the HA is with this (insanely complex!) strategy? Do you think the average casino would get exercised in a player printed it out and used it at the table (they shouldn't, but...)?

You were spot-on concerning the median hand.
It's between 10's and jacks one pair with an A-10 or A-J. You can also consider a Royal with a 32 top a 50% hand, but an unvolitile 50% hand. The 10's with AJ, or J's with A-10, is more given to wining 30% of the time, losing the same, and pushing 40% of the time.

All of this work gives a fraction of a percent more HA than a well-designed one-page strategy, maybe 0.5% tops.
The only thing that makes a real difference is good two-pair handling, keeping straights and flushes with an AK top, and keeping a straight or flush if the two pair hands are really bad, all in one page. Then, a ten-page strategy won't get 0.2% on you. (example, the hand 6543322 play as 32/65432, and not as 65/33224 or split two pairs,22/33654; two low pairs with a king top is a decent and stable hand, but splitting 3's and 2's are volitile with a lower HA. I'd play two low pairs with a King top over a flush with a J or less top).

Also, notice the four of a kind handling: generally keep four of a kinds together with any ace top, unless face card quads without an AJ+ top. Sweep the table with the quads, and have the ace top pick up the wins. I once as a dealer had to split the hand KQ77773 into lousy two pairs in spite of the KQ top, and LOST the four of a kind hand to a guy splitting Jacks and 10's, and pushed a straight with a 98 top. The "split the quads" mania of most house ways just turns a lot of great hands into lousy two pairs, and the floorman's call of "it's the house way, it must be right," is wrong.

Remember, if it's the house way, "it's only good enough for government work," so it has no place in the gaming industry.

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